Asset Allocation

1. Asset Allocation Chapter 5

2. Key Learning Outcomes • Summarize the function of strategic asset allocation in portfolio management • Discuss the role of strategic asset allocation in relation to exposures to systematic risk • Compare and contrast strategic and tactical asset allocation • Appraise the importance of asset allocation for portfolio performance

3. Learning Outcomes • Explain an advantage and a disadvantage of implementing a dynamic versus a static approach to strategic asset allocation • Discuss and interpret the specification of return and risk objectives in relation to strategic asset allocation • Evaluate whether an asset class or set of asset classes has been appropriately specified • Select and justify an appropriate set of asset classes for an investor • Evaluate the theoretical and practical effects of including an additional asset class such as inflation-protected securities, international developed markets or emerging market securities, or alternative assets in an asset allocation

4. Learning Outcomes • Formulate the major steps in asset allocation • Determine and justify a strategic asset allocation, given an investment policy statement and capital market expectations • Critique and revise a strategic asset allocation, given an investment policy statement and capital market expectations • Determine and justify tactical asset allocation (TAA) adjustments to asset-class weights given a description of a TAA strategy and expectational data

6. Asset Allocation Strategies • Integrated asset allocation • capital market conditions • investor’s objectives and constraints • Strategic asset allocation • constant-mix • Tactical asset allocation • mean reversion • inherently contrarian • Insured asset allocation • constant proportion

7. Function of Strategic Asset Allocation in Portfolio Management • Strategic asset allocation combines investor’s objectives and constraints with long-term capital market expectations into IPS-permissible asset classes • Purpose is to satisfy investor’s objectives and constraints • Process leads to a set of portfolio weights called the policy portfolio

8. Strategic Asset Allocation and Systematic Risk • Strategic asset allocation aligns portfolio’s risk profile with investor’s objectives • Investors expect compensation for accepting non-diversifiable (systematic) risk • Distinct asset classes have distinct risk exposures • Strategic asset allocation effectively controls systematic risk exposures • Strategic asset allocation also provides the investor with a set of benchmarks for appropriate asset mix and long-term risk tolerance

9. Strategic versus Tactical Asset Allocation • Strategic allocation sets investor’s long-term exposures to systematic risk • Tactical asset allocation (TAA) involves short-term adjustments to asset weights based on short-term predictions of relative performance • TAA is an active and ongoing investment discipline, whereas strategic asset allocations are revisited only periodically or when the investor’s circumstances change

10. Asset Allocation and Portfolio Performance • Some studies have indicated that asset allocation explains the vast majority of portfolio returns, far outweighing timing and security selection • Cross-sectional studies have shown asset allocation to explain much less (though still a very significant amount) of portfolio returns • However, other studies have shown that the dispersion of results can vary more due to security selection than asset allocation, and thus indicate that skillful investors would gain more from security selection

11. Asset Allocation Strategies • Selecting an allocation method depends on: • Perceptions of variability in the client’s objectives and constraints • Perceived relationship between the past and future capital market conditions • importance of asset allocation • Does Asset Allocation Policy Explain 40, 90, or 100 Percent of Performance? • Ibbotson and Kaplan FAJ Jan/Feb 2000

12. Asset and Asset/Liability Management Approaches • Asset/Liability Management (ALM) models future liabilities and adopts an asset allocation best suited to funding those liabilities • Asset-only approach does not explicitly model liabilities • Dynamic Approach • Asset allocation, actual returns and liabilities in one period directly affect the optimal decision for the following period • Static Approach • Does not consider links between time periods • Less costly and complex to model and implement

13. Risk and Return in Strategic Asset Allocation • Return objective • Qualitative objectives describe fundamental goals • Quantitative objectives specify return needed to achieve goals • Compounding must be considered through geometric return and multiplicative rather than additive formulations • Risk objective • Qualitative (below average or above average) • Quantitative • numerical risk aversion measured through interview • Acceptable level of volatility • Shortfall/downside risk • Safety-first criterion • Behavioral biases

14. Criteria for Specifying Asset Classes • Assets within a class should be relatively homogeneous • Asset classes should be mutually exclusive • Asset classes should be diversifying • Asset classes as a group should comprise the majority of world investable wealth • Asset class should have the capacity to absorb a significant fraction of the investor’s portfolio without compromising liquidity

15. Traditional Asset Classes • domestic common equity • domestic fixed income • international common equity • international fixed income • real estate • cash and cash equivalents • others to consider: • alternative – real estate often considered part of this along with private equity, commodities, currencies, and investment strategies of hedge funds • TIPS

17. When to Include an Asset Class • Assets should be considered in a portfolio if they improve the portfolio’s mean-variance efficient frontier • This occurs if the asset class Sharpe ratio exceeds the product of the existing portfolio’s Sharpe ratio and the correlation between the asset class return and the portfolio’s return • For example, an asset with a Sharpe ratio of 0.2 and a correlation of 0.9 to the return of a portfolio with a Sharpe ratio of 0.15 should be added because 0.2 > 0.15(0.9) = 0.135

19. Asset Allocation Steps • Investor Specific • Consider investor’s net worth and risk attitudes • Apply a risk tolerance function • Determine the investor’s risk tolerance • Capital Market Situation • Identify capital market conditions • Implement a prediction procedure • Generate expected returns, risks and correlations • Combined Investor-Market Relationship • Use an optimizer to determine allocation given investor’s risk tolerance • Select asset mix • Actual returns determine feedback for process

20. Background Assumptions • As an investor you want to maximize the returns for a given level of risk. • Your portfolio includes all of your assets and liabilities • The relationship between the returns for assets in the portfolio is important. • A good portfolio is not simply a collection of individually good investments.

21. Risk Aversion Given a choice between two assets with equal rates of return, most investors will select the asset with the lower level of risk.

22. Evidence That MostInvestors are Risk Averse • Many investors purchase insurance for: Life, Automobile, Health, and Disability Income. The purchaser trades known costs for unknown risk of loss • Yield on bonds increases with risk classifications from AAA to AA to A….

23. Not all Investors are Risk Averse Risk preference may have to do with amount of money involved - risking small amounts, but insuring large losses

24. Markowitz Portfolio Theory • Quantifies risk • Derives the expected rate of return for a portfolio of assets and an expected risk measure • Shows that the variance of the rate of return is a meaningful measure of portfolio risk • Derives the formula for computing the variance of a portfolio, showing how to effectively diversify a portfolio

25. Expected Rates of Return • For an individual asset - sum of the potential returns multiplied with the corresponding probability of the returns • For a portfolio of investments - weighted average of the expected rates of return for the individual investments in the portfolio

26. Standard Deviation of Returns for an Individual Investment Standard Deviation

27. Covariance of Returns • For two assets, i and j, the covariance of rates of return is defined as: Covij = sum{[Ri - E(Ri)] [Rj - E(Rj)]pi} • Correlation coefficient varies from -1 to +1

28. Portfolio Standard Deviation Formula

29. Portfolio Risk-Return Plots for Different Weights E(R) 2 With two perfectly correlated assets, it is only possible to create a two asset portfolio with risk-return along a line between either single asset Rij = +1.00 1 Standard Deviation of Return

30. Portfolio Risk-Return Plots for Different Weights E(R) f 2 g With uncorrelated assets it is possible to create a two asset portfolio with lower risk than either single asset h i j Rij = +1.00 k 1 Rij = 0.00 Standard Deviation of Return

31. Portfolio Risk-Return Plots for Different Weights E(R) f 2 g With correlated assets it is possible to create a two asset portfolio between the first two curves h i j Rij = +1.00 k Rij = +0.50 1 Rij = 0.00 Standard Deviation of Return

32. Portfolio Risk-Return Plots for Different Weights E(R) With negatively correlated assets it is possible to create a two asset portfolio with much lower risk than either single asset Rij = -0.50 f 2 g h i j Rij = +1.00 k Rij = +0.50 1 Rij = 0.00 Standard Deviation of Return

33. Portfolio Risk-Return Plots for Different Weights Exhibit 7.13 E(R) Rij = -0.50 f Rij = -1.00 2 g h i j Rij = +1.00 k Rij = +0.50 1 Rij = 0.00 With perfectly negatively correlated assets it is possible to create a two asset portfolio with almost no risk Standard Deviation of Return

34. Efficient Frontier for Alternative Portfolios Figure 8.9 Efficient Frontier B E(R) A C Standard Deviation of Return

36. The Efficient Frontier • The efficient frontier represents set of efficient portfolios at various levels of risk • part of the minimum variance frontier which represents portfolio with the smallest variance of return for its level of expected return • MVF has a global minimum variance portfolio which is the smallest variance of all minimum variance portfolios • represents feasible set of investment opportunities • find an efficient portfolio with combination of risk and return that is appropriate for investor • use mean-variance optimization (or other processes to determine asset class weights)

37. Mean-Variance Optimization • Investors should choose from efficient portfolios consistent with the investor’s risk tolerance • Unconstrained: asset class weights must sum to one • Sign-constrained: no short sales (negative weights) • quality of inputs • recommended asset allocations are highly sensitive to small changes in inputs • estimation error in expected returns is about 10 times as important as estimation error in variances and 20 times as important as estimation error in correlation (covariance)

38. Capital Market Theory: An Overview • Capital market theory extends portfolio theory and develops a model for pricing all risky assets • Capital asset pricing model (CAPM) is early attempt at determining the required rate of return for any risky asset • problems with this model in part due to unrealistic assumptions • current research attempts to find “true” asset pricing model but no one accepted model • concepts from CAPM used in practice even though model has problems • for example, beta as a measure of systematic risk

39. Risk-Free Asset • An asset with zero variance • Zero correlation with all other risky assets • Provides the risk-free rate of return (RFR) • Will lie on the vertical axis of a portfolio graph • asset class of cash and cash equivalents

40. Risk-Free Asset Covariance between two sets of expected returns is *instead of (/n), multiply by probability if calculating covariance of expected returns Because the returns for the risk free asset are certain, Thus Ri = E(Ri), and Ri - E(Ri) = 0 Consequently, the covariance of the risk-free asset with any risky asset or portfolio will always equal zero. Similarly the correlation between any risky asset and the risk-free asset would be zero.

41. Market Portfolio • Under CAPM, in equilibrium each asset has nonzero proportion in M • All assets included in risky portfolio M • All investors buy M • If M does not involve a security, then nobody is investing in the security • If no one is investing, then no demand for securities • If no demand, then price falls • Falls to point where security is attractive and people buy and so it is in M

42. CML and the Separation Theorem • CML represents new EF • all investors have the same EF but choose different portfolios based on risk tolerances (with homogeneous investors - assumption of CMT) • investor spreads money among risky assets in same relative proportions and then borrows/lends • separation theorem • optimal combination of risky assets for investor can be determined without knowledge of investor’s preferences toward risk and return • investment decision • financing decision

44. The CML and the Separation Theorem The decision of both investors is to invest in portfolio M along the CML (the investment decision) CML B M A PFR

45. Number of Stocks in a Portfolio and the Standard Deviation of Portfolio Return Standard Deviation of Return Figure 9.3 Unsystematic (diversifiable) Risk Total Risk Standard Deviation of the Market Portfolio (systematic risk) Systematic Risk Number of Stocks in the Portfolio

46. The Capital Asset Pricing Model: Expected Return and Risk • The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier • An asset’s covariance with the market portfolio is the relevant risk measure • This can be used to determine an appropriate expected rate of return on a risky asset - the capital asset pricing model (CAPM)

47. The Security Market Line (SML) • The relevant risk measure for an individual risky asset is its covariance with the market portfolio (Covi,m) • This is shown as the risk measure • The return for the market portfolio should be consistent with its own risk, which is the covariance of the market with itself - or its variance:

48. Determining the Expected Return for a Risky Asset In equilibrium, all assets and all portfolios of assets should plot on the SML Any security with an estimated return that plots above the SML is underpriced Any security with an estimated return that plots below the SML is overpriced A superior investor must derive value estimates for assets that are consistently superior to the consensus market evaluation to earn better risk-adjusted rates of return than the average investor

49. Empirical Tests of the CAPM • Stability of Beta • Comparability of Published Estimates of Beta • Number of observations and time interval used in regression vary • Value Line Investment Services (VL) uses weekly rates of return over five years • Merrill Lynch (ML) uses monthly return over five years • There is no “correct” interval for analysis • Weak relationship between VL & ML betas due to difference in intervals used • Interval effect impacts smaller firms more • Market portfolio

50. Microeconomic-Based Risk Factor Models • Specify the risk in microeconomic terms using certain characteristics of the underlying sample of securities extension of Fama-French 3-factor model includes a fourth factor that that accounts for firms with positive past return to produce positive future return - momentum