Global Investment Management

Global Investment Management
Prof Bruno Solnik

Portfolio Construction Risk Management Performance Evaluation
Asset Allocation Portfolio Construction Risk Management Performance Evaluation Prof Bruno Solnik

Objective of Portfolio Management
Maximize return for a given level of risk Minimize risk for a set objective of return. This is all about risk management: Eliminate bad risks, diversify risks, and take risks that will generate extra returns. Prof Bruno Solnik

Strategic Asset Allocation
Decide of an asset allocation over the long run Often takes the form of a benchmark Based on Long-term Capital market expectations Based on risk estimates Prof Bruno Solnik

Tactical Asset Allocation
Strategic is the long-term anchor (say many years) Based on current market conditions and revisions in expectations/risks, managers apply “tactical” revisions (shorter-term). Prof Bruno Solnik

Asset Allocation Principles
An optimal strategic asset allocation is derived based on: CME (Capital Market Expectations) Investment objectives Investor’s risk tolerance Investor’s investment constraints Investor’s liabilities Risk estimates Prof Bruno Solnik

Optimization Investment firms use an optimizer
The basic one is the Mean-Variance optimizer). This is a quadratic program with constraints. Some more sophisticated versions are sometimes used (shortfall risk, Bayesian updates, Tail risk, etc..). We will talk about tail risk later. For the time-being, it is useful to think in terms of Mean-Variance optimization as all asset management companies mostly do. Prof Bruno Solnik

Some Mathematics (for specialists)

Optimization: Efficient frontier

Optimization Risk measures (volatility, correlation,..) are rather stable and can be easily updated. Expected returns are difficult to asses and the most difficult part of the asset allocation optimization. Prof Bruno Solnik

Strategic Asset Allocation
Derive “neutral” market expectations, meaning expected returns that are implied by market equilibrium. Update those based on some beliefs of the portfolio manager (CME or Capital Market Expectations) Construct an asset allocation based on those CME and a risk optimization. Prof Bruno Solnik

Three Major Methods Use Historical returns for neutral expected return
There are three major methods used to derive neutral CME: Use Historical returns for neutral expected return Derive neutral expected return from CAPM Derive neutral expected return from reverse optimization (Black-Litterman) Prof Bruno Solnik

1. Long Term Capital Market Expectations: Historical
Historical records for mean returns, volatility, and correlation can simply be projected to repeat in the future. BUT: Economic conditions in the past, especially the distant past, may not be relevant for the future. A market that has done exceptionally well (or poorly) in the past because of some specific events (e.g., liberalization of the economy) may not do so in the future because that specific event will not repeat. Prof Bruno Solnik

Long Term Capital Market Expectations: Historical
The exceptional equity risk premium in the twentieth century (6 percent for U.S. stocks) was caused by two factors: Earnings per share grew steadily. Valuation multiples, such as the price / earnings ratio, grew dramatically over time. Prof Bruno Solnik

Long Term Capital Market Expectations: Historical
Stock prices went up in part because of real growth, but more importantly, because valuation multiples rose impressively until To expect a similar equity risk premium in the future, an analyst must make the assumption that valuation multiples will continue upward to unprecedented levels. Prof Bruno Solnik

Exhibit 13.4: Stocks, Bonds, Bills, Inflation: The Global Record ( ) (Nominal returns in local currency in %: means calculated using geometric mean) Country Equity Bonds Bills Inflation MAR SD Australia 11.9 18.0 5.7 13.0 4.5 4.2 4.0 5.5 Canada 9.7 16.8 4.9 9.0 3.7 3.1 Denmark 10.4 22.6 7.0 10.6 4.1 6.6 France 12.3 24.7 6.9 8.8 4.3 2.3 8.0 14.6 Germany 9.9 36.4 2.8 13.6 4.6 3.4 5.2 15.8 Italy 12.1 34.4 6.7 9.1 4.7 3.3 9.2 36.8 Japan 13.1 30.5 6.1 15.1 1.9 7.7 40.4 The Netherlands 22.7 7.6 2.4 3.0 5.0 Sweden 12.2 23.7 5.8 6.8 UK 10.2 21.9 5.4 12.6 5.1 3.9 US 10.3 20.0 8.1 3.2 Source: Dimson Marsh and Staunton (2002) MAR: Mean Annual Return SD: Standard Deviation

Update for Equity Risk Premium (1900-2010)
Prof Bruno Solnik

Infer expected returns for each asset class using the CAPM.
2. Long Term Capital Market Expectations: Forward-Looking (UBS and some others) This method 2 is primarily used for asset allocation across asset classes (equity, bonds, real estate, etc..) Calculate an updated covariance matrix (volatility and correlation of asset classes). Infer expected returns for each asset class using the CAPM. Adjust expected returns for possible market segmentation and illiquidity. Prof Bruno Solnik

Recap of CAPM in matrix notations
By transformation Prof Bruno Solnik

Exhibit 13.5: The Reward for Risk for Conventional & Alternative Investments
Source: Terhaar, Staub and Singer (2003)

Long Term Equilibrium CME is the sum of:
Cash Return (Expected real rate plus inflation) Market Risk Premium (à la CAPM) Illiquidity/Segmentation Risk Premium Non-Normality Risk Premium (hedge funds) See UBS documents Prof Bruno Solnik

Strategic Allocation After optimization the SAA is derived with targets and range as in the example below: Prof Bruno Solnik

Example: UBS Global Perspectives Fall 2009
Neutral/Equilibrium SAA Tactical deviations based on misvaluation model. The model is more complex than briefly described in the document. The idea is that UBS derives an over/undervaluation of each asset class and assume convergence in three years. Hence an expected return that will deviate from the long-term expectations.

3. Black & Litterman (Goldman Sachs & others)
This method 3 is primarily used for allocation within equity class. The Black-Litterman model starts with equilibrium expected returns. According to the Capital Asset Pricing Model (CAPM), prices will adjust until the expected returns of all assets in equilibrium are such that if all investors hold the same belief, the demand for these assets will exactly equal the outstanding supply. This set of expected returns is the neutral reference point of the Black-Litterman model. The investor then can express her views about the markets. Prof Bruno Solnik

Steps of Black-Litterman Portfolio Optimisation
Prof Bruno Solnik

Reverse Optimization (see Efficient frontier equations)
Prof Bruno Solnik

Inputting Investor’s Views (Bayesian) source J.P. Morgan
Views are incorporated in the form of matrices as inputs into the model. Prof Bruno Solnik

Impact on Portfolio Weights source J.P. Morgan
Prof Bruno Solnik

The Whole Process source J.P. Morgan
Prof Bruno Solnik

Conclusions Method 2 is primarily used for allocation across asset classes. Method 3 is primarily used for allocation within the equity asset class. They both rely on some theoretical foundations and are preferable to a simple mean-variance optimization which is too sensitive to the expected returns inputs and can yield extreme results. Of course, a simple alternative to Method 3 is simply a passive investment in international index funds. Prof Bruno Solnik

Key Takeaways: Asset Allocation 1
Markets are very efficient, we only play at margin. Risk Allocation/Management is crucial in portfolio management. We build a neutral/strategic allocation inspired by market considerations (CAPM) We deviate tactically based on current views. Prof Bruno Solnik

Key Takeaways: Asset Allocation 2
In allocation optimization we have three vectors: E (expected returns) X (allocation weights) V (covariance matrix) Given V and E X optimal weights Given V and X E implied returns Traditional optimization uses 1. and typically derives returns from history, CAPM and various personal inputs. Reverse optimization uses 2. Derives equilibrium returns, adjust them by personal input and redo a direct optimization. Prof Bruno Solnik

CLASS 1: Markets and Major Players
Prof Bruno Solnik

Equity (stocks) Bonds Others
Investment Markets Equity (stocks) Bonds Others Prof Bruno Solnik

Stock Markets Prof Bruno Solnik

Automated trading systems have followed two different paths:
Historical Differences in Trading Procedures – Price-Driven vs. Order Driven Markets Automated trading systems have followed two different paths: A market organization dominated by dealers making the market (also known as a price driven or quote driven market). A market organization with brokers acting as agents in an auction system (also known as an order driven market). Prof Bruno Solnik

Price-Driven Systems (Dealer Markets)
For example, NASDAQ, Forex Market makers stand ready to buy or sell at posted prices. The bid and ask quotes are firm commitments by the market maker to transact at those prices for a specified transaction size. Only American stock markets have retained a price driven model. This system is useful for trading large blocks. Also for small stocks to provide liquidity. But is costly for “average trades”. Prof Bruno Solnik

Price-Driven Systems (Dealer Markets)
Advantages: Easier to execute large block trades than an order-driven system. Provides liquidity for “small” (illiquid) stocks. Disadvantages: More expensive to operate than the order driven markets. Requires more human intervention. Prof Bruno Solnik

Order-Driven Systems (Auction Markets)
For example, Paris, Frankfurt, Tokyo and elsewhere Traders publicly post their orders and the transaction price is the result of the equilibrium of supply and demand. Most markets (including emerging markets) have adopted this system. All buy and sell orders are entered in a central order book and a new order is immediately matched with the book of limit orders previously submitted. To improve liquidity, most have retained periodic call auctions. Prof Bruno Solnik

Example on order book LVMH (Moët Hennesy Louis Vuitton) is a French firm listed on the Paris Bourse. You can access the central limit order book directly on the Internet and find the following information (the limit prices for sell orders are ask prices and those for buy orders are bid prices): Sell Orders Buy Orders Quantity Limit 1,000 58 49 2,000 3,000 54 48 500 52 47 51 46 50 44 10,000 Prof Bruno Solnik

Order-Driven Systems (Auction Markets)
Advantages: Requires little human intervention. Less costly to operate. Markets with lesser transaction volumes have found it more efficient to adopt. Disadvantages: The absence of developing market making (orders with no price limits). Difficulty in executing large trades. Prof Bruno Solnik

Risks in Order-Driven and Price-Driven
In Price-Driven, dealers stand a risk of being “picked up”. In Order-Driven, limit orders stand a risk of being “picked up”. Prof Bruno Solnik

What about the NYSE? The NYSE has developed a hybrid market that combines traditional floor-trading and electronic auction trading. The automated platform is based on the Archipelago system. The electronic system allows one to find the best transaction price on the NYSE or elsewhere. BUT competing markets have developed in the USA, especially for large trades. Prof Bruno Solnik

BUT competing markets have developed in the USA, especially for large trades.
Prof Bruno Solnik

What about Hong Kong? In 1891 the first formal securities market, the Association of Stockbrokers in Hong Kong, was established. A few decades later it was renamed the Hong Kong Stock Exchange (HKSE) or the Stock Exchange of Hong Kong (SEHK). A second exchange, the Hong Kong Stockbrokers' Association was opened in The two exchanges merged to form the Hong Kong Stock Exchange in 1947. The HKSE also merged with other four national exchanges in the end of the 20th century. The new exchange started trading through a computer-assisted system on 2 April The unified exchange had 570 participating organizations. In 1993, the Exchange launched the Automatic Order Matching and Execution System (AMS) that was replaced by the third generation system (AMS/3) in October The new system enabled the exchange participants to trade from their offices. The HKSE launched its traded stock options market in In 1999, the HKSE opened the Growth Enterprise Market (GEM) that made the access to the capital market easier for riskier businesses. Finally, the Stock Exchange of Hong Kong together with Hong Kong Futures Exchange Ltd. established in 1976 and Hong Kong Securities Clearing Company Ltd. incorporated in 1989 merged to form a unified company Hong Kong Exchanges and Clearing Limited (HKEx) in 2000. Prof Bruno Solnik

Market Sizes of Stock Markets (in billion US$, End 2014, right column is “largest regional markets”)
Prof Bruno Solnik

Evolution of Market Share
Total World market cap end 2014: US$ 67 trillion Total World market cap early 1975: US$ 1 trillion Reached US$ 63 trillion end-2007 The relative market capitalization of national equity markets has changed dramatically over time. The share of the U.S. equity markets moved from two-thirds of the world market in the early 1970s to only one-third by the early 1990s, when Japan had about the same market size as the United States. In 2014, American equity markets represented 45% of the world market cap, with Asia-Pacific accounting for approximately 31% and Europe 24%. Prof Bruno Solnik

Cross-Holding: An Overevaluation of Market Cap
Company A is founded with 100 shares worth 1. Company B is founded with 100 shares worth 1. Total market capitalization is = Then, each company issue 100 new shares and swap them. So company A controls 50% of company B, and company B controls 50% of company A. Total market capitalization = ? Prof Bruno Solnik

Balance Sheet before new share issue
A Assets A Equity 100 B Assets B Equity 100

Balance Sheet after new share issue
A Assets A Equity 100 200 Shares B: B Assets B Equity 100 200 Shares A:

Cross-holding artificially inflates market capitalization
This is frequent in Asia (Korean Chaebol, Japanese keiretsu, Family groups in HK, etc… ) An adjustment has to be made by subtracting crossholdings. Adjusted free float = value of total outstanding shares − value of shares held by other companies of the Group Prof Bruno Solnik

Cross-holding Adjustments – An Example
Question Company A owns 40% of Company B Company B owns 30% of Company C Company C owns 20% of Company A Each company has a total market capitalization of 200 million. You wish to adjust for cross-holding to reflect the weights of these companies in a market weighted index. What adjustment would you make to reflect the free float? Prof Bruno Solnik

Cross-holding Adjustments – An Example
Solution: The apparent market cap of these three companies taken together is 600 million. But the “float” (shares available to investors outside the Group) of Company A should be reduced by the 20% held by Company C: 200 – 20% × 200 = 160 The adjusted market capitalization is: = 420 million Prof Bruno Solnik

Formula to compute Free Float
Adjusted free float = value of total outstanding shares in company i − value of shares held by other companies of the Group Examples: Adjusted market value of company A = 200 − 20% × 200 = 160 Adjusted market value of company B = 200 − 40% × 200 = 120 Adjusted market value of company C = 200 − 30% × 200 = 140 Prof Bruno Solnik

Liquidity Turnover ratio is computed as transaction volume relative to market capitalization. Sometimes called “share turnover velocity”. Illiquidity tends to imply higher transaction costs. Depending on the years observed, comparison of national market liquidity based on turnover ratio can lead to different conclusions. Prof Bruno Solnik

Liquidity: Annual Turnover on Major Stock Markets
Prof Bruno Solnik

Concentration Investors need to know whether a national market is made up of a diversity of firms or concentrated in a few large firms. A market that is dominated by a few large firms provides fewer opportunities for risk diversification and active portfolio strategies. On the NYSE and Tokyo Stock Exchange, the top 10 firms represent less than 20% of total market cap. Conversely, in Switzerland, the top 10 firms account for approx. 70% of total market cap. In Finland, Nokia was larger than the sum of all the other Finnish companies. Prof Bruno Solnik

Concentration: Share of the Ten Largest Listed Companies in the National Market capitalization
Prof Bruno Solnik

Tax Aspects Taxes can be applied in: Investor’s country
Investment’s country Transactions, capital gains and income The international convention on taxing income is to make certain that taxes are paid by the investor in at least one country, which is why withholding taxes are levied on dividend payments. Hong Kong does not have tax treaty with many countries, but that is changing. Prof Bruno Solnik

Formula for Tax paid at home: Dividends
Net dividend received in foreign currency DR= Dividend per share in foreign currency × no. of shares × (1 − dividend withholding tax rate) Gross Taxable Dividend income to be declared at home DI = Dividend per share in foreign currency × no. of shares × exchange rate Tax credit to be claimed at home: TC = Dividend per share in foreign currency × no. of shares × exchange rate × withholding tax If t is your home tax rate on dividends, tax to be paid = DI × t - TC Prof Bruno Solnik

Formula for Tax paid at home: Capital Gains
Capital gains are not taxed in foreign country Capital gains in home currency = Sale of shares in local currency − Purchase of shares in local currency Apply your home capital-gain tax rate. Capital gains are not taxed in foreign country Prof Bruno Solnik

Example The shares of Volkswagen trade on the Frankfurt stock exchange. A U.S. investor purchased 1,000 shares of Volkswagen at €56.91 each, when the exchange rate was €1 = $ (this is the value of one euro, or €/$, or $ per €). Three months later, the investor received a dividend of €0.50 per share, and the investor decided to sell the shares at the then prevailing price of €61.10 per share. The exchange rate was €1 = $ The dividend withholding tax rate in Germany is 15% and there is a tax treaty between the U.S. and Germany to avoid double taxation. How much did the U.S. investor receive in dividends in dollars, net of tax? What were the capital gains from the purchase and sale of Volkswagen’s shares? How would the dividend income be declared by the investor in the U.S. tax returns? Prof Bruno Solnik

Solution 1. Net dividend in Euros, after deducting withholding tax = €0.50 per share × 1,000 shares × (1 – 0.15) = €425. So, the net dividend in dollars = €425 × $0.9810/€ = $ The investor bought the shares for €56.91 per share × 1,000 shares = €56,910, or €56,910 × $0.9795/€ = $55, The investor sold the shares for €61.10 per share × 1,000 shares = €61,100, or €61,100 × $0.9810/€ = $59, Thus capital gains = 59,939.1 – 55, = $4, The investor would need to declare the total dividends, that is, without deducting the withholding tax, as dividend income. So, the dividend income to be declared is €0.50 per share × 1,000 shares × $0.9810/€ = $ Note that because of the tax treaty between the U.S. and Germany, however, the investor can deduct from income tax a tax credit for the dividends withheld in Germany; the tax credit is – = $ (The tax credit can be computed alternatively as €0.50 per share × 1,000 shares × 0.15 × $0.9810/€ = $73.57.) Prof Bruno Solnik

Execution Costs Execution costs can reduce the expected return and diversification benefits of an international strategy. Best execution refers to executing client transactions so that the total cost is most favorable to the client under the particular circumstances at the time. Prof Bruno Solnik

Execution Costs We can look at three costs (listed in order of decreasing reliability of estimation): Commissions, Fees and Taxes. Explicit and easily measurable. Market Impact. Dependent on order size, market liquidity for the security and the speed of execution desired by the investor. Opportunity Costs. Loss (or gain) incurred as the result of delay in completion of, or failure to complete in full, a transaction following an initial decision to trade. Prof Bruno Solnik

Estimation and Uses of Execution Costs
Global Surveys: These give market averages for a typical trade in each country. Total execution cost is a function of transaction size and market depth. VWAP (volume-weighted average price): The difference between the actual trade price and the VWAP benchmark price is an indication of execution costs. Implementation Shortfall: Difference between the value of the executed portfolio (or share position) and the value of the same portfolio at the time the trading decision was made. Prof Bruno Solnik

For “small” Orders Measure the bid-ask spread as quoted by Dealer or as implicit in the Order Book. Execution costs: Commission & Tax Half the bid-ask spread (assumes that the “true” market value is the mid-point) Prof Bruno Solnik

Execution Costs in Basis Points (2010)

Using Expected Execution Costs
The annual expected return net of execution costs is measured as: Net expected return = E(R) − Turnover ratio × Execution costs Prof Bruno Solnik

Impact of Execution Costs – an example
Question: Basil Richards follows an active international asset allocation strategy and observes the following data. The average execution cost for a buy or a sell order is forecasted at 0.75 percent. The portfolio has a turnover ratio of 1.2 times a year. The annual expected return before transaction costs is 11%. What is the annual expected return net of execution costs? Prof Bruno Solnik

Impact of Execution Costs – an example
Solution: Net expected return = E(R) − Turnover ratio × Execution costs Net expected return = 11% − 1.2 × 1.5% = 9.2% Prof Bruno Solnik

Bond Markets: for comparison purposes
Prof Bruno Solnik

World Bond Market The World bond market is made up of three different types of markets: Domestic Markets Foreign bonds International bonds (formerly known as Eurobonds) Prof Bruno Solnik

World Bond Market Capitalization (all maturities)
Total market cap as of 2013: around US$ 90 trillion National Markets (incl. foreign bonds): US$ 65 trillion International bonds: US$ 25 trillion Prof Bruno Solnik

Other Markets Derivatives: futures, forward, options
Alternative investments (detailed later) Prof Bruno Solnik

Private investors Institutional Investors Investment Professionals
Major Players Private investors Institutional Investors Investment Professionals Prof Bruno Solnik

Private Investors Prof Bruno Solnik

Number and Financial assets of HNWIs, 2014 World Wealth Report, CapGemini-RBC Wealth Management
In 2014, there were some 14 million HNWIs (financial wealth over $1 million). Their wealth around $53 trillion. Ultra-HNWIs (financial wealth over $30 million) own some $17 trillion. They are 1% of the HNWI population but 35% of the wealth. The financial assets of high net worth individuals (HNWI) are huge and present an attractive market for investment professionals. Asia, Europe and North America have approximately equal wealth of 12 to 15 trillion. The rest is in the Middle East, Latin America and Russia. Prof Bruno Solnik

Total Wealth of HNWI, CapGemini-RBC
Prof Bruno Solnik

Asset Allocation The investment behavior of individual investors is somewhat different from that of institutional investors described below. Individuals tend to invest relatively more in non-tradable assets such as real estate, hedge funds or structured products. But there are also marked differences in the profile and behavior of HNWI across regions. Prof Bruno Solnik

HNWI’s Allocation of Financial Assets
Prof Bruno Solnik

Institutional Investors
Prof Bruno Solnik

Institutional Investors
Mutual Funds (unit trusts) Pension Funds (called Retirement Schemes, MPF in HK) Insurance Companies (Life and P&C) Endowment and Foundation Prof Bruno Solnik

Mutual funds Open-end funds (vast majority): NAV
Redemption (different clauses, games) Fees ETF, see later Closed-end funds See Global Investments Prof Bruno Solnik

Pension Systems Various types:
PYG (pay as you go): current workers contribute for benefits (pension) of current retirees. Capitalized: current workers invest (contribute) in savings (pension fund) that will pay benefits when they retire. Prof Bruno Solnik

HONG KONG Two types of retirement schemes:
In December 2000 was launched a Mandatory Provident Fund (MPF) system, providing retirement based on mandatory and voluntary contributions by employers. Around 40 MPF providers (schemes) with AUM over HK$540 billion in 2014. Prior to it, voluntary ORSO (Occupational Retirement Schemes Ordinance). Each scheme can be different. AUM around HK$290. There are some statutory pension or provident funds (civil servants, public school teachers,…). Prof Bruno Solnik

Pension Funds The investment approach of pension funds is greatly affected by the way future benefits are planned. There are basically two plan types and a combination thereof: A defined benefit pension plan (DB) which promises to pay beneficiaries a defined income after retirement. The benefit depends on factors such as the workers’ salary and years of service. A defined contribution plan (DC) where the amount of contributions paid is set, usually as a percentage of wages, but future benefits are not fixed. Prof Bruno Solnik

Pension Funds — Types In a traditional pension fund, all contributions are pooled and the total money is managed collectively. A board of Trustees sets the investment policy of the fund. A recent trend is to give more investment decision power to each employee. (E.g., 401(k) plans in the U.S., or MPF in HK) Prof Bruno Solnik

Institutional Investors: Endowments and Foundations
Concerned about total return in the long run. Capital gains and income on the assets can be used to meet budgetary needs. Tend to have great investment freedom, because they operate under few regulatory constraints. Often the most aggressive institutional investors, with many having extensive global and alternative investments. Prof Bruno Solnik

Institutional Investors: Insurance Companies
Collect premiums on life insurance and on property and casualty insurance, which are invested until claims are paid. Heavily regulated in each country and state in which they operate. Tend to adopt conservative investment policies. Tend to focus on fixed income assets, in order to assure their claim-paying ability. This is a financial intermediary with large AUM. Prof Bruno Solnik

The Economics of an Insurance Company
Business profits come from combined ratio: Financial profits come from return on invested premiums Prof Bruno Solnik

Example of Zurich Group, in US$ billion, June 2007
Prof Bruno Solnik

A simple illustration of the importance of ALM
Typical Balance Sheet with total assets & liabilities of 100. Investment portfolio of 75 made up of 15 in equity and 60 in bonds Shareholder’s equity 10 Prof Bruno Solnik

A simple illustration of the importance of ALM
Typical balance sheet1 of an insurance company (excluding unit-linked business) 100 100 Shareholders’ Equity Asset Allocation: 20% Equities of Group Investments or 15% of total assets Interest Rate Mismatch Modified Duration: - Fixed Income: 5 years - Insurance Liabilities: 7 years Equities Group Investments Fixed Income Insurance Liabilities Simple example Of an insurance company “Surprising” impacts of capital market movements Simplified economic balance sheet Asset and liabilities Assets dominated by investment 20% allocation to equities - 15% of total assets Dominance of fixed income duration 5 years. Simple liabilities Modified duration 7 years. Like negative bond - duration of 7 years. This investment strategy looks normal What happens to the balance sheet Case of recession. equities fall 40% interest rates fall by 2%. Typical scenario in 2001 to 2003. Other Assets Other Liabilities Assets Liabilities

Reminder on Bonds and Duration
There is an inverse relationship between the price of a bond and changes in interest rates. If the bond's cash flows are fixed, the price is solely a function of the market yield. Practitioners usually define interest rate sensitivity, or duration, as the approximate percentage price change for a 100 basis points (1%) change in market yield. Mathematically, the duration D can be written as: where P/P is the percentage price change induced by a small variation r in yield. Prof Bruno Solnik

Negative equity markets can have a significant impact on shareholders’ equity
Typical balance sheet1 of an insurance company (excluding unit-linked business) Balance sheet1 after a 40% decrease in equity markets 100 100 94 94 4 9 Shareholders’ Equity Equities Group Investments Fixed Income Insurance Liabilities -40% equities 60 70 Other Assets Other Liabilities 25 20 Assets Liabilities Assets Liabilities 1 Balance sheet on an economic basis Prof Bruno Solnik

In addition falling interest rates lead to a further deterioration of economic capital
Balance sheet1 after a 40% decrease in equity markets Balance sheet1 after a fall of interest rates by 2% 100 100 94 94 Shareholders’ Equity Equities 9 4 Group Investments -2% interest rates Fixed Income Insurance Liabilities 60 70 Other Assets Other Liabilities 25 20 Assets Liabilities Assets Liabilities 1 Balance sheet on an economic basis Prof Bruno Solnik

First step is to model liabilities
Depending on the type of contract (Life insurance, P&C, ...), the model can be quite different. While a Bond-like model is a first approximation for each type of liability, there are some optional contract clauses to be incorporated. Typically the liabilities can be summarized in a bond-like benchmark with some average duration. This will be the “risk-free” benchmark. Prof Bruno Solnik

Insurance Company: Asset Allocation Optimization Principles
Economic: We value assets and liabilities at market value and perform asset liability optimization. Accounting: Some securities are “held to maturity” and hence not marked to market. Present value of insurance liabilities are not frequently revalued. Hence a focus on the “accounting” net income from investments. Regulatory: Regulators have their own views of risk. They use (and so do insurance companies) Risk Based Capital. Prof Bruno Solnik

Major Players: Investment Professionals
Prof Bruno Solnik

Consultants and Advisers Custodians
Investment Managers Brokers Consultants and Advisers Custodians Prof Bruno Solnik

Investment Managers Range from the asset management department of banks to independent asset management boutiques specializing in offering specific investment products. Hedge funds are a recent breed of investment managers. Some asset managers cater to retail clients as well as institutional clients, while others serve the needs of one type of client. Prof Bruno Solnik

Brokers Play an important role in terms of implementing security trades and in research of companies and markets. Sell-side analysts: work for brokerage firms and make recommendations to clients. All CFA® charter holders and CFA candidates must follow the CFA Institute® Code of Ethics and Standards of Professional Conduct, wherever they work and invest. Prof Bruno Solnik

Consultants and Advisers
Better known for their work with pension funds, but they also work with private clients and other types of investors. Play a major role in the asset management industry. Independent consulting firms have traditionally advised U.S. pension funds, while actuaries played a similar role in the U.K. Consultants also focus on services such as recommending asset allocation, selecting investment managers and monitoring performance, and giving tax and legal advice. Their most sensitive role is the process of selecting, hiring and firing external managers. Prof Bruno Solnik

Custodians Securities owned by investors are deposited with a custodian, which often uses a global network of sub-custodians. Information technology is an important component of custodial services With the high development costs of software, many banks have sold their custodial activities, and further consolidation is expected in the future, because economies of scale can be significant in this business. Prof Bruno Solnik

Key Takeaways: Major Markets and Players 1
Financial markets are diverse. A good understanding of their mechanisms can help get better trading prices. Market Cap is important because many investors benchmark to market indices. Need to better understand free float. Execution costs are of great importance and should be focused on. Explained how global taxes work. Prof Bruno Solnik

Key Takeaways: Major Markets and Players 2
Investors are diverse and we reviewed some of their asset allocation. To better understand how some institutional investors act, we spent time on one of the lesser-known but huge investor type, insurance companies. Stressed the importance of ALM This also provides a link to the next topic : asset allocation Prof Bruno Solnik

From Asset Allocation to Portfolio Management
Equity Fixed Income (Brief, see Module 6) Prof Bruno Solnik

Global Equity Investment
Passive approach (ETF) Factor Models (Roll & Ross, BARRA) Prof Bruno Solnik

Global Investment Philosophies
An investment management organization must make certain major choices in structuring its global decision process, based on: Its view of the world regarding security price behavior Its strengths, in terms of research and management Cost aspects Its location and prospective domestic / global marketing strategy Prof Bruno Solnik

From Passive to Very Active
Asset Allocation: Strategic Asset Allocation Active Asset Allocation (TAA) Index Funds (ETF, trackers etc…) Portfolio construction: Managing/Selecting Risk Exposures Looking for Alphas (individual securities) “Deals” Prof Bruno Solnik

From Passive to Very Active
Portfolio Management is about taking risks: Avoid bad risks Diversify risks (free lunch) Take some bets (good risks) A passive index is usually assigned as benchmark. Increase/reduce the risk exposure (betas) of the portfolio opportunistically Try to generate alphas by selecting undervalued securities. Note: We do not do company valuation here (see Module 6) 112

Risk-Adjusted measure: Asset Allocation
From an Asset allocation viewpoint, one looks at the total risk taken and compare return to a no-risk investment (risk-free asset). The total risk is simply the sigma (s) and the risk-adjusted return is the Sharpe ratio: Where R0 is the risk-free rate. Prof Bruno Solnik

Risk-Adjusted measure: Portfolio
Looking at an asset class (say US equity), one looks at the risk taken relative to the benchmark (tracking error) measured as the standard deviation of excess returns. Then one compares the realized excess return over the risk taken (tracking error). More in Class 6 Prof Bruno Solnik

Global Investment Philosophies: Passive Approach
This approach simply attempts to reproduce a market index of securities (index fund approach). It is an extension of modern portfolio theory, which claims that the market portfolio should be efficient. The trend toward global indexing is strongly felt among institutional investors. Prof Bruno Solnik

Global Investment Philosophies: Passive Approach
Various indexing methods can be used: Full replication Stratified sampling Optimization sampling Synthetic replication Prof Bruno Solnik

There are many ETF traded in Hong Kong, and Singapore or elsewhere.
Index Funds Mutual Fund ETF (Exchange Traded Fund or Trackers). The big names are BlackRock (iShares), State Street Global Advisors (Spiders), Vanguard.. There are many ETF traded in Hong Kong, and Singapore or elsewhere. Prof Bruno Solnik

Fund Management Fees Investment companies charge fees, some as one-time charges and some as annual charges. - For managed funds, loads are simply sales commissions charged at purchase (front-end) as a percentage of the investment. A redemption fee (back-end load) is a charge to exit the fund. Redemption fees discourage quick trading turnover and are often set up so that the fees decline the longer the shares are held (in this case, the fees are sometimes called contingent deferred sales charges). Loads and redemption fees provide sales incentives but not portfolio management performance incentives. Prof Bruno Solnik

Fund Management Fees Investment companies charge fees, some as one-time charges and some as annual charges. - Annual charges are composed of operating expenses including management fees, administrative expenses, and continuing distribution fees. - Typical example for active stock portfolio could be: Load of 3%, expense ratio of 1.5% (1% management fee, 0.25% administrative expenses, 0.25% distribution fee). Prof Bruno Solnik

What are Exchange Traded Funds (ETFs)
They are shares of a portfolio, not of an individual company. ETFs are index-based investment products that allow investors to buy or sell exposure to an index through a single financial instrument. The market maker commits to bid and ask prices around the index value. For active ETFs the bid-ask spread is small. (See detailed description in Global Investments textbook) Prof Bruno Solnik

Exchange Traded Funds (ETFs)
ETF is a special case of a fund that tracks some market index but that is traded on a stock market as any common share. Prof Bruno Solnik

Exhibit 8.1 Creation/Redemption Process of Exchange Traded Funds

II. Factor Models Prof Bruno Solnik

The factors are measured as the return on some index portfolio representative of the factor (“mimicking portfolios”). For example, the oil industry factor could be proxied by the return on a global stock index of oil firms. Various statistical techniques can be used to optimize the factor structure. Prof Bruno Solnik

The exposure can be assessed a priori by using information on the company studied. This usually leads to a 0/1 exposure. For example, Exxon would have a unitary exposure to the oil industry factor and zero exposures to all other industry factors, because it is an oil company. The exposure can be estimated using a multiple regression approach. The exposures would then be the estimated betas in a time-series regression. Prof Bruno Solnik

Macro factor: Roll-Ross APT Attribute factor: Barra
Prof Bruno Solnik

Confidence factor Time horizon factor Inflation factor
II a) Roll & Ross APT Confidence factor Time horizon factor Inflation factor Business cycle factor Market-timing factor Prof Bruno Solnik

Roll & Ross (APT) Confidence factor (ƒ1). This factor is measured by the difference in return on risky corporate bonds and on government bonds. The default-risk premium required by the market to compensate for the risk of default on corporate bonds is measured as the spread between the yields on risky corporate bonds and government bonds. A decrease in the default-risk spread will give a higher return on corporate bonds and implies an improvement in the investors’ confidence level. Prof Bruno Solnik

Confidence factor (ƒ1) continued
Roll & Ross (APT) Confidence factor (ƒ1) continued Confidence risk focuses on the willingness of investors to undertake risky investments. Most stocks have a positive exposure to the confidence factor (1 > 0), so their prices tend to rise when the confidence factor is positive (ƒ1 > 0). Prof Bruno Solnik

Time horizon factor (ƒ2)
This factor is measured as the difference between the return on a 20-year government bond and a one-month Treasury bill. A positive difference in return is caused by a decrease in the term spread (long minus short interest rates). This is a signal that investors require a lesser premium to hold long-term investments. Prof Bruno Solnik

Time horizon factor (ƒ2) continued
Growth stocks are more exposed (higher 2) to time horizon risk than income stocks. The underlying idea is to view the stock price as the discounted stream of its future cash flows. The present value of growth stocks is determined by the long-term prospects of growing earnings while current earnings are relatively weak (high PE ratio). An increase in the market-required discount rate will penalize the price of growth stocks more than the price of value stocks. Prof Bruno Solnik

Inflation factor (ƒ3). This factor is measured as the difference between the actual inflation for a month and its expected value, computed the month before, using an econometric inflation model. An unexpected increase in inflation tends to be bad for most stocks (3 < 0), so they have a negative exposure to this inflation surprise (ƒ3 > 0). Luxury goods stocks tend to be most sensitive to inflation risk, whereas firms in the sectors of foods, cosmetics, or tires are less sensitive to inflation risk. Real estate holdings benefit from increased inflation. Prof Bruno Solnik

Business cycle factor (ƒ4).
This factor is measured by the monthly variation in a business activity index. Business cycle risk comes from unanticipated changes in the level of real activity. The business cycle factor is positive (ƒ4 > 0) when the expected real growth rate of the economy has increased. Most firms have a positive exposure to business cycle risk (4 > 0). Retail stores are more exposed to business cycle risk than are utility companies, because their business activity (sales) is much more sensitive to recession or expansion. Prof Bruno Solnik

Market-timing factor (ƒ5).
This factor is measured by the part of the Benchmark total return (e.g. S&P 500 for US) that is not explained by the first four factors. It captures the global movements in the market that are not explained by the four macroeconomic factors. The inclusion of this market-timing factor makes the CAPM a special case of the APT. If all relevant macroeconomic factors had been included, it would not be necessary to add this market-timing factor. Prof Bruno Solnik

How to use Factor Models
Factor models are linear. Hence the betas (exposures) of a portfolio are simply the weighted-average betas of the stocks in the portfolio The benchmark (market index) has some exposure to the various factors. A difference between the portfolio betas and the benchmark betas implies that the future return on the portfolio is going to be different from the return on the benchmark. A manager takes bets on the various factors to try to beat the benchmark. Prof Bruno Solnik

A Simple Example Discuss the various exposure (start with S&P 500)
What are the exposures of a portfolio invested half in Tata and half in SuperMark. You believe that confidence and business activity will improve without affecting inflation. Which company would you overweight?

A Simple Example: solution 2) & 3)
If confidence and business activity will improve without affecting inflation, I should overweight Tata.

II b) BARRA Models (BIM, etc…)
World factor Country factor Industry factor Style factor (Size, value, Momentum) inspired by Fama and French model Other factors (leverage, volatility) Currency Prof Bruno Solnik

Styles or Attributes Value stocks do not behave like growth stocks. A value stock is a company whose stock price is “cheap” in relation to its book value, or in relation to the cash flows it generates (low stock price compared to its earnings, cash flows, or dividends). A growth stock has the opposite attribute, implying that the stock price capitalizes growth in future earnings. This is known as the value effect. Prof Bruno Solnik

Styles or Attributes Small firms do not exhibit the same stock price behavior as large firms. The size of a firm is measured by its stock market capitalization. This is known as the size effect. Winners tend to repeat. In other words, stocks that have performed well (or badly) in the recent past, say in the past six months, will tend to be winners (or losers) in the next six months. This is known as the momentum, success or relative strength effect. Prof Bruno Solnik

Currency Factor See article FT: Multinationals drive US rally on weak dollar, Oct 2, 2007. “2007 will go down as the year the rest of the world saved America,” said Joseph Quinlan, chief investment strategist at Bank of America. “The belief that the dollar is going to weaken further is prompting investors to own int’l large-cap stocks.”…Companies with large overseas operations have been at the forefront of the rally. Since the Dow’s previous record – on July 19 – eight of the top ten performers have been multinational companies, led by P&G but also including Hewlett-Packard, Johnson & Johnson and McDonald’s. The weakness in the dollar, which has hit a series of all-time lows against major currencies, benefits multinational companies in two ways: it makes their US-made products cheaper on international markets and increases the dollar value of their overseas earnings. Prof Bruno Solnik

A Hot Topic: Smart Beta Smart Beta strategies attempt to deliver a better risk and return trade-off than conventional market cap weighted indices by using alternative weighting schemes (rules) based on measures such as volatility or various fundamental factors. Usually a very passive approach. The basic idea is that you can construct non-market-cap-weighted portfolio with better return and lower volatility than a typical market index. There are many variants of Smart Beta strategies from simple (equal-weighting) to complex (factor/fundamental investing). All require some periodic rebalancing (transaction costs) and do not work all the time. Prof Bruno Solnik

One can go beyond equal-weighting to minimize volatility.
Low Volatility is a typical strategy that avoid the index concentration in big cap stocks that induce high volatility. An equal-weighted index has lower volatility than a market-cap-weighted index. The claim is that such portfolio (with a bias toward small cap) delivers similar or better performance with less risk. One can go beyond equal-weighting to minimize volatility. S&P DJ, Russell, MSCI, … all provide low volatility indices and ETF have been created to match them. Invesco PowerShares are an example of the “intelligent” ETFs. Low volatility strategies have done quite well but have also underperformed during significant periods of time Prof Bruno Solnik

Factor or Fundamental Investing allocates to various factors (value, size, momentum, Book Value, Free Cash Flow, Total Sales, Total Cash Dividend..) while controlling volatility. The claim is that you can generate better return/risk performance than a typical market-cap-weighted index or ETF. For example Research Affiliates provide a RAFI fundamental index used in FTSE RAFI Low Volatility and Russell Fundamental indices. This leads to a semi-passive approach tilting the portfolio away from market-cap indices based on factor exposures. But the exposures can be dynamically tilted. Prof Bruno Solnik

Fixed Income Investment Management
Prof Bruno Solnik

Dual currency, currency option
Yield curves Yield play (ride,…) Duration Multi-currency Dual currency, currency option Prof Bruno Solnik

Prof Bruno Solnik

Interest Rate Forecast
Remember the “duration” relation:

Interest Rate Forecast – Example
On the U.S. dollar yield curve, the current (mid-2007) yields are 4.6% for both five-year and ten-year. You expect the yields to drop uniformly to 4.1% in the near future. What should you do on your U.S. bond portfolio? Prof Bruno Solnik

Interest Rate Forecast – Solution
The approximate capital gain for both maturities are: Five-year: Ten-year:

Interest Rate Forecast – Example
On the U.S. dollar yield curve, the current (mid-2007) yields are 4.6% for both five-year and ten-year. You expect the yields to drop to 3.1% for 5-year and 3.9% for 10-year in the near future. What should you do on your U.S. bond portfolio? Prof Bruno Solnik

Interest Rate Forecast – Solution
The approximate capital gain for both maturities are: Five-year: Ten-year:

“Break-even” or “Implied” Forward exchange rate:
Currency Forecast “Break-even” or “Implied” Forward exchange rate: Where: S is spot rate e.g. $1.5 per € Ft is the implied forward for maturity t r is the interest rate for the quoted currency (€), e.g., 4% r* is the interest rate for the measurement currency ($), e.g., 5%

For one-year forward euro we get: F = 1.5000 x (1.05)/(1.04) = 1.5144
Currency Forecast For one-year forward euro we get: F = x (1.05)/(1.04) = If euro is above $ a year from now, an investor in one-year euro bond is better off. If euro is below $ a year from now, an investor in dollar bond is better off. Prof Bruno Solnik

Currency Forecast - Example
For example, the 5-year yields given on the previous Exhibit are 4.6% in dollars and 1.25% in yen. The Spot exchange rate is ¥120 per $. The quoted currency is the $ and the measurement currency is the ¥. The implied 5-year forward exchange rate, or breakeven exchange rate, is equal to: Which amounts to a 15% depreciation of the dollar. If your expectations for the next 5 year is that the dollar would depreciate by more than 20%, then Yen bonds look attractive. But bonds in other currencies could look even more attractive.

Key Takeaways: Portfolio Management
Portfolio Management is about taking risks: Avoid bad risks Diversify risks (free lunch) Take some bets (good risks) A passive index is usually assigned as benchmark. Increase/reduce the risk exposure (betas) of the portfolio opportunistically Try to generate alphas by selecting undervalued securities. To manage an equity portfolio, one uses a factor model (BARRA, Sungard APT, Axioma, Northfield,…). Factor models are either ‘macro factors’ model or ‘attribute factors’ models, or some (difficult) mix. Prof Bruno Solnik

CLASS 3 Should We Hedge Currency Risk in Global Asset Management ?
Prof Bruno Solnik

Structure Some General Considerations
Hedging with Currency FUTURES/FORWARD Optimal Currency Hedging The Contribution of Behavioral Finance Currency Overlay Managers Prof Bruno Solnik

1. Currency Risks: Some General Considerations
Prof Bruno Solnik

Currency risk can be significant in the short run.
For example, an American investor who decided not to hedge currency risk would have incurred a currency loss of some 40% on its eurozone assets from late 1998 to late 2000. Prof Bruno Solnik

Currency risk can be significant in the short run.
Let’s look at a Japanese investor: The dollar was 260 yen per dollar 20 years ago, 85 ten years ago, 135 early 2002, 75 in late 2012, 115 in Nov 2014. The euro was introduced in 1999 at 130 yen, two years later it was down to 90 yen, went to 167 in July 2007, 100 in late 2012, 144 in Nov 2014. Prof Bruno Solnik

Prof Bruno Solnik

Short term variations of exchange rates are extremely hard to predict.
Currency Risks There are many current and expected variables (Purchasing power, deficits, interest rates, growth, politics...) that influence exchange rates at different times. Short term variations of exchange rates are extremely hard to predict. Prof Bruno Solnik

My Model for the ¥/€ Exchange Rate
Xt is the number of bottles of Cognac drunk in Tokyo at time t Z is the number of tries scored by the Japanese team in the Rugby World Cup yt is the probability of a typhoon in Japan, divided by the probability of an earthquake in Europe Prof Bruno Solnik

Currency changes are quite volatile.
Currency risk can be cheaply hedged. Currency risk is relatively small in well-diversified global equity portfolios. But very high in global bond portfolios. Prof Bruno Solnik

Unrelated Parenthesis: My Personal thoughts on the euro
Prof Bruno Solnik 171

Currency Considerations
The return and risk of an asset depend on the currency used. For example, the dollar value of an asset is equal to its local currency value (V ) multiplied by the exchange rate (S) (number of dollars per local currency): The rate of return over the period is: where R = return in local currency s = percentage exchange rate movement Prof Bruno Solnik

Illustration You are US investor and invest $20,000 in British equity. The exchange rate is 1£ = $2. The British market goes up by 10% and the new exchange rate is 1£ = $2.1 (5% appreciation of the £). What is your return in $? Prof Bruno Solnik

British market goes up 10% and £ goes up 5%
Prof Bruno Solnik

Return The new value is $23,100 or a dollar return of 15.5% =
(23,100 – 20,000)/20,000 The rate of return is 15.5% = 10% (capital gain in £) + 5% (currency gain on initial capital) + 0.5% (currency gain on capital gain) Prof Bruno Solnik

2. HEDGING with CURRENCY FUTURES/FORWARD
Prof Bruno Solnik

Use in Hedging a Portfolio
Table of Content Definition Quotation Gain/Loss at maturity Valuation Principles Use in Hedging a Portfolio Prof Bruno Solnik

Definition A Forward or Futures contract is a commitment to purchase (buyer) or deliver (seller) a specified quantity of an underlying asset on a designated date in the future, for a price (“futures/forward price”) determined competitively when the contract is transacted. Prof Bruno Solnik

Definition For example, suppose that today’s spot exchange rate is S = 1 dollar per euro. An investor could buy forward 100,000 euros for delivery on December 10, at a Forward price F = 1.01 dollars per euro. Prof Bruno Solnik

Forward and Futures Contracts
FORWARD contract: A private contract between two parties (one is usually a bank). Nothing happens till maturity. A margin is usually deposited. FUTURES contract: A standardized contract transacted on a futures exchange. Standardized in terms of size, delivery date. With a marking-to-market procedure. Prof Bruno Solnik

Prof Bruno Solnik

Simply quote the Futures/Forward price
Quotation Simply quote the Futures/Forward price Prof Bruno Solnik

Gain/loss at Maturity: Straightforward
Prof Bruno Solnik

The Futures price F is linked to the Spot price S by arbitrage.
Valuation Principles The Futures price F is linked to the Spot price S by arbitrage. The “cost of carry” of the arbitrage is simple. Example: S = 1 dollar per euro R$ = 5% R€ = 4% F = ? Prof Bruno Solnik

Example: S = 1 dollar per euro R$ = 5% R€ = 4% F = ?
Valuation Principles Example: S = 1 dollar per euro R$ = 5% R€ = 4% F = ? Prof Bruno Solnik

Use in Hedging The “naïve” approach is simply sell the foreign currency for an amount equal to the portfolio position in the foreign currency. Prof Bruno Solnik

Hedged Portfolio - Example
An Italian investor owns a portfolio of U.S. stocks worth US $10 million. The current spot rate and one-month forward exchange rates are €1 per $. Interest rates are equal in both countries. The investor sells forward $10 million to hedge currency risk because he is concerned about the outcome of the US elections. A week later, the US stock portfolio has gone up to $10,350,000, and the spot and forward exchange rates are now €0.94 per $. Analyze the return on the hedged portfolio. Prof Bruno Solnik

The U.S. stock portfolio went up by 3.5%, but the dollar lost 6 percent relative to the euro. If the portfolio had not been hedged, its return in euros would have been: Prof Bruno Solnik

As per equation 11.3, the profit on the hedge portfolio in euros is: Profit = 10,350,000 x 0.94 – 10,000,000 x 1 – ,000,000 x (0.94 – 1) Profit = 329,000 The rate of return on the hedged portfolio is 329,000/10,000,000 = 3.29% Or we could directly apply Equation 11.4: Return = – 2.71% + 6% = 3.29% Prof Bruno Solnik

3. Optimal Currency Hedging: The traditional approach (MV)
Prof Bruno Solnik

Minimum-Variance Hedge Ratio
One objective is to search for minimum variability in the value of the hedged portfolio. Investors would like to set the hedge ratio, h, so as to minimize the variance of the return on the hedged portfolio. Prof Bruno Solnik

Minimum Variance Hedge Ratio
Where R* = rate of return on the original portfolio (unhedged) RF = % times change in futures price , approximately equal to exchange rate variation = s REMEMBER: Here * means in the investor’s currency, no * means in the asset local currency. Prof Bruno Solnik

Derivation of Optimal Hedge Ratio
𝜎 𝐻 2 = 𝜎 𝑅 −ℎ 2 𝜎 𝑠 −ℎ 𝑐𝑜𝑣 𝑅,𝑠 Minimize relative to h Hence 𝑑 𝜎 𝐻 2 𝑑ℎ =−2 1−ℎ 𝜎 𝑠 2 −2𝑐𝑜𝑣 𝑅,𝑠 =0 ℎ=1+ 𝑐𝑜𝑣 𝑅, 𝑠 𝜎 𝑠 2 Prof Bruno Solnik

Minimum Variance Hedge Ratio
The minimum-variance hedge ratio is equal to: where translation risk hedge is: economic risk hedge is: The optimal hedge ratio is sometimes called the regression hedge ratio ℎ=1+ 𝑐𝑜𝑣 𝑅, 𝑠 𝜎 𝑠 2 ℎ 1 =1 ℎ 2 = 𝑐𝑜𝑣 𝑅, 𝑠 𝜎 𝑠 2 Prof Bruno Solnik

A hedge ratio of 1 will minimize translation risk.
Translation risk comes from the translation of the value of the asset from the foreign currency to the domestic currency. A hedge ratio of 1 will minimize translation risk. Prof Bruno Solnik

Economic Risk Economic risk comes when the foreign currency value of a foreign investment reacts systematically to an exchange rate movement. If an investor worries about the total influence of a foreign exchange rate depreciation on her portfolio value, measured in domestic currency, she should hedge both translation and economic currency risk. Prof Bruno Solnik

Economic Risk The hedge ratio required to minimize economic risk can be estimated by: This is the slope that we would get on a regression of the foreign currency return of the asset on the exchange rate movement. Prof Bruno Solnik

Stock indexes developed Stock indexes emerging Bonds
Illustrations Individual firms Stock indexes developed Stock indexes emerging Bonds Prof Bruno Solnik

A Global Survey of Institutional Investors
What is the typical currency hedging benchmark of institutional investors? - Very diverse! Prof Bruno Solnik

Distribution of Accounts by Base Currency and Hedge Ratio Russell Mellon
Prof Bruno Solnik

4. The Contribution of Behavioral Finance
Prof Bruno Solnik

Behavioral Finance: The Early Days
Prof Bruno Solnik

Behavioral Finance It has long been recognized that a source of judgment and decision biases is that cognitive resources such as time, memory, and attention are limited. Since human information processing capacity is finite, there is a need for imperfect decision-making procedures, or heuristics, that arrive at reasonably good decisions cheaply. Prof Bruno Solnik

Behavioral Finance However, there are other possible reasons for systematic decision errors. Feeling or emotion-based judgments can explain mood effects (market sentiment). Prof Bruno Solnik

Behavioral Finance: Examples
Overreaction A cognitive bias (investor overreaction to a long series of bad/good news) could produce predictable mispricing of stocks; DeBondt and Thaler (1985). Extrapolation Investors use past performance as an indicator of future performance in mutual fund and stock purchase decisions; Sirri and Tufano (1998), Grinblatt et al. (1995), Carhart, (1997). Prof Bruno Solnik

Behavioral Finance: Examples
Overconfidence Individuals trade too much, overconfidently thinking that they can pick winners, whereas the stocks they buy do worse than the stocks they sell; Odean (1998, 1999), Barber and Odean (2000). Disposition effect Investors are reluctant to sell losers (and mentally “declare” the loss), even though tax considerations should make them prefer selling a loser to selling a winner; Shefrin and Statman (1985), Odean (1998). Prof Bruno Solnik

Reactions to Behavioral Finance
Traditional Finance Professor It is a collection of ad-hoc stories. Small anecdotes of little general value. Psychology produces too many answers and no theory. Prof Bruno Solnik

Reactions to Behavioral Finance
Practitioners It is not really useful. Cannot make money on anomalies: Many “anecdotes” apply to minuscule market value. all attempts on “January effect”, “day of the week effect”, etc, have been unsuccessful. For example, private investors are overconfident, so what! Does not tell me how to structure a portfolio. Little implications for investment choices. Prof Bruno Solnik

Regret Theory Prof Bruno Solnik

Nobel Prize Thinking “I should have computed the historical covariance of the asset classes and drawn an efficient frontier. Instead I visualized my grief if the stock market went way up and I wasn’t in it-or if it went way down and I was completely in it. My intention was to minimize my future regret, so I split my [pension scheme] contributions 50/50 between bonds and equities.” - Harry Markowitz. As quoted in Jason Zweig, "How the Big Brains Invest at TIAA-CREF", Money, 27(1), p114, January 1998 Prof Bruno Solnik

Regret Regret is defined as a cognitively-mediated emotion of pain and anger when, with hindsight, we observe that we took a bad decision in the past and could have taken one with better outcome. Ex post, one compares the investment outcome with the best outcome that could have been achieved. Prof Bruno Solnik

Regret Contrary to mere disappointment (prospect Theory), which is experienced when a negative outcome happens relative to prior expectations, regret is experienced relative to the best outcome of alternative choices that could have been made (foregone alternatives). As the opening quote suggests, the anticipation of future regret was strong enough to turn Harry Markowitz away from his very own portfolio allocation theory when faced with a financial decision on his pension plan. Prof Bruno Solnik

Regret is very present in life (“missed opportunities”)
Regret influences investment choices. We look at the performance of peers (competitors). It is more than looking at passive benchmarks. As stressed by Statman (2005), currency hedging is a dimension where regret clearly applies. Prof Bruno Solnik

Currency Hedging is a Dimension where Regret Applies
The euro was introduced in 1999 at 130 yen, two years later it was down to 90 yen, went to 167 in July 2007, 100 in November 2012, 144 in Nov 2014. For example, a Japanese investor who decided not to hedge currency risk would have incurred a currency loss of some 30% on its eurozone assets from 1999 to 2001, with a vast regret of not having fully hedged. Prof Bruno Solnik

Currency Hedging is a Dimension where Regret Applies
Conversely a fully-hedged Japanese investor would have missed the huge appreciation of the euro from late 2001 to late Again, a vast regret of not having taken the "right" hedging decision (90 to 167). But an unhedged Japanese investor would have lost a huge amount on the currency side from 2007 to 2012. Prof Bruno Solnik

The 50% Hedging Rule is Not New Among Investment Managers
"A partial hedging policy – such as 50/50 or 70/30 – means the investor won’t ever experience the major highs of an unhedged portfolio, but won’t be subject to the lowest returns either.“ "To Hedge or not to hedge", Simon Segal, SuperReview.com.au, 21 march 2003 Prof Bruno Solnik

"The 50% hedge benchmark is gaining in popularity around the world as it offers specific benefits. It avoids the potential for large underperformance that is associated with "polar" benchmark, i.e. being fully unhedged when the Canadian dollar is strong or being fully hedged when it is weak. This minimizes the "regret" that comes with holding the wrong benchmark in the wrong conditions.“ "Managing Currency Risk: A Canadian Perspective", Gregory Chrispin, State Street Global Advisor, Essays and Presentations, March 23, 2004. Prof Bruno Solnik

The 50% hedge ratio is the simplest currency hedging policy that attempts to deal with regret. Prof Bruno Solnik

In a recent paper (Michenaud-Solnik, 2008), we apply regret theory to the determination of optimal currency hedging. This is a tough mathematical task. Investors care about the portfolio expected return and volatility (as in mean variance) but also about expected regret. We find optimum hedging depending on the level of risk aversion and of regret aversion of the investors. Prof Bruno Solnik

With large regret aversion, the optimal hedge ratio nears 50%.
100% - regret term + speculative term + covariance term With large regret aversion, the optimal hedge ratio nears 50%. But regret aversion does not necessarily dominates traditional risk aversion. Prof Bruno Solnik

In Practice: Use the Model to Derive Optimal Hedging
Expected currency return (currency risk premium?) Correlation between asset and currency return Regret aversion compared to risk aversion Prof Bruno Solnik

Using Currency Options
Currency options allow to « insure » the portfolio rather than « hedge ». But there is the cost of the premium. Prof Bruno Solnik

Key Takeaways: Currency Hedging
Using currency futures/forward to hedge is easy. The “naïve” approach is simply to sell the foreign currency for an amount equal to the portfolio position in the foreign currency (hedge ratio = 1 or 100%). The minimum-variance hedge ratio takes into account translation risk (hedge ratio of 1) but also economic risk (the sensitivity of the local-currency asset price to exchange rate movements). Investors have very different hedging policy. So there is not obvious one-fits-all optimal policy. Regret theory is often used for currency hedging decisions. Prof Bruno Solnik

The Eurozone Crisis and Implications for Investment Management Some Provocative Views
Bruno Solnik Module 4 – Prof Bruno Solnik

This is not a Euro crisis but a Eurozone crisis
Financial markets and Politicians have different objective functions A fixed exchange rate system is explosive as shown historically Past research has shown that brutal medicine is often better than lingering sickness There are REAL problems and NOMINAL ones. The Eurozone has primarily real problems. In a crisis, there is always some serious underlying cause but it needs a trigger: : too much leverage in households and banks; trigger: subprime. : too much leverage of governments; trigger: Greek creative accounting. Module 4 – Prof Bruno Solnik

What Determines Exchange Rates
Real Aspects (competitiveness) Purchasing Power Parity (CPI, unit labor costs) Current Account Expected growth Nominal Aspects Monetary policy Investments Aspects Financial attractiveness (return and risk) Module 4 – Prof Bruno Solnik

The Euro is not under gigantic speculative pressure
Module 4 – Prof Bruno Solnik

Current Eurozone: 17 out of 27 EU countries

Fixed parity: History Historically, a regime of fixed exchange rate has always been unsustainable because the speculative tensions and moral hazard built into the system. The system is asymmetric. Small countries must be stronger than big countries. But that has a cost too (Hong Kong) Module 4 – Prof Bruno Solnik

What is specific to the Eurozone
There is a fixed parity with strong disparity among countries. Following the introduction of the euro, some countries (esp PIIGS) got huge subsidies 1) from EU and 2) from increased borrowing capacity (who wants to lend in risky escudos or drachmas?). But rather than seizing this opportunity to engage in structural reforms to lift the country to international standards and competitiveness, several countries got into free spending. This was aggravated by the politicians’ plans to offset the 2008 credit/liquidity crisis resulting in wild spending. The “trigger” was the discovery of Greek creative accounting. Note that each country has some specific problems (e.g. Spain engaged in huge real estate bubble sponsored by regions, cities and banks) Module 4 – Prof Bruno Solnik

Real Problems: Competitivity

Module 4 – Prof Bruno Solnik

Situation is not really improving Eurozone-wide
France current account deficit in 2011: $55 billion France current account deficit in 2012: $63 billion France current account deficit in 2013: $59 billion Germany current account surplus 2011: $224 billion Germany current account surplus 2012: $239 billion Germany current account surplus 2013: $257 billion But situation is somewhat slowly improving in Southern Europe. Module 4 – Prof Bruno Solnik

Real Problem: Down to Earth
“A decade ago, France was more price-competitive than Germany; today it is the other way around. That's evident in the macroeconomic numbers as well as on the ground. France used to produce as much asparagus as Germany, but these days Germany cultivates more than four times as much. Labor is the biggest cost in the asparagus business, and German seasonal workers cost half as much as their French counterpart." Time magazine, 16 July, 2012, page 27. Module 4 – Prof Bruno Solnik

How can a country remain competitive when it 3% when 1% and a debt level above 100% of GDP Module 4 – Prof Bruno Solnik

Government 10-year bond yield 30 January 2015
Eurozone Yield Germany 0.3% France 0.5% Italy 1.6% Spain 1.4% Netherlands 0.4% Portugal 2.6% Greece 10.8% Module 4 – Prof Bruno Solnik

Other Aspects: Monetary Policy and Financial Attractiveness
Eurozone countries have no monetary independence. So they cannot adjust disparity among member countries by monetary policy. If you want to invest in Euro, would you consider investing in countries like Greece or Portugal given the social unrest and the risks involved? Hence such countries have both a current account deficit, because they are not competitive, and a potentially-large financial account problem that will not offset the current account deficit as in the U.S. case. Module 4 – Prof Bruno Solnik

How can the PIIGS problems be solved
Devaluation and foreign debt restructuring, leading to inflation and domestic debt devaluation (deemed politically impossible: Eurozone). Default (called debt restructuring) without devaluation (politically difficult and creates problems for banks, reduces past debt but not current or future needs). Belt tightening and structural solutions (long-term solution, burden is borne unevenly, local politics make it very difficult if not impossible: no government can survive on this program). Non-PIIGS taxpayers keep financing PIIGS (the easy politician’s solution: thank you Germany, thank you ECB). Module 4 – Prof Bruno Solnik

The structural problems are not fully addressed because:
politicians are politicians guided by elections not the long-term good. very painful to do structural adjustments very fast; a devaluation is so much easier. Past research has shown that brutal medicine is better than lingering sickness So resort to tricks (ECB buys sovereign bonds and finance banks to take them). EuroBonds with guarantee from all Eurozone governments…. Without severe structural changes, the sickness will linger for many years. The major adjustment can be through deflation. But how popular is reducing drastically pension benefits, civil servant wages,… Drastic reforms are not compatible with political will and electoral cycles in Southern countries. Module 4 – Prof Bruno Solnik

Implosion (divorce) Lingering sickness (prozac)
Implications for Financial Markets : Two Scenarios Implosion (divorce) Lingering sickness (prozac) Module 4 – Prof Bruno Solnik

Foreign Exchange The Eurozone will implode or linger sick. The sooner it implodes the better (I wish they had done it early 2010 rather than wasting trillions). Several countries (many) will leave the euro and only the strong Northern countries (and some satellite) will keep it. A devaluation of some of Eurozone countries is the least-bad solution to the real problem, not the cause of the problem The uncertainty will be bad for the euro exchange rate. But only the strong countries will retain the euro, so its fundamental value should increase. Unless South keeps the euro and North the DM. The question is what will happen to the existing sovereign debt (restructuring?). And the private debt? Module 4 – Prof Bruno Solnik

Financial markets: Bonds
Before the euro implosion Bond yield will rise in most countries (e.g. France). But how can you sustain such huge differential in financing cost with Germany. The trigger of the euro implosion might be some elections somewhere. Triggers are hard to predict. Could happen in Greece, Portugal, Spain, Italy, France… Many government bonds are more risky than corporate bonds. But only large corporations have access to the bond market; smaller corporation have difficult time borrowing from banks, adding to the recession. There is no corporate/loan bond market in Europe like in the US and European banks are deleveraging. One has to be very selective with sovereign and credit exposure Module 4 – Prof Bruno Solnik

After the euro implosion
There will be more “emerging” currencies and huge spreads. Module 4 – Prof Bruno Solnik

Financial markets: Equity
A divorce is usually very messy. Prozac is no better. Recession can be bad in many European countries and will affect the rest of the world to some extent. But many real assets will retain real value. A short-lived crisis addressing fundamentals is better than being on Prozac while the problems get worse and worse (note that Greece still Governments will have learnt to be more thrifty, although new politicians will quickly forget and politicians’ objective function will remain the same. Module 4 – Prof Bruno Solnik

Europe Stocks vs U.S. Stocks, past 5 years

One has to be selective Exposure to the European “political” risks vary greatly among European companies. Some sectors are more exposed than others Some European companies have less European exposure. In the short run they followed the market index. In the long run their profits will be quite different. Example of Peugeot vs BMW There are no fire sales, but… Module 4 – Prof Bruno Solnik

CLASS 4: OPTIONS IN INVESTMENT MANAGEMENT

I. The Basics: Insuring with Options II. Use of Options
III. Using Options to Manage Currency Risk IV. Currency overlay V. Introduction to Structured Products Module 4 – Prof Bruno Solnik

I. The Basics of Options (reminder)
Definition Quotation Gain/Loss at maturity Valuation Principles Use in Insuring a Portfolio Module 4 – Prof Bruno Solnik

Definition In general, an option gives the buyer the right, but not the obligation, to buy or sell an asset, and the option seller must respond accordingly. Many types of option contracts exist in the financial world. The two major types of contracts traded on organized options exchanges are calls and puts. Module 4 – Prof Bruno Solnik

Definition A call gives the buyer of the option contract the right to buy a specified number of units of an underlying asset at a specified price, called the exercise price or strike price, on or before a specified date, called the expiration date or strike date. A put gives the buyer the right to sell a specified number of units of an underlying asset at a specified price on or before a specified date. Module 4 – Prof Bruno Solnik

Definition In all cases, the seller of the option contract, the writer, is subject to the buyer’s decisions, and the buyer exercises the option only if it is profitable to him or her. The buyer of a call benefits if the price of the asset is above the strike price at expiration. The buyer of a put benefits if the asset price is below the strike price at expiration. Module 4 – Prof Bruno Solnik

The buyer of an option can only win and never loses!
Wonderful!!!!!!!!!! The buyer of an option can only win and never loses! - Example of a car insurance Module 4 – Prof Bruno Solnik

The terms of the option are FIXED Quote the Option Price or Premium
Quotation The terms of the option are FIXED Quote the Option Price or Premium Module 4 – Prof Bruno Solnik

Gain/Loss at Maturity Module 4 – Prof Bruno Solnik

The Premium p is linked to the Spot price S by arbitrage.
Valuation Principles The Premium p is linked to the Spot price S by arbitrage. The Premium p is equal to the intrinsic value plus the time value. Module 4 – Prof Bruno Solnik

Call Option Intrinsic Value, as a Function of Asset Price (S)

Determinants of Option Premium
Asset Price relative to Strike Price Volatility Time to expiration Interest rate(s) Module 4 – Prof Bruno Solnik

Speculation (with limited risk) Insuring a portfolio
II. Use of Options Speculation (with limited risk) Insuring a portfolio Module 4 – Prof Bruno Solnik

Example of Speculation with Futures on HSI
Futures on HSI, multiplier HK$10  Index This is Mini-HSI contract. Full is HK$50 times index Quote for December Futures is 30,000. ASSUME that the margin is set at HK$15,000 per contract (1,500 per index). You believe that the market will go down. What can you do using HSI futures? Look at the result for ONE contract, if the HSI is equal to 40,000; 35,000; 30,000; 25,000; and 20,000 in December. Module 4 – Prof Bruno Solnik

Example of Speculation with Futures on HSI
Short futures HSI Gain / Loss 40,000 -100,000 35,000 -50,000 30,000 25,000 50,000 20,000 100,000 Module 4 – Prof Bruno Solnik

Example of Speculation with OPTIONS on HSI
OPTIONS on mini-HSI, multiplier HK$10Index HSI is at 30,000 December CALL at the money (K=30,000) quote at 2,000 per index. December PUT at the money (K=30,000) also quote at 2,000 per index. You believe that the market will go down. What can you do using HSI options? Look at the result for ONE contract, if the HSI is equal to 40,000; 35,000; 30,000; 25,000; and 20,000 in December. Module 4 – Prof Bruno Solnik

Example of Speculation with OPTIONS on HSI
Long put HSI Gain / Loss 40,000 -20,000 35,000 30,000 25,000 20,000 80,000 Module 4 – Prof Bruno Solnik

Insuring a Portfolio: Example of Stock Portfolio
A portfolio manager has an allocation of €4 million to French equity. The French portfolio is well diversified and tracks the local CAC stock index. The manager believes that the French market offers excellent returns prospects. However, the manager is worried that French elections taking place next month (April) could lead to a severe market correction. Although the probability of such an outcome is quite small, the manager wishes to insure against it. The current value of the CAC index is 4,000. Futures on the CAC with maturity in June also trade at 4,000. Module 4 – Prof Bruno Solnik

Put options with maturity in June trade as follows: Strike Price Premium (€ per unit of index) 3,900 30 4,000 100 Module 4 – Prof Bruno Solnik

CAC options and futures have a multiple of €10 times the index. Thus, the total premium for one put with exercise price €3900 is 30 x €10 = €300, for example. The manager hesitates between selling 100 futures contracts, buying 100 puts with a strike of 3,900, or buying 100 puts with a strike of 4,000. Calculate the outcome of each strategy if the CAC is equal to 3,500, 4,000, or 4,500 at expiration of the contracts in June. 2. Recommend a strategy to the portfolio manager. Module 4 – Prof Bruno Solnik

Solution The value of the portfolio under the various strategies is given below: Value of CAC at expiration Initial Portfolio (No Futures or Options) Portfolio Hedged with Futures Portfolio Insured with Puts 3,900 Portfolio Insured with Puts 4,000 3,500 3,500,000 4,000,000 3,870,000 3,900,000 4,000 3,970,000 4,500 4,500,000 4,470,000 4,400,000 Module 4 – Prof Bruno Solnik

Solution 2. Hedging with futures provides the best protection in case of a drop in the market, but it deprives the manager of any profit potential. Buying puts provided protection in case of a market drop while keeping most of the upside potential (the put premium is deducted from the portfolio value). Given the manager’s expectations, buying puts is a natural strategy. Out-of-the-money puts are cheaper, so they are more attractive in case of an up-movement, but offer less protection in case of a down-movement. To get the best downside protection while retaining upside potential, the portfolio manager should buy 100 puts with a strike price of 4,000. Module 4 – Prof Bruno Solnik

III. Insuring Currency risk with Options
The difficulty with currency option is to pick the correct option as an exchange rate implies two currencies. Module 4 – Prof Bruno Solnik

An Example You are a U.S. investor holding a portfolio of European assets worth €1 million. The current spot exchange rate is $1=1 euro but you fear a depreciation of the euro in the short term. The three-month forward exchange rate is $ = 1 euro. You are quoted the option premiums for calls euro and puts euro with a three-month maturity. These are options to buy (call) or sell (put) on euro at the dollar exercise price mentioned for each option. The contract size on the CME is €125,000. Module 4 – Prof Bruno Solnik

Euro Options (All Prices in U.S. Cents per Euro)
Another Example The quotations are as follows: Euro Options (All Prices in U.S. Cents per Euro) Strike Call Euro Put Euro 105 0.50 6.50 100 2.10 3.00 95 6.40 Module 4 – Prof Bruno Solnik

Another Example You decide to use options to insure your portfolio.
Should you buy (or sell) calls (or puts)? What quantity? You decide to buy at-the-money options (strike price of 100 U.S. cents) for €1 million. Suppose that you can borrow the necessary amount of dollars to buy these options at a zero interest rate. Calculate the result at maturity of your strategy, assuming that the euro value of your portfolio remains at €1 million. You have the choice of three different strike prices. What is the relative advantage of each option? What is the advantage relative to hedging, using forward currency contracts? Module 4 – Prof Bruno Solnik

Solution To insure, you need to buy options. Here, you want to be able to translate euros at a fixed exchange rate, so you should buy euro puts for €1 million, or eight contracts. Module 4 – Prof Bruno Solnik

If the euro rises in value, the put will expire worthless.
Solution You buy at-the-money puts on €1 million. The cost (premium) is equal to €1,000,000 x $0.03 / € = $30,000 If the euro rises in value, the put will expire worthless. If the euro depreciates, you gain exercise the put and get $1,000,000 minus the option premium of $30,000, or $970,000. Module 4 – Prof Bruno Solnik

Exchange Rate at Maturity (US cents per Euro)
Solution The simulation of the dollar value of the position for a different value of the exchange rate at maturity is given in the first column of the following table. The portfolio is insured for down movements in the euro and benefits from up movements. But the cost of the insurance premium has to be deducted in all cases. Exchange Rate at Maturity (US cents per Euro) Using Puts 100 105 95 Hedging with Forward 110 1,070,000 1,035,000 1,095,000 996,000 1,020,000 985,000 1,045,000 970,000 995,000 945,000 90 Module 4 – Prof Bruno Solnik

Solution 3. The preceding table simulates the results of using the various options as well as the forward. An “expensive” option (in-the-money, put 105) gives better downside protection at the expense of a lesser profit potential in case of an appreciation of the euro. A “cheap” option (out-of-the-money, put 95) provides less downside protection but a larger profit potential. Using forward contracts freezes the value of the portfolio at $996,000. You are well protected on the downside, but you cannot benefit from an appreciation of the euro. Module 4 – Prof Bruno Solnik

Solution You will decide on the strategy, depending on your scenario for the euro exchange rate. If a depreciation of the euro seems very likely, you will hedge; if a depreciation seems very unlikely, you will buy out-of-the-money options, which are the cheapest. The other two strategies lie in between. Module 4 – Prof Bruno Solnik

General Comment To find the exchange rate that will be relevant when insurance is needed (option exercised) you compute the “all-in-cost/revenue”: 1. If the direction of quotation requires to buy a put, the relevant exchange rate (‘you receive’) is: Strike price – put premium In the example you receive an exchange rate of 0.97 2. If the direction of quotation requires to buy a call the relevant exchange rate (‘you pay’) is: Strike price + call premium Module 4 – Prof Bruno Solnik

IV. Currency Overlay Managers
Delegation of Currency Position: Management of Currency Risk Profile Currency as an Asset Class Module 4 – Prof Bruno Solnik

Management of Currency Risk Profile
Technical Approach Fundamental Approach “Currency for alpha” funds Module 4 – Prof Bruno Solnik

V. Using Structured Products in Global Asset Management
A Deal: Example of LTCM-UBS Structure Notes Module 4 – Prof Bruno Solnik

1. Example of LTCM-UBS Module 4 – Prof Bruno Solnik

2. Other Example: Structured Notes
A structured note is a bond issued with some unusual option-like clause. These notes are bonds issued by a name of good credit standing and can therefore be purchased as investment-grade bonds by most institutional investors, even those that are prevented by regulations from dealing in derivatives. Another attraction for investors is that these structured notes offer some long-term options that are not publicly traded. Structured notes with equity participation are in strong demand in many countries, especially in Europe, where they are sometimes called guaranteed notes. Module 4 – Prof Bruno Solnik

Guaranteed notes with equity participation are bonds having guaranteed redemption of capital and a minimum coupon; in addition, some participation in the price movement of a selected index is offered if this price movement is positive. Module 4 – Prof Bruno Solnik

An Example For example, let’s consider a two-year note that guarantees the initial capital (redemption at 100%) plus an annual coupon of 3 percent and offers a 50 percent participation rate in the percentage price appreciation in the Japanese Nikkei index over the two years. At time of issue, the yield curve was flat at 8 percent. The 50 percent participation rate works as follows: If the stock index goes up by x percent, the investor will get 50 percent of x. For example, if the Nikkei stock index goes up by 30 percent from the time of issue to the time of redemption, the option will yield a profit of 15 percent and the bond will be redeemed for 115 percent. The participation rate is, in effect, the percentage of a call option on the index obtained by the investor. Module 4 – Prof Bruno Solnik

a straight bond with a coupon of 3 percent
In summary, the structured note can be viewed by investors as the sum of a straight bond with a coupon of 3 percent plus 50 percent of an at-the-money call option on the Nikkei All of these bonds can be analyzed as the sum of a straight bond with a low coupon plus an option play Module 4 – Prof Bruno Solnik

Problem Consider the guaranteed note on the Nikkei described in the text: Value the call option implicit in the bond. Assume that you offer a similar bond but with a coupon set at zero. What is the equity participation that you could offer? Module 4 – Prof Bruno Solnik

Solution Question 1. The present value of the straight bond is
Because the bond is issued at 100 percent, the implicit value of 50 percent of a call option on the Nikkei is therefore equal to And the implicit value of 100 percent of one call option on the Nikkei index is equal to Module 4 – Prof Bruno Solnik

Solution Question 2. There is clearly a negative relation between the amount of the guaranteed coupon and the participation rate that can be offered in the option. A structured note with a zero coupon will leave more money to invest in the call option: The difference between the redemption value and the current market value of the zero-coupon bond (14.27% = 100  85.73) can be invested by the issuer in call options. The number of call options that can be purchased is equal to the participation rate that is set in the structured note. In the example, one call option on the Nikkei index is worth 17.84, and is available to invest in options. Hence, this allows a participation rate of: instead of 50 percent, as above. Module 4 – Prof Bruno Solnik

CPI: Bullish on EUR Module 4 – Prof Bruno Solnik

How can we Offer (Construct) such a CPI?

Bearish on EUR Module 4 – Prof Bruno Solnik

Modest bullish/bearish AUD

Key Takeaways: Insuring with Options
Options on an index can be used to speculate, up or down, with limited risk. Options on an index can be used to insure a portfolio against market risk. To insure you always need to BUY an option, not sell (write) an option. Writing options is reserved to specialist traders. Insuring with an expensive (in the money) option provides good protection against adverse movements but with a cost, hence reduces profit potential. Insuring with a cheap (out of the money) option provides less protection against adverse movements but with a lower cost, hence better profit potential. Module 4 – Prof Bruno Solnik

Key Takeaways: Currency Options
The difficulty with currency option is to pick the correct option as an exchange rate implies two currencies. To find the exchange rate that will be relevant when insurance is needed (option exercised) you compute the “all-in-cost/revenue”: 1. If the direction of quotation requires to buy a put, the relevant exchange rate (‘you receive’) is: Strike price – put premium 2. If the direction of quotation requires to buy a call the relevant exchange rate (‘you pay’) is: Strike price + call premium Module 4 – Prof Bruno Solnik

Key Takeaways: Structured products
Options are extensively used in large “deals”. Structured products using optional features are (still) extensively used for retail and institutional clients. They can be decomposed as a mixture of zero-coupon bonds and options. Module 4 – Prof Bruno Solnik

CLASS 5 ALTERNATIVE INVESTMENTS
Private Equity, Hedge Funds LTCM

Alternative Investments
Many kinds, have in common relative illiquidity: Real Estate Venture Capital, Private Equity Distressed securities Commodities Anything

Private Equity (very brief, see other Modules)

Private equity investing has grown rapidly in the 2000s.
Private equity investments are equity investments that are not traded on exchanges. The limited partnership is called the “Fund”. General partners are sometimes designated as the “Management Company”.

There are three main categories of private equity:
Venture capital Leverage buyout Distressed investing

Private equity – Leveraged buyout investing
The largest category of private equity Investors put up an equity stake (20-40%) and borrow the rest. Company is then taken private. Private equity firm then gets involved in the management of the acquired company and takes steps to increase its value. The objective is to resell the company a few years later at a higher price.

Hedge Funds

Definition Legal structure Type of strategy Fee structure Funds of funds The pros and cons Index / performance

Hedge Funds: Definition
Huge Industry: The 1990s witnessed rapid growth in hedge funds. In 2007, assets under management surpassed $2 trillion. In 2007, the number of hedge funds exceeded 13,000. In 2008, AUM peaked to $2.5 trillion, then dropped sharply late 2008/mid Recovered a bit late 2009. As of End-2014, AUM $2.85 trillion for Hedge funds (including 0.45 for FoFs).

Hedge Funds: Definition
Today, funds using the “hedge fund” appellation follow all kinds of strategies and cannot be considered a homogeneous asset class. Hedge funds can be defined as: Funds that seek absolute returns Having a legal structure that avoids some government regulations Have option-like fees, including a base management fee and an incentive fee proportional to realized profits.

Hedge fund managers can create leverage in trading by:
Hedge Funds Hedge fund managers can create leverage in trading by: Borrowing external funds to invest more or sell short more than the equity capital that they put in. Borrowing through a brokerage margin account Use of financial instruments and derivatives.

Legal Structure in US The legal structure of a hedge fund largely depends on who its investors will be. For example, a private investment vehicle formed for the benefit of persons who reside outside of the United States will be organized differently than an investment vehicle formed for the benefit of United States residents.

Legal Structure in US Domestic US: A Limited partnership (LP) where investors are limited partners and the manager is General partner. Under Investment Act, no more than 100 investors, and no public solicitation

Legal Structure in US International: For the purpose of managing the assets of persons residing outside of the US, and also tax-exempt US investors, an offshore fund is ordinarily structured as a corporation and organized in a tax haven jurisdiction (e.g. Bermuda, British Virgin Islands, Cayman Islands, Ireland).

Legal Structure in US Often, the manager of an offshore fund forms a corporate entity to provide advisory services to the fund. This entity serves as the investment manager of the fund. If the hedge fund manager already manages the assets of a domestic partnership through a single corporate entity, the general partner of the partnership may also serve as the investment manager of the offshore fund.

Master Feeder Structure (“hub and spoke”)
- “Feeder” refers to the legal structure used. - The master fund is generally an offshore fund

Types of Investment Strategies
Classifications are arbitrary and vary across data providers. Hedge funds can be classified as: Long/short Market neutral Fixed income Global macro Emerging market funds Managed futures funds Event driven Distressed securities funds Risk arbitrage in M&A

Long / Short Long/short funds are the traditional type of hedge funds, taking short and long bets in common stocks. They vary their short and long exposure according to forecasts, use leverage, and now play on numerous markets throughout the world.

Long / Short These funds often maintain net positive or negative market exposures; so they are not necessarily market-neutral. In fact, a subgroup within this category is funds that have a systematic short bias, known as dedicated-short funds, or short-seller funds. The distinction with traditional funds is getting blurred, as some mutual funds offer a 130/30 strategy (or 120/20 etc..). And some hedge funds started to compete with similar products.

Example: Long / Short A hedge fund has a capital of 10 million and invests in a market neutral long/short strategy on the British equity market.

Example: Long / Short Shares can be borrowed from a primary broker with a cash margin deposit equal to 18% of the value of the shares. Given the high level of cash margin, no additional costs are charged to borrow the shares. The hedge fund has drawn up a list of shares regarded as undervalued (list A) and a list of shares regarded as overvalued (list B). The hedge fund expects that shares in list A will outperform the British index by 5% over the year, while shares in list B will underperform the British index by 5% over the year.

Example: Long / Short The hedge fund wishes to retain a cash cushion of 1 million for unforeseen events. What strategy would you suggest?

Answer The hedge fund would sell short shares from list B and use the proceed to buy shares from list A for an equal amount. Some capital needs to be invested in the margin deposit. The hedge funds could take long/short positions for 50 millions:

Answer Keep 1 million in cash Borrow 50 million of shares B from a broker, Deposit 9 million in margin (18%50 million), Sell shares B for 50 million in cash, Use the sale proceeds to buy 50 million worth of shares A The positions in shares A & B are established so that the portfolio’s beta is close to zero. The ratio of invested assets to equity capital is roughly 5:1.

Answer (2) If expectations materialize, the long/short portfolio of shares should have a gain over the year of 10% on 50 million whatever the movement in the general market index. To be market neutral, the fund would aim for a beta of zero. This 5 million gain will translate into an annual return before fees of 50% over the invested capital of 10 million.

Answer (2) This calculation does not take into account the return on invested cash (1 million) and assumes that the dividends on longs will offset dividends on shorts.

Market Neutral hedge funds
Market-neutral funds are a form of long / short funds that attempt to be hedged against a general market movement. They take bets on valuation differences of individual securities within some market segment.

Market Neutral hedge funds
Long / Short equity funds are a form of market neutral funds. But there are all kinds of market neutral strategies, mostly based on some form of arbitrage: equity long/short fixed-income hedging, pairs trading, warrant arbitrage, mortgage arbitrage, convertible bond arbitrage, closed-end fund arbitrage, and statistical arbitrage.

Example : Merger Risk Arbitrage
A merger has been announced between a French company A and a German company B. A will acquire B by offering one share of A for two shares of B.

Example : Merger Risk Arbitrage
Shares of B were trading in a €15 to €20 range prior to any merger discussion. Shares of B currently trade at €24, while shares of A trade at €50. The merger has been approved by both boards of directors but is awaiting ratification by all shareholders (that is extremely likely) and approval by the EU commission (there is a slight risk because the combined company has a large European market share in some products). How could a hedge fund take advantage of the situation? What are the risks?

Answer The hedge fund should construct a hedged position where it buys two shares of B for every share of A that it sells short. As the proceeds of the short sale of one share of A (€50) can be used to buy two shares of B (€48), the position can be highly leveraged. Of course the cost of securities lending and margin deposit should also be taken into account. When the merger is completed, the hedge fund will make a profit of approximately 2 euros for each share of A.

Answer The risk is that the merger will be cancelled. It is hard to tell what will be the stock price reaction to this announcement, but it is clear that the stock price of B will drop more, because it was to be acquired at a price well above its pre-merger market value. That would mean a sizable loss for the hedge fund.

Total fee = Base (fixed) fee + Incentive (performance) fee
Fee Structure Total fee = Base (fixed) fee + Incentive (performance) fee Typically 2% (fixed) plus 20% (performance). The calculation of performance fee varies and is somewhat complicated because of “high watermark”.

Funds of Funds Definition: Funds of funds (FOF) have been created to allow easier access to small investors, but also to institutional investors. A FOF is open to investors and, in turn, invests in a selection of hedge funds. Additional fee: typically 1% and 10%, on top of the hedge funds fees (typically 2% and 20%).

Fund of Funds – Advantages
Retailing Diversification Managerial expertise Due diligence process (but is it really done?)

Fund of Funds – Disadvantages
Potentially high fees Little evidence of persistence performance Absolute return loss through diversification

The Pros and Cons of Hedge Funds
Major Pro: Hedge Funds attract talent. Major Con: Hedge Funds can be more risky than they claim.

Hedge Funds – Pros Hedge funds mostly search for absolute returns, not alphas. Much more flexible than traditional asset management. You invest in “strategies” not “asset classes”. Correlation with traditional asset classes likely to be low. In bull markets, hedge funds are likely to do not as great; but would fare better in down markets.

Performance of Hedge Funds

Hedge Funds – Cons (Risks)
The unique risks of hedge funds include: Liquidity risk Pricing risk Counterparty credit risk Settlement risk Short squeeze risk Financing squeeze risk

Impact of the financial Tsunami
Many hedge funds use highly-leveraged strategies. The credit market closed in Given the high volatility, prime brokers dramatically increased the amount of required collateral. It is improving.

Hedge Fund Index/database
There are a number of indexes that track the hedge fund industry. The list of hedge fund index providers is long: Specialized hedge fund firms (such as HFR, Van Hedge, Hennessee, Greenwich) Banks such as Barclays or Dow Jones Crédit Suisse

Index providers (such as MSCI, S&P, FTSE), and even universities (CISDM, EDHEC) offering dedicated hedge fund indexes. These indexes are also broken down in subindexes for various classifications of hedge funds according to the investment strategy they follow. But the classifications vary across providers.

The launching date of these indexes differs markedly. Some were launched in the 1990s, others in the 2000s. In some cases, the historical value of the index was back-calculated to an earlier date, with the risk of only including surviving hedge funds and biasing the performance upward.

Biases in Reported Performance
Investors should exercise caution when using historical track record of hedge funds in reaching asset allocation decisions. The biases present in performance reporting: Self selection bias Instant backfilling bias Survivorship bias on return and risk Smoothed pricing on infrequently traded assets Option-like investment strategies Fee structure-induced gaming

Key Takeaways: Alternative Investments
Alternative Investments are characterized by illiquidity. Funds using the “hedge fund” appellation follow all kinds of strategies and cannot be considered a homogeneous asset class. They have an option-like fee structure with a fixed fee plus a performance fee with some high-water mark. Hedge funds are characterized by the strategy they follow. Many hedge funds resort to leverage, sometimes high leveraging. Risks are not easy to assess because of illiquidity (stale pricing) and “non-normal” strategies followed. 51

Value at Risk (VaR) Module 4 − Prof Bruno Solnik

Motivation and Definition Measurement of VaR
Value at Risk Motivation and Definition Measurement of VaR Some important assumptions Too good to be true! Module 4 − Prof Bruno Solnik

Motivation A single, summary, statistical measure of possible portfolio losses resulting from “normal” market movements. Losses greater than VaR are suffered only with a specified small probability Once one crosses the hurdle of using a statistical measure, the concept of VaR is straightforward to understand. Module 4 − Prof Bruno Solnik

t is typically one day, one week or one month.
Definition VaR is the loss that is expected to be exceeded with a probability x percent and a holding period of t days. x is typically 1%, 2 ½% or 5% t is typically one day, one week or one month. Module 4 − Prof Bruno Solnik

hence there is a 99% chance of losing less than VaR.
Definition If x = 1 percent, one assumes that only 1% of market fluctuations are “abnormal”. The maximum loss in “normal” market conditions is therefore equal to VaR. hence there is a 99% chance of losing less than VaR. Note however, that there is a 1% chance of losing more, even much more, than VaR. Module 4 − Prof Bruno Solnik

Monte Carlo Simulation
Measurement of VaR Delta-Normal Historic Monte Carlo Simulation While the degree of sophistication varies (modeling complex securities/arbitrage,..), all methods basically rely on some assumptions about sigmas and correlations. Module 4 − Prof Bruno Solnik

Simple Relations under Normality
VaR(5%) =  - E(R) VaR(1%) =  - E(R) VaR(1%)  VaR (5%) VaR(T days)  T VaR(1 day) However, note that the expected value is multiplied by T while the standard deviation only by T . Module 4 − Prof Bruno Solnik

Module 4 − Prof Bruno Solnik

Beyond VaR: Tails and Stress-Testing
Module 4 − Prof Bruno Solnik

VaR is grossly misunderstood
VaR only deals with normal risks VaR is not the maximum loss that can be incurred. It is the maximum loss under “normal” market conditions. A major risk is what happens in “abnormal” market conditions. Module 4 − Prof Bruno Solnik

Stress Testing What is it? What scenario to use?
We always fight the last war. Module 4 − Prof Bruno Solnik

Daily VaR (1%) and Trading Revenue of BNP Paribas (annual report 2007, in 000€)

Daily VaR and Trading Revenue of BNP Paribas (annual report 2007, in 000€)
The green line reports daily trading revenue. The grey line reports daily VaR estimated at 1%. If the model is good we expect that daily losses exceed VaR in 1%250days = 2.5 days. Actual number is 3 days, so model looks good. But with the financial tsunami, market conditions became “abnormal” in 2008. Module 4 − Prof Bruno Solnik

Lessons from the Crisis and new Research in Risk Management
Academic research is often presented as one of the guilty party of the current crisis. Financial economics is primarily about concepts. One major conclusion is that excess return cannot be generated without taking systematic risk, risks that CANNOT be diversified away. Financial mathematics is another branch of modern finance originating in option pricing and dynamic hedging. It developed powerful models. In particular they assume that markets are liquid with continuous prices. Parameters of the processes must be estimated using past and present data. Even if future volatility can be inferred from current option prices, the assumption is that this volatility estimates are good estimates of future volatility. In turn, these models are used to implement sophisticated risk management systems. Module 4 − Prof Bruno Solnik

Lessons from the Crisis and new Research in Risk Management
Over time finance has become more mathematics and less economics. In itself such a trend is not bad, but increased model sophistication gives a false sense of security and makes models appear as infallible black boxes. It is sad to see that many concepts such as VaR and risk management are poorly understood by board of directors and top management of financial institutions, rating agencies or regulators. Module 4 − Prof Bruno Solnik

Lessons from Crises Market crash of 1987 Demise of LTCM in 1998
Illiquidity can fail models badly estimated parameters such as delta/hedge ratio can be very wrong ex_post, especially with disruptions in market volatility. Demise of LTCM in 1998 All models are primarily based on past data (possibly adjusted); estimated parameters can be very wrong ex-post especially with disruptions in market volatility. Correlation is extremely important in risk management. Market crashes can lead to extreme rise in correlation across all markets. Financial Tsunami of 2007/2008 Module 4 − Prof Bruno Solnik

Implication of Recent Market Situation
Illiquidity: implies serial correlation (big losses followed by big losses) Periods of high volatility: amplitude of Profit/Losses increases because higher sigma. Return distributions are not unconditionally normal: Fat tails, etc… High correlation across assets: amplitude of Profit/Losses increases, because no diversification of risks Module 4 − Prof Bruno Solnik

Daily VaR and Daily Realized Profit & Loss

The Case of SocGen 2008 (Annual Report)
Daily VaR at 99% implies that in a year, the daily loss should exceed VaR around 2 or 3 days per year (1% of 250 trading days). In 2008, it happened 26 days. Periods of high volatility Illiquidity induced serial correlation Dramatic increase in correlation across markets/asset classes (loss of diversification benefits) has an huge impact on P&L Module 4 − Prof Bruno Solnik

Example of the Impact of Correlation Rise
One trade of 100, with daily  of return 1%, VaR at 99% is (Investment ×  × 2.326) Ten uncorrelated trades (r = 0): then daily  of return 0.316%, VaR at 99% is 7.35 (Investment ×  × = 1000 × 0.316% × = 7.35, not ten times 2.326) Assume that Correlation is actually One between the ten trades. Then daily  of return 1% (no diversification benefits), VaR at 99% is (ten times 2.326, the VaR of each project). Further assume that markets volatility has doubled to a daily 2%. VaR at 99% is (1000 × 2% × 2.326). VaR rise from 7.35 to Module 4 − Prof Bruno Solnik

Recent Academic Research (very partial)
I believe that we focused too much on modeling individual asset prices/risks, and not enough on modeling correlation (except on CDOs). “Extreme Value Theory” brings useful contribution. A seminal paper: "Extreme Correlation of International Equity Returns ", F. Longin and B. Solnik, Journal of Finance, April 2001. Yes, extreme events are rare, but there are techniques that allow to get better estimations and models of correlation during crises. That is a very fruitful area of research. Risk managers live in the « fat tails » and they also need quantitative tools in those fat tails. Common sense is needed to « fly » the starship in this space, but that is not enough, you also need instruments. Module 4 − Prof Bruno Solnik

Final Words I also believe that education has badly failed.
Risk management models are based on assumptions and estimated parameters. When these assumptions (illiquidity) and parameters (past data not good estimates of future) fail, one needs to adapt very quickly. Institutions where risk management was a “culture” and top management was well “educated” fared much better than others. The mission of researchers is not only to build further black boxes, but also, and maybe more importantly , educate the whole institutions (from traders/asset managers to top management) in terms that they can understand. There is no alternative to quantitative techniques. Module 4 − Prof Bruno Solnik

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