The swing of risk/return

The applications of the Markowitz’s Model The Markowitz model is used to build the efficient frontier… … but it is used to determine the strategic asset allocation (= the optimal portfolio for long term) for each investor or for a class of investors (utility function is not easy to measure) When you build the efficent frontier there are some problems

Risk/Return

The definition of strategic asset allocation Some problems to debate: 1.Which measure of risk? 2. How many and which asset classes? 3. How to estimate expected returns, volatility and correlations ? On what time scale? 4. How to pass from the efficent frontier to real portfolio for each investor? 5. What is the relationship between the efficient theoretical frontier and the "true" product purchased by the customer?

1.Which measure of risk? Standard deviation is a two-sided measure: you can use also alternative measures based on the downside-risk (standard semi-deviation, or Value at Risk) You can use them based on probabilistic concepts such as Value at Risk (maximum potential loss over a time span and a certain confidence interval ) Shortfall probability (the probability of not reaching a final return at a future date)

Performance distribution Alternative measures instead of standard deviation Shortfall Performance distribution Downside risk Shortfall The probability of not reaching a final return at a future date VaR threshold Return Frequency VaR at 95% Performace distribution 95% Value at Risk maximum potential loss over a time span and a certain confidence interval

2. How many and which asset classes? The portfolio optimization is based on the estimation of the expected returns, volatility and correlations Is it better to select not many asset classes (e.g. short term securities, bonds in Euro, bonds in different currency,european stocks or international stocks), or you can make a more analytical choice? How do you divide bonds and stocks?

Asset allocation strategic asset allocation ( medium long term) tactical asset allocation (short term) The goal is finding the right equilibrium between A)stocks and bonds; B) domestic or foreign assets; C) traditional asset class or alternative asset class.

The right composition of portfolio The selection of asset class: bond(rating ,maturity, issuer) stocks(large,small, growth,value), The frequency of change of composition of portfolio The measures of each asset class (the expected return, risk and correlations) The impact of financial forecast for each asset class: macroeconomics factors ( the level of interest rate and inflation rate) evalutative factors (the reliability of used models) psychological factors (sentiment, VIX, ratio return = stock return/bond return, ratio call/put)

Financial crisis The skill of asset manager will decrease during the crisis He will not able to forecast the future market’s trend He uses excess trading ( behavioral finance) to reduce his losses Excess trading means to improve trading costs

asset allocation styles Conservative(portfolio with short term products close to risk free rate) Moderate (asset manager selects a equity component close to the market (beta =1)or he selects ETF and/or a residual component of bonds (government bonds , or investment grade bonds) to keep a medium/low risk Aggressive (mid-cap or small-cap) growth with high (P/E) and low dividend/price. Speculative grade bond ( he will wait for a upgrading to take a profit from credit risk)

Portfolio policy Strategic ( efficient market, you like the diversification without considering the timing. The strategic investor knows the benchmarks. This strategy is called beta o market risk) Tactical -inefficient market , timing (active beta could be obtained through the market timing, that is, varying the exposure to the market); selectivity of asset class to under or overweight compared to the selected benchmark. Dynamic – inefficient market. Asset manager wants to beat the benchmark, but in bad conditions of the market he is ready to keep a minimum return of portfolio( floor portfolio).

Asset Allocation: right choice? Gary P.Brinson, L.Randolph Hood, Gilbert L.Beebower, “Determinants of Portfoglio Performance”, Financial Analysts Journal, July-August 1986 Gary P.Brinson, Brian D.Singer, Gilbert L.Beebower, “Determinants of Portfoglio Performance II: An Update”, Financial Analysts Journal, May-June 1991

Discretionary intervention compare to benchmark Active and Passive Management PASSIVE ACTIVE TRACKING ERROR Discretionary intervention compare to benchmark INDEXED FUNDS HEDGE FUNDS Quantitative Quantitative/Qualitative Asset Management TEV= tracking error volatility

3. How to estimate expected returns, volatility and correlations 3. . How to estimate expected returns, volatility and correlations ? On what time scale? The expected return mean reversion return and the problem of historical used sample The expected returns based on subjective or long term valuations? The problem of time scale of investor Volatility Historical volatility vs. implicit volatility Time scale and the frequency of data samples

3. Correlations? Correlations The stability of market conditions (ex. Euro effect) Total return vs domestic return+currencies The frequency of data samples (no daily data!)

4. How do you get through the efficent frontier to real portfolio for each investor? The selection can not be based on the utility function (see the optimal portfolio) At the end asset managers divide into segments the efficient frontier for given levels of standard deviation…

5. The optimal portfolio vs.“true”portfolio When asset managers detemine portfolio optimization they need to translate it in a true portfolio They build a benchmark . It could be made up of 30% bonds in Euro, 20% bonds Ex Euro, 25% stocks in Euro, 25% stocks ex Euro Implications/risks How efficient the selected benchmark is? Who defines the asset allocation? The risk of commercial optimization” How to set the risk of limits for asset manager?

The map of risk/return