William F. Sharpe

ASSET ALLOCATION: MANAGEMENT STYLE AND PERFORMANCE MEASUREMENT

is widely agreed that asset allocation accounts for a large part of the variability in the return on a typical investor’s portfolio. This is especially true if the portfolio is invested in multiple funds, each including a number of securities. Asset allocation is generally defined as the allocation of an investor’s portfolio across a number of ”major” asset classes. Clearly such a generalization cannot be made operational without defining such classes. Once a set of asset classes has been defined, it is important to determine the exposures of each component of an investor’s overall portfolio to movements in their returns. Such information can be aggregated to determine the investor’s overall effective asset mix. If it does not conform to the desired mix, appropriate alterations can then be made. Once a procedure for measuring exposure to variations in returns of major asset classes is in place, it is possible to determine how effectively individual fund managers have performed their functions and the extent (if any) to which value has been added through active management. Finally, the effectiveness of the investor’s overall asset allocation can be compared with that of one or more benchmark, asset mixes. An effective way to accomplish all these tasks is to use an asset class factor model. After describing 7 5 w 8

Corporate pension funding policy

Abstract What policy should a corporation adopt concerning the funding of a defined-benefit pension plan and the investment of the assets held in trust for the plan? Until recently, pension plans did not have to be insured, and some risk could be borne by intended beneficiaries. Federal legislation has now mandated such coverage. This paper analyzes corporate policy under three conditions which correspond, roughly, to the earlier situation (‘uninsure’ loans), the current situation (‘partially insured’ loans), and the situation required by law to be implemented in the future (‘completely insured’ plans). We show that if insurance premiums are set correctly, corporate policy in this area may not matter; otherwise the optimal policy may simply be that which maximizes the difference between the value of the insurance and its cost.

Liabilities— A New Approach

A dramatic new develoument motivates 48 3 this paper: the emergence of virtuaily risk-free securities linked to the U.S. consumer price level. The new securities were issued first by the Franklin Savings Association of Ottawa, Kansas, in January 1988 in two different forms. ‘The first is certificates of deposit, called Inflation-Plus CDs, insured by the Federal Savings and Loan Insurance Corporation (FSLIC), and paying an interest rate tied to the Bureau of Labor Statistics’ Consumer Price Index (CPI). Interest, paid monthly, is equal to a stated real rate plus the proportional increase in the CPI during the previous month. As of this writing in November 1988, the real rate ranges from 3% per year for a one-year maturity CD to 3.3% per yeilr for a ten-year maturity. The second form is twenty-year non-callable collateralized bonds, called Real Yield Securities, or REALs. These offer a floating coupon rate of 3% per year phs the previous year’s proportional change in the CI’I, adjusted and payable quarterly. A recent issue of similar bonds includes a put option. Two other financial institutions have followed the lead of Franklin Savings.’ If the trend continues, we have reached a milestone in the history of this country’s financial markets. Consider that for years prominent economists at all points of the ideological spectmm have argued that the U.S. Treasury should issue mch securities, while scholars have speculated why private markets for them have not hitherto developed.2 The current innovative environment in 5rl gj American financial markets appears finally to have put an end to this speculation by ]producing private indexed bonds in several forms. This article analyzes the gain to investors of this new investment alternative, considers likely changes in portfolio behavior that it might induce, and explores ways that it may be used in the future, principally to guarantee a safe stream of real benefits in retirement. The analytical framework is the familiar mean-variance model of portfolio selection of Markowitz and Tobin and the Capital Asset Pricing Model.3 I begin by analyzing the difference between portfolio optimization in nominal i3nd in real terms, then show how the introduction of bonds offering a real risk-free rate of interest can improve portfolio efficiency. Next I discuss the difference between hedging against inflation in the short run and in the long run and show why long-term index-linked bonds are the only true hedge against long-run inflation risk. Finally I explain how index-linked bonds can be the basis for providing inflation-protected retirement benefits. In an appendix I derive the set of equilibrium expected real rates of return on stocks, bonds, and bills that is consistent with the 3% per year real riskfree rate now offered by the index-linked securities.

Bank Capital Adequacy, Deposit Insurance and Security Values

Since the first owner of a gold depository discovered that profits could be made by lending some of the gold deposited for safekeeping, there has been a concern for the “capital adequacy†of depository institutions. The idea is simple enough. If the value of an institutions assets may decline in the future, its deposits will generally be safer, the larger the current value of assets in relation to the value of deposits. Defining capital as the difference between assets and deposits, the larger the ratio of capital to assets (or the ratio of capital to deposits) the safer the deposits. At some level capital will be “adequate,†i. e., the deposits will be “safe enough.â€

Choosing Outcomes versus Choosing Products: Consumer-Focused Retirement Investment Advice

Investing for retirement is one of the most consequential yet daunting decisions consumers face. We present a way to both aid and understand consumers as they construct preferences for retirement income. The method enables consumers to build desired probability distributions of wealth constrained by market forces and the amount invested. We collect desired wealth distributions from a sample of working adults, provide evidence of the technique’s reliability and predictive validity, characterize individual- and cluster-level differences, and estimate parameters of risk aversion and loss aversion. We discuss how such an interactive method might help people construct more informed preferences.

Factors in New York Stock Exchange security returns, 1931–1979

In Figure 1 the ”zero” factor is .94% per month. This is the return on a “typical” security with zero yield. The “yield factor” is .02% per month. This indicates that, ”in general,” higher yield securities outperformed lower yield securities during the month, with (for example) the typical 4% yield stock outperforming the typical 3% yield stock by .02%. For the security plotted at point i, eIt was .01%: The stock‘s excess return was higher (by .01%) than the 1.08% ”typical” for securities with its yield (b,,J of 7%. In effect, Figure 1 and equation 1 attribute each security’s excess return in each period to three elements:

Imputing Expected Security Returns from Portfolio Composition

The normative procedures of Markowitz [4], Sharpe [6], and others can be utilized to determine an optimal portfolio (set of security holdings) given estimates of risk, relevant constraints, and expected returns on securities. Building on these foundations, the positive models of Sharpe [7], Lintner [3], Mossin [5], and others assume that investors form portfolios as if they were following such procedures. We observe considerable differences in portfolio composition, some of which undoubtedly stem from differences in expectations. Yet the predictions of most investors are either made implicitly or, if made explicitly, are jealously guarded and hence cannot be observed by outsiders.

Budgeting and Monitoring Pension Fund Risk

This article describes a set of mean–variance procedures for setting targets for the risk characteristics of components of a pension fund portfolio and for monitoring the portfolio over time to detect significant deviations from those targets. Because of the significant correlations of the returns provided by the managers of a typical defined-benefit pension fund, the risk of the portfolio cannot be characterized as simply the sum of the risks of the individual components. Expected returns, however, can be so characterized. I show that the relationship between marginal risks and implied expected excess returns provides the economic rationale for the risk budgeting and monitoring being implemented by a number of pension funds. I then show how a funds liabilities can be taken into account to make the analysis consistent with goals assumed in asset/liability studies. I also discuss the use of factor models and aggregation and disaggregation procedures. The article concludes with a short discussion of practical issues that should be addressed when implementing a pension fund risk-budgeting and -monitoring system.

THE CAPITAL ASSET PRICING MODEL: A “Multi-Beta” Interpretation

Publisher Summary In recent years, considerable attention has been accorded the capital asset pricing model. It suggests that in equilibrium the expected excess return on a security over and above the pure interest rate equals some constant times its ex ante risk, measured by the securitys so-called beta coefficient. The beta coefficient equals the covariance of the securitys return with that of the market portfolio divided by the variance of the return on the market portfolio, where all measures refer to ex ante probability distributions. Many have used these ideas for practical investment policies. Moreover, a number of tests have been performed to determine the extent to which ex post results conform to the relationships predicted by the theory for ex ante values. A securitys beta relative to the market portfolio can be expressed as a weighted average of beta values relative to any desired number of portfolios, the collection of which equals the market portfolio.

Expected Utility Asset Allocation

Most asset allocation analyses use the mean-variance approach for analyzing the trade-off between risk and expected return. Analysts use quadratic programming to find optimal asset mixes and the characteristics of the capital asset pricing model to determine reasonable optimization inputs. This article presents an alternative approach in which the goal of asset allocation is to maximize expected utility, where the utility function may be more complex than that associated with mean-variance analysis. Inputs for the analysis are based on the assumption of asset prices that would prevail if there were a single representative investor who desired to maximize expected utility.