Presentation Transcript

1. Asset allocation

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2. 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 e.g., pension benefits indexed to inflation
3. Cash Flow (4% coupon)
4. 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
5. 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 (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 = 2.60% - 0.41% = 1.75% * * Bloomberg September 27, 2013
6. 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)
7. A simple rule of thumb Whether or not to include an asset class in the portfolio Does it improve the portfolio’s mean-variance efficient frontier? Rule of Thumb If the asset class’s Sharpe Ratio exceeds the product of the existing portfolio’s Sharpe ratio and the correlation between the asset class and the existing portfolio Numerical example: Asset class with a Sharpe ratio of 0.2 and a correlation of 0.9. Existing portfolio has a Sharpe ratio of 0.15
8. Rule of thumb 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., if same Sharpe Ratio as the existing portfolio
9. Some recent correlations Wall Street Journal September 4, 2013
10. Mean-variance optimization Investors should choose from efficient portfolios consistent with the investor’s risk tolerance
11. Unconstrained Mean-Variance Optimization Weights can take on any value (positive or negative), only constraint is that the weights sum to one Black (1972) provided a short cut for finding minimum variance portfolios: Black’s Two-Fund Theorem: Asset weights of any minimum variance portfolio is a linear combination of the asset weights of any other two minimum variance portfolios Mathematical proof provided in the 1972 paper
12. Unconstrained Mean-Variance Optimization Numerical example Suppose we have three asset classes: equities (S), fixed income (B), and real estate(RE) Composition of the minimum variance portfolio with E(r) = 10% is (70%, 20%, 10%) Composition of the minimum variance portfolio with E(r) = 8% is (50%, 30%, 20%) What is the composition of the minimum variance portfolio with E(r) = 9.5%?
13. Constrained M-V Optimization Minimum asset class weight = 0 Most relevant for strategic asset allocation May short assets within a class, but not the entire class To generate the efficient frontier, use the corner portfolio theorem of Markowitz (1959, 1987) There are infinitely many efficient portfolios, only need a limited number of “corner portfolios” to identify them all Corner portfolios: They are located when an asset class is either added or dropped along the efficient frontier (i.e., weight going from zero to strictly positive or from strictly positive to zero)
14. Constrained M-V Optimizationcorner portfolios Every efficient portfolio is a linear combination of the two corner portfolios immediately adjacent to it (on either side of it). Thus, by locating all corner portfolios, you can generate the entire efficient frontier Markowitz (1959, 1987 – two books) provides the “critical line algorithm” to do this Our textbook calls this the “Corner Portfolio Theorem” To program it using Excel – e.g., Clarence Kwan’s notes
15. Constrained M-V OptimizationNumerical example
16. Constrained M-V Optimizationcorner portfolios GMV
17. Diagrammatical representationcorner portfolios
18. Numerical example Find the composition of the mean-variance efficient portfolio E(r) = 8% Which two corner portfolios does it lie in between? Solve for the weights: UK equities = ? Ex-UK equities = ? Intermediate bonds = ? Long term bonds = ? International bonds = ? Real estate = ?
19. Numerical example Now that you have the weights (composition of the E(r) = 8% portfolio), what is the variance?
20. Re-sampled Efficient Frontier Optimization Re-sampling: running several efficient portfolio simulations using different parameters for E(r), , and as sensitivity analysis For each level of E(r), average the weights of each asset class from different efficient portfolios (that were estimated using different inputs) These can then be integrated into a re-sampled efficient frontier Re-sampled efficient frontier tends to be more diversified and more stable over time
21. Monte-Carlo Simulation in Asset Allocation Most likely application: Given an existing asset allocation, calculate terminal wealth using random draws from historical distributions of returns Provides information concerning the range of possible results and the relative likelihood of each (e.g., “80% of the times, will have terminal wealth greater than $1 million, given current portfolio”) Check Morningstar Direct
22. Experience Based Approaches to Asset Allocation Rely on tradition, experience and/or rules of thumb Inexpensive to implement 60/40 stock bond allocation as neutral starting point Allocation to bonds increases with risk aversion Allocation to stocks increases with time horizon Allocation to equities = 100 - age
23. Post Modern portfolio theory Rest of the chapter – ideas for 1st project PMPT – going beyond M-V optimization Optimize with respect to different measures of downside risk, instead of standard deviation Check Morningstar Direct
24. Risk parity investment strategy 1st generation: “balanced” portfolio of 60/40 Not really balanced in terms of risk. Equity contributed 90% of the risk in the portfolio, especially during the financial crisis 2nd generation: include more asset classes to diversify the risk In particular, diversify across different risk exposures, such as: interest rate risk commodity risk style risk premia, such as value, momentum and volatility liquidity risk (which types of assets?) sovereign risk
25. Side note: Capital market expectations Client profile + capital market expectations  efficient frontier and the optimal portfolio/asset allocation
26. Side note: Capital market expectations Yield assumption for forecasting bond market returns Assumption based on 20-year average. Yield at the time (Feb 2013) = 1.75% Consultant expects yield to reach 3.0% in 10 years