Chapter 5: Asset Allocation

1. Chapter 5: Asset Allocation

2. What is Strategic Asset Allocation? • Strategic asset allocation • Combines an investor’s objectives and constraints with long-term capital market expectations • In other words, how the “pie” (i.e. portfolio) should be divided for a specific investor, given forecasted market conditions, and the investor’s objectives and constraints • Process leads to a set of portfolio weights called the “policy portfolio”

3. Policy PortfolioHarvard Management Company(Endowment Fund)

4. Policy Portfolio (Harvard) • “The Policy Portfolio is a theoretical portfolio allocated among asset classes in a mix that is judged to be most appropriate for Harvard University from both the perspective of potential return and risk over the long term.” • “review ... for continued fit with the University’s risk profile and our projections of long-term market returns, volatility and correlations.” • “The Policy Portfolio (is) a guide...to the actual allocation in the investment portfolio and also serves as a measuring stick against which we judge the success of our active investment management activities.”

5. Performance History Overall impact of alternative investments? Impact of alternative investments in the last 5 years? Impact of active management? Note: BIG – Broad Investment Grade

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

7. Example 5-2 • John Stevenson is an analyst for an endowment fund. His recent research strongly suggests that domestic equities will underperform international equities in the next 6 months. He asks the CIO for a special meeting with the Board of Trustees to review the fund’s strategic asset allocation policy (to reduce the weight of domestic equities in the policy portfolio). • Is such a meeting appropriate?

8. Asset Allocation and Portfolio Performance • Suppose portfolio returns can be attributed to the following three elements: • Asset allocation • Market timing (tactical) • Security selection (e.g., stock picking) • How important is the asset allocation decision, out of the three?

9. Asset Allocation and Portfolio Performance • Empirical findings • Time-series studies (same pension fund over time) suggest that asset allocation explains 90%+ of the variations in portfolio returns on average • Brinson, Hood and Beebower (1986), Brinson, Singer and Beebower (1991), and Blake, Lehmann, and Timmermann (1999) • Interpretation: funds with similar asset allocation have similar returns. • Financial Crisis of 2008: Canadian pension plans had returns ranging from -25% to +6% (average: -18%)

10. Asset Allocation and Portfolio Performance • Cross-sectional studies (different balanced mutual funds within the same period) show that asset allocation explains ~ 40% of the variations in portfolio returns • Ibbotson and Kaplan (2000) • Overall, asset allocation is the most important factor in determining portfolio returns; the other factors (tactical and security selection) are secondary.

11. Asset-Only versus Asset/Liability Management (ALM) • Asset-only approach does not explicitly model liabilities, though they are indirectly considered via investor objectives and constraints (e.g., to achieve a target return) • Asset/Liability Management (ALM) explicitly models future liabilities and adopts an asset allocation best suited to funding those liabilities (e.g., inflation protection, manage interest rate risk) • Particularly important if investor is averse to loss – managing shortfall risk becomes more important

12. Dynamic versus Static Approaches to Asset Allocation • Dynamic Approach • Asset allocation, actual returns and liabilities in one period directly affect the optimal decision for the following period • Example: If mean reversion exists in stock returns, then stocks are less risky if horizon is long, and optimal allocation to stocks should be higher • Static Approach • Does not consider links across time periods • Less costly and less complex to model and implement

13. Risk and Return in Strategic Asset Allocation • Risk objective • General description can be qualitative: Below average or above average risk tolerance • But in conducting strategic asset allocation, need to quantify risk attitude • Individuals: Numerical risk aversion score, measured through interview, questionnaire (see TD Mutual Funds example) • Recall the utility function: U = E(R)-0.005A2 • Translate/map risk aversion score to an A for your client, and compare the utility derived from different investments

14. Risk Objective in Asset Allocation • Example: if A = 4 Portfolio P: E(R) = 9.7%,  = 15% Portfolio Q: E(R) = 7%,  = 10% UP = 5.2% UQ = 5% • Another way to quantify risk tolerance: Specify an acceptable level of volatility (e.g.,  = 10%, thereby eliminating portfolio P above) • Downside risk: If investor is averse to loss (LPSD instead of ) • Or if there is a target, then can consider shortfall risk. For example, risk that return will fall below a certain percentage

15. Risk Objective in Asset Allocation • Roy’s safety-first criterion • A simple shortfall risk criterion Where RP is the portfolio return, RL is the threshold level of return, and P is the std. dev. of RP

16. Example 5-4 • Inheritance of £1,200,000. Expects to withdraw £60,000 in 12 months from the investment income without having to invade the initial principal • Three portfolios to choose from:

17. Example 5-4 (Cont’d) • If the investor has an above-average risk tolerance (A=2), which portfolio would she prefer? • What is the shortfall level of return given that the investor does not want to dip into the principal for the £60,000 expenditure? • According to Roy’s criterion, which portfolio is best? • Recommend a portfolio to the investor, taking into account all of the above

18. Sortino Ratio • Similar to Roy’s Safety First Ratio, but uses downside risk instead in the denominator: • where DDP is downside deviation (standard deviation calculated using only returns below the target, RL)

19. Return Objective in Strategic Asset Allocation • Return objective • Quantitative return objectives are easier to define: Specify return needed to achieve goals • If a compound growth rate is used in the calculations for long-term investors, then report geometric mean returns, rather than arithmetic mean returns • Example: 10% return in first year, 8% in second year • If arithmetic: mean = ? • If geometric: mean = √[(1+0.1)(1+0.8)] – 1 = 0.08995 • One approximate of the relationship if distribution is normal: Geometric = arithmetic – 0.52

20. Selection of Asset Classes • Criteria for specifying asset classes • What constitute an asset class? • Popular choices, in addition to domestic stocks and bonds: • International assets • Inflation-sensitive assets • Alternative investments

21. Criteria for specifying asset classes • Assets within a class should be relatively homogeneous • Have similar attributes/features • Asset classes should be mutually exclusive • Global equities and U.S. equities • Asset classes should be diversifying • Correlation? • Asset classes as a group should comprise the majority of world investable wealth • Asset class should not compromise the investor’s desired liquidity • When there is a need to rebalance to the strategic asset allocation, should not be moving asset prices or incurring high transaction costs

22. A Simple Rule-of-Thumb • An asset class should be considered in a portfolio if it improves the portfolio’s mean-variance efficient frontier • This occurs if its Sharpe ratio exceeds the product of the existing portfolio’s Sharpe ratio and the correlation between the asset class and the portfolio • E.g., an asset class 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. It should be added, because 0.2 > 0.15(0.9) = 0.135 • Correlation matters a great deal if the asset class has a lower Sharpe Ratio (e.g., same Sharpe Ratio as the existing portfolio)

23. International Assets • When investing in international assets, investors should consider the following special issues: • Currency risk affects both return and volatility, and investors must decide whether to hedge • Increased correlations in times of stress • Emerging markets are less liquid, less transparent and more likely to exhibit non-normal return distributions (but if markets are efficient, investors will receive compensation for bearing these risks)

24. Inflation-Sensitive Assets • Assets that provide a good hedge against inflation • Gold, on average, maintains its value over time. If bought a dollar's worth of gold 200 years ago, after adjusting for inflation, it would be worth $1.07 in the fall of 2010 • CPPIB: In addition to real return bonds, also Infrastructure, real estate • OTPP: Also includes commodities • “We invest in commodities, which typically mirror short-term changes in inflation, as a hedge against the cost of paying inflation-protected pensions.”

25. Inflation Protected Bonds • Bonds with an inflation hedge • Principal/par value is indexed to the Consumer Price Index (CPI) • Fixed coupon rate (e.g., 4%) is applied to the inflation-indexed principal • Hence, cash flow is fixed in real terms • Low correlation with other assets improves diversification • Particularly suitable for managing liabilities that are also affected by inflation

26. Cash Flow (4% coupon)

27. Inflation Protected Bonds • Product developed in the 1980s • Treasury Inflation-Protected Securities (TIPS) in U.S., Real-Return Bonds (RRB) in Canada • Also available in many countries, e.g., Sweden, Australia, the U.K., France. • Small investors can participate through a real-return bond mutual fund, or through an ETF

28. Inflation Protected Bonds • For each inflation-indexed bond, a “real yield” plus an inflation protection are quoted. The real yield is a proxy for the real rate of interest • Hence, (nominal yield – real yield) is a proxy for the market’s inflation expectation • E.g. U.S. 10-year Treasury yield minus 10-year TIPs yield = 1.92% - 0.17% = 1.75%

29. Alternative Investments • Label of convenience for a diverse set of assets including real estate, hedge funds, infrastructure, and private equity • Resources necessary to research such investments not available to all investors • Liquidity an issue • Correlations between various alternative assets and traditional assets require separate consideration • For example, lack of benchmark for alternative assets

30. Recap: Asset Allocation Process • Investor Specific • Consider investor’s net worth and risk attitudes • Determine the investor’s risk tolerance • Capital Market Opportunities • Identify capital market conditions • Implement a prediction procedure • Generate expected returns, risks and correlations • Combined Investor-Market Information • Determine allocations to different assets given investor’s risk tolerance, e.g., use an optimizer to determine optimal asset mix • Actual returns determine feedback for process

31. 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)

32. Efficient Frontier (Excel)

33. Efficient Frontier (Excel)