SUMMARY

This reading has surveyed how appropriate asset allocations can be determined to meet the needs of a variety of investors. Among the major points made have been the following:

• The objective function of asset-only mean–variance optimization is to maximize the expected return of the asset mix minus a penalty that depends on risk aversion and the expected variance of the asset mix.

• Criticisms of MVO include the following:

  • The outputs (asset allocations) are highly sensitive to small changes in the inputs.

  • The asset allocations are highly concentrated in a subset of the available asset classes.

  • Investors are often concerned with characteristics of asset class returns such as skewness and kurtosis that are not accounted for in MVO.

  • While the asset allocations may appear diversified across assets, the sources of risk may not be diversified.

  • MVO allocations may have no direct connection to the factors affecting any liability or consumption streams.

  • MVO is a single-period framework that tends to ignore trading/rebalancing costs and taxes.

• Deriving expected returns by reverse optimization or by reverse optimization tilted toward an investor’s views on asset returns (the Black–Litterman model) is one means of addressing the tendency of MVO to produce efficient portfolios that are not well diversified.

• Placing constraints on asset class weights to prevent extremely concentrated portfolios and resampling inputs are other ways of addressing the same concern.

• For some relatively illiquid asset classes, a satisfactory proxy may not be available; including such asset classes in the optimization may therefore be problematic.

• Risk budgeting is a means of making optimal use of risk in the pursuit of return. A risk budget is optimal when the ratio of excess return to marginal contribution to total risk is the same for all assets in the portfolio.

• Characteristics of liabilities that affect asset allocation in liability-relative asset allocation include the following:

  • Fixed versus contingent cash flows

  • Legal versus quasi-liabilities

  • Duration and convexity of liability cash flows

  • Value of liabilities as compared with the size of the sponsoring organization

  • Factors driving future liability cash flows (inflation, economic conditions, interest rates, risk premium)

  • Timing considerations, such longevity risk

  • Regulations affecting liability cash flow calculations

• Approaches to liability-relative asset allocation include surplus optimization, a hedging/return-seeking portfolios approach, and an integrated asset–liability approach.

  • Surplus optimization involves MVO applied to surplus returns.

  • A hedging/return-seeking portfolios approach assigns assets to one of two portfolios. The objective of the hedging portfolio is to hedge the investor’s liability stream. Any remaining funds are invested in the return-seeking portfolio.

  • An integrated asset–liability approach integrates and jointly optimizes asset and liability decisions.

• A goals-based asset allocation process combines into an overall portfolio a number of sub-portfolios, each of which is designed to fund an individual goal with its own time horizon and required probability of success.

• In the implementation, there are two fundamental parts to the asset allocation process. The first centers on the creation of portfolio modules, while the second relates to the identification of client goals and the matching of these goals to the appropriate sub-portfolios to which suitable levels of capital are allocated.

• Other approaches to asset allocation include “120 minus your age,” 60/40 stocks/bonds, the endowment model, risk parity, and the 1/N rule.

• Disciplined rebalancing has tended to reduce risk while incrementally adding to returns. Interpretations of this empirical finding include that rebalancing earns a diversification return, that rebalancing earns a return from being short volatility, and that rebalancing earns a return to supplying liquidity to the market.

• Factors positively related to optimal corridor width include transaction costs, risk tolerance, and an asset class’s correlation with the rest of the portfolio. The higher the correlation, the wider the optimal corridor, because when asset classes move in sync, further divergence from target weights is less likely.

• The volatility of the rest of the portfolio (outside of the asset class under consideration) is inversely related to optimal corridor width.

• An asset class’s own volatility involves a trade-off between transaction costs and risk control. The width of the optimal tolerance band increases with transaction costs for volatility-based rebalancing.