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**Risk Management Selected Concepts**

Agenda Definitions Basic Concepts of Modern Portfolio Theory Selected Risk Management Metrics Investment Policy and Conclusions

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Definitions

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What is Risk? Quite often risk is perceived only with negative connotations… Dictionary.com defines risk as: 1. The possibility of suffering harm or loss; danger. 2. A factor, thing, element, or course involving uncertain danger; 3. a. The danger or probability of loss to an insurer. b. The amount that an insurance company stands to lose. 4. a. The variability of returns from an investment. b. The chance of nonpayment of a debt. 5. One considered with respect to the possibility of loss: a poor risk. However, risk may also contain another element … The Chinese use two symbols to define risk: 1. The first symbol is for “danger” 2. The second is for “opportunity”

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**What is Risk Management ?**

From our previous definition, Risk Management (RM) would entail administering a mix of danger and opportunity. A more classic approach defines RM as a process (an attempt, really) to identify, measure, monitor and control uncertainty in an orderly and methodical manner (often using mathematical models). Both approaches to RM are correct. However, RM is more of avoiding dangers than seeking the opportunities. RM in a modern acception entails following a pre-established management process and performing mathematical models (Greek letters and other sophisticated financial metrics). RM is about understanding human behavior and finding a “comfortable” trade-off between expected reward and potential loss. RM entails managing exposure and uncertainty.

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**in the Investment Management context**

Risk Topology in the Investment Management context Equity/commodity (price) Market Risk Interest Rates Currency Issuer Credit Investment Risks Portfolio Concentration Liquidity Counterparty Risk Operational Regulatory Systemic Human Factor Legal

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Market Risk Market risk is the uncertainty of changes in the asset’s returns relative to changes in the market. Derives from market-wide factors which affect issuers and investors. Such factors will include (but will not limited to): Interest rates; Inflation rates; Currency exchange rates; Demographics (remember Michael Cichon’s comments about demographic implications!); Unemployment rates; General legislation; Risk of natural disasters (Katrina, Rita, earthquakes, floods, fire, etc.).

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Credit Risk - Credit risk is the uncertainty in a counterparty’s (or obligor’s) ability to meet payment of its obligations. Associated concepts: Default probability is the likelihood that the obligor will default on its obligation either over the life of the transaction or at an specific timeframe. Credit exposure is the amount of outstanding at the time of a potential default. Recovery rate is the fraction of the exposure that might be recovered. Credit quality is the perceived ability (usually by a credit rating agency) of an issuer or counterparty to meet its obligation. Credit rating is assigned by credit analysts to the counterparty (or specific obligation) and can be used for making credit decisions.

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**Standard & Poor’s Credit Ratings**

AAA Best credit quality - Extremely reliable with regard to financial obligations AA Very good credit quality - Very reliable A More susceptible to economic conditions - still good credit quality BBB Lowest rating in investment grade BB Caution is necessary - Best sub-investment credit quality B Vulnerable to changes in economic conditions - Currently showing the ability to meet its financial obligations CCC Currently vulnerable to nonpayment - Dependent on favorable economic conditions CC Highly vulnerable to a payment default C Close to or already bankrupt - Payment on the obligation currently continued D Payment default on some financial obligations has actually occurred Simple, market wide, common, homogeneous (to a broad range of assets), easily available and (+ - ) objective. But have limitations (remember Enron!).

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Liquidity Risk Liquidity risk is the uncertainty of being able to easily and without undue cost avail oneself of cash either through converting financial assets to cash (“liquidate a position”) or through credit. A person or institution might be exposed to liquidity risk if sudden unexpected cash outflows occurs and the markets on which it depends are subject to loss of liquidity, or if a financial asset it holds losses “marketability” or if the credit rating of the institution falls. A position can be hedged against market risk but still entail liquidity risk. Accordingly, liquidity risk has to be managed in addition to market, credit and other risks. Cash flow exercises and stress testing (along with asset-liability matching) cab be applied to assess liquidity risk. However, Comprehensive metrics of liquidity risk due to systemic failures are not easily available. Remember James Thompson’s comment about matching assets and liabilities, this reduces exposure to liquidity risk!.

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Systemic Risk Risk that a localized problem in the financial markets could cause a chain of events which ultimately cripple the market. A default by a major market participant (i.e. Government default, and even maybe foreign currency depletion and/or inability to access international markets) might cause liquidity problems for a number of that institution’s counterparties. This might cause those counterparties to fail to make payment on their own obligations, and a liquidity crisis could spread throughout the market. One of the purposes of financial regulation is to ensure that the market operates in a manner that minimizes systemic risk. This issue might be discussed by Edgardo Podjarny for the Argentina case.

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**Basic Risk Management Concepts**

“Risk management” as it is understood today, largely emerged during the early 1990’s. It is different from earlier forms (it is more oriented to financial solutions using derivatives). The four approaches to risk management are: Risk Transfer: through the purchase of traditional insurance products, or through the acquisition of derivative products to “hedge” exposures. Termination (or mitigation) of risks: via safety measures, quality control and hazard education. Risk transformation: also through the use of derivatives. Tolerate risks: alternative risk financing, including self-insurance and captive insurance (assume expected value of impact or loss is lower than cost of hedging, transferring risk or preventive measures).

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**Basic Concepts of Modern Portfolio Theory**

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**Modern Portfolio Theory (MPT)**

Markowitz (1952) “Portfolio Selection” Harry Markowitz proposed that investors focus on selecting portfolios based on their overall risk-reward characteristics instead of merely compiling portfolios form securities that have (individually) attractive risk-reward characteristics. MPT treats volatility and expected return as proxies for risk and reward. Out of the entire set of possible portfolios, a certain sub-set will optimally balance risk and reward. (sub-set = efficient frontier of portfolios) An investor should select a portfolio that lies on the efficient frontier. MPT provides a broad context for understanding the structuring of a portfolio.

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Efficient Frontier Today, it is possible to monitor daily the values (reflecting price changes, coupon payments, dividends, stock splits, etc.) for most of the traded financial instruments. However, their future values behave in what seems a random pattern. Observing their past behavior and using several algorithms we may estimate their future returns and volatilities and correlations (for each pair of instruments). With these inputs (expected returns, volatilities and correlations) we may calculate the expected return and volatility of any portfolio. The notion of “optimal” portfolio can be defined in one of two ways: For any expected return, consider all the portfolios which have that expected return and select the one which has the lowest volatility. For any level of volatility, consider all the portfolios which have that volatility and select the one which has the highest expected return.

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Efficient Frontier 15% 10% 5% 0% -5% 0% % % % % Risk (Volatility of Expected Return) Average Annual Expected Rate of Return The green region corresponds to set of achievable risk-return portfolios (basket of instruments). Portfolios on the efficient frontier are optimal in both the sense that they offer maximal expected return for some given level of risk and minimal risk for some given level of expected return. Typically, the portfolios which comprise the efficient frontier are the ones which are most highly diversified.

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**Diversification A corollary of MPT….**

Diversification (“don’t put all your eggs in one basket”) A portfolio that is invested in multiple instruments whose returns are uncorrelated will have an expected simple return which is the weighted average of the individual instruments’ returns, but its expected volatility (risk) will be less than the weighted average of the individual instruments’ volatilities. Expected behavior need to be uncorrelated To diversify it is not sufficient to add instruments to a portfolio. Suitable diversification requires reduction of risk concentrations and unrelated risks taken on.

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**Risk (Return Volatility)**

Capital Market Line 15% 10% 5% 0% -5% 0% % % % % Risk (Return Volatility) Expected Return Risk-Free Rate CML Borrow at risk free rate and purchase more efficient portfolio Loan at risk free rate and sell efficient portfolio James Tobin (1958) added the notion of leveraging the “efficient” portfolio by combining it with a risk-free asset. Investors who hold the super-efficient portfolio using the risk-free asset may: Leverage their position by shorting the risk-free asset and investing the proceeds in additional holdings in the super-efficient portfolio. De-leverage their position by selling some of their holdings in the super-efficient portfolio and investing the proceeds in the risk-free asset.

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**Capital Asset Pricing Model (CAPM)**

William Sharpe (1964) extended MPT by introducing notions of systematic and specific risk. CAPM demonstrates that (given simplifying assumptions), the super-efficient portfolio must be the market portfolio. All investors should hold the market portfolio (leveraged or de-leveraged to achieve whatever level of risk they desire). CAPM decomposes a portfolio’s risk into: Systematic risk: risk of holding the market portfolio for which an investor is compensated. Specific risk: risk which is unique to an individual asset and can be diversified (the investor doesn’t receive compensation for it). When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk, but through diversification the risk may be nullified (the net exposure ends up as only systematic risk of the market portfolio).

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**Capital Asset Pricing Model (CAPM)**

Beta measures the volatility of a security relative to the asset class (or to the market portfolio). If a security’s Beta is known, then CAPM can establish the required return (a higher Beta –that is higher expected risk- requires higher expected returns). CAPM simplifies the task of finding the efficient frontier because it is necessary to calculate the correlations of every pair of asset classes (proxies of the market) instead of every pair of instruments in the entire universe. Investing in the asset class is possible and simple via investing in index funds that effectively replicate the market.

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Metrics

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Duration Duration is a weighted measure of when an investor will get his money back from a fixed income investment. Duration considers coupon payments. The duration of a zero-coupon bond equals its maturity. For two bonds that mature at the same time, the bond with the higher coupon payment will have lower duration. Duration is also a metric of interest rate sensitivity. With a single number duration summarizes an instruments sensitivity to changes in interest rates. Of the many risks facing investors (in fixed income), interest rate is probably the most worrisome. Duration is one of the key metrics that allows identifying, measuring and controlling interest rate risk. The value of the instrument will decline if interest rates rise – and rise if interest rates fall. Bonds with higher duration face higher interest rate risk.

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**Change in interest rates**

Duration Geometrically, duration is defined to be the slope of that tangent line, multiplied by negative one. 0.10 0.05 -0.05 -0.10 Change in interest rates ∆0r Change in price ∆0p / p A good rule of thumb regarding duration and changes in interest rates: Duration Change in price Rates fall 1% Rates rise 1% 1 year +1% -1% 5 years +5% -5% 10 years +10% -10%

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**The asset on the left is more risky (more volatile of the two)**

Volatility Example: Time series of prices of two assets price time price time The asset on the left is more risky (more volatile of the two) Volatility may be defined as the uncertainty surrounding an expected value… Volatility usually refers to movements in financial prices and rates. Fluctuations (of prices or rates in financial markets) are generally random and independent from one period to the next (there are no serial correlations or other dependencies). Usually, we refer to volatility as the mean of the standard deviation of expected returns.

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**Variance and Standard Deviation**

Example: High vs. Low Variance Probability density functions (PDFs) are indicated for two random variables. The one on the left is more dispersed (it has a higher variance) than the one on the right. The variance is a metric of the spread of random variable’s probability distribution (around the arithmetic mean – average). The most commonly used measure of spread is the standard deviation (which is calculated as the square root of the variance).

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Value at Risk (VaR) Value at Risk (VaR) is metric that summarizes in a single number the portfolio’s market risk. VAR measures the maximum loss over an established time horizon (i.e. worst case scenario of losses in one month). VaR is applicable to any liquid portfolio (any portfolio that can reasonably be marked to market on a regular basis and that its assets may be readily converted to cash). VaR uses standard deviation and statistical analysis (of price and volatilities) to determine the worst loss scenario for a given probability (confidence level). If the returns are normally distributed (bell-shaped curve distribution), approx. 68% of the outcomes will fall within one standard deviation on either side of the expected value (mean) and approximately 95% will fall within 2 standard deviations on either side of it. The higher the variance and standard deviation, the greater the variability of possible returns from the investment (the greater the risk).

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**Credit rating transition matrix**

Credit VaR Credit VaR is similar to “market” VaR, but it refers specifically to the maximum exposure and expected maximum loss (through default or price change) a firm is willing to take in an investment (or loan) portfolio. This approach is based on the credit transition matrix, which defines the probability of one asset ”migrating” or “transiting” to lower credit ratings. Industry limits, country and counterparty limits may be established to limit the credit exposure. Credit rating transition matrix Standardized Rating 1 AAA 2 AA 3 A 4 BBB 5 BB+ to C 6 Default Short term 1 2 3 4 5 6 93.92% 3.60% 0.56% 1.91% 0.00% 0.54% 98.04% 0.81% 0.41% 0.21% 0.29% 2.76% 90.20% 4.08% 2.57% 0.10% 2.42% 1.69% 91.37% 1.85% 2.66% 1.33% 1.35% 97.32% 100.00% Source: CONSAR. March 2005

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**Alpha (α) and Information Ratio**

Alpha is a measure of the incremental reward (or loss) that an investor gained in relation to the market. This is measured as performance of a selected portfolio relative to a market benchmark. Alpha can be used to directly measure the value added or subtracted by a a fund’s manager. It is calculated by measuring the difference between a fund’s actual returns and its expected performance. Tracking error is the standard deviation of the excess return. The information ratio (IR) is one measure of volatility-adjusted return. IR is defined as alpha divided by tracking error.

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**Alpha as a tool of “active” investors**

Alpha is used by investors that follow an active management style. That is, they diverge from the benchmark or index trying to generate more returns (alpha). The benchmark (usually an index, represents the market or asset class). The assumption is the market is efficient Divergence versus the chosen benchmark Short Long Duration Flattening Slope Yield curve Under-weight Over-weight Investment Instrument Under-weight Over-weight Foreign currency Short Long Volatility

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**Active Management & Asset classes**

+ Active Risk Different Active Management Market Risk β Passive Management Cash Short & medium term bonds Long term bonds US & Euro Equities Emerging Markets Equities High yield bonds Asset class or portfolio composition

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**Setting Investment Policy and Conclusions**

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**Prudent Risk Management Starts by Setting an “Adequate” Investment Policy**

1st Clearly articulate the primary objective and nature of the Fund Balance risks and returns 2nd Investment Targets Returns Risks Asset classes Credit ratings Limits Currencies Preferences 3rd Investment Restrictions Absolute Return 4th Investment style & Relative Return Benchmarks Risk-Averse Risk-Indifferent Risk-Seeking Active 5th Risk Tolerance Passive

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**Investment Policy IMSS as an example remember Dr. Levy’s presentation**

Reserve Structure Economic Fluctuations Catastrophes Random fluctuations in income and expenditure Future benefit expenditures (pre-funding) Buffer fund for pensions DB (normalize expenditure level) Clearly state the primary objective (or nature) of the Fund Investment Objectives Risks < 1.5% VaR Returns X bps > indices One asset class, no derivatives Investment grade Limits (VaR, Credit VaR, Tracking error, issuer, sector, international markets) No Hedging Accepted currencies, US dollar, Euro, MX peso Investment Restrictions “Mostly passive” i.e. For RO’s 50% PIP Guber. 50% PIP Bancario Investment style Benchmarks Risk Tolerance Risk-Averse – positive real returns & certain liquidity requirements

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**Conclusions Risk involves exposure and uncertainty.**

RM is a process to identify, measure, monitor and control uncertainty in an orderly and methodical manner (often using mathematical models). Harry Markowitz’s Modern Portfolio Theory showed that all the information needed to choose the best portfolio for any given level of is risk is contained in three simple metrics: Expected investment returns; Standard deviation of expected returns; Correlations of the pairs of instruments in the portfolio. A portfolio is a basket or set instruments that presents, in a comprehensive and accumulated manner, a risk return profile that responds to the goals and risk tolerance of the investor.

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Conclusions James Tobin showed that it is possible to combine the efficient portfolios with the risk free asset, thus creating a set of portfolios with superior characteristics (super efficient frontier). William Sharpe’s idealized model* proposed Tobin’s tangent portfolio must be the market portfolio. Investors use asset classes to determine Strategic Asset Allocation (for which the number of correlations is small and more of less stable and easier to determine). Practical Lessons: Volatility worsens as the time horizon shrinks ( there are benefits to long term investing, remember Sudhir Rajkumar’s presentation on 20 yr. volatility of US stocks! ); Diversification reduces volatility efficiently;

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**Conclusions Practical Lessons:**

A practical way to invest in a diversified portfolio is through representative market indices or index funds; Don’t go for Alpha until investment and risk management process is mature (remember Lesson 8 of Jay Collins’ presentation! ); Modern Portfolio Theories provide simple, intuitive solutions to investing, but have their limitations and should be one of many elements to be considered; Strong governance and prudence! should be prerequisites for safe and efficient investment of Social Security Funds; Sound Risk Management starts with an adequate policy statement. Thank you.

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Some Background Assumptions Markowitz Portfolio Theory

Some Background Assumptions Markowitz Portfolio Theory

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