Dean Leistikow

The Behavior of Equity and Debt Risk Premiums

he most widely recognized source of risk premium data is the pioneering study by Ibbotson and Sinquefield [1982], updated T annually by Ibbotson Associates (see Siegel [1990]). Accordmg to Siegel [1990, p. 1031, the best forecast for a future-period risk premium is given by the arithmetic average of its associated values observed since 1926, which is the initial year in Ibbotson and Sinquefield’s study.’ Ibbotson and Sinquefield define four types of risk premiums equity, bond horizon, small stock, and default risk premiums. The equity risk premium is defined as the excess of the S&P 500 Index Rate of Return (denoted ROR) over the T-bill ROR. Similarly, the bond horizon risk premium (hereafter referred to simply as the “horizon risk premium”) is defined as the excess of the long-term T-bond ROR over the T-bill ROR. The s m a l l stock risk premium is defined as the excess of the composite ROR of the fifth quintile (by market capitalization) of NYSE-listed common stocks over the S&P 500 Index ROR; and the default risk premium is defined as the excess of the long-term corporate bond ROR over the long-term T-bond ROR. The Ibbotson Associates approach assumes that the random process generating each of the risk premiums is stationary.2 Because portfolio managers, investors, utility regulators, and corporate financial officers use these forecasted risk premiums as guides in decision-making and performance evaluation, it is

Chicken Little Gets It Wrong Again

Many investors see little opportunity for active portfolio managers to exploit relative returns in environments with high return correlation. Contrary to what current-day Chicken Littles believe, the authors empirically find a positive relation between the S&P 500’s average constituent stock relative-return volatility and its average between-constituent return correlation. Moreover, the S&P 500’s index-return variance, average between-constituent return correlation, average constituent relative-return variance, and average constituent residual-return variance are all positively related to a statistically significant degree. The authors also provide a theoretical foundation for these empirical findings.

The Effect of Value Estimation Errors on Portfolio Growth Rates

This article analyzes the impact of value estimation errors on portfolios’ growth rates and relative growth rates for several portfolio weighting methods. In contrast to previous articles, this one addresses the effect of estimation errors on portfolio growth rates due to increased return volatility. The portfolio weighting methods examined include capitalization weights, estimation error independent weights, Fundamental weights, and Diversity weights. The article provides theoretical support, in the context of estimation error, for the empirical findings that many non-capitalization weighted portfolios’ returns beat the market’s capitalization-weighted portfolio return over time. It also provides a theory for the size effect.

Arithmetic and Continuous Return Mean-Variance Efficient Frontiers

The arithmetic mean-variance frontier shows that taking more risk is always rewarded with higher expected arithmetic return. This article shows that there is a danger from being too aggressive that is not reflected in the arithmetic return mean-variance frontier because expected arithmetic return is a poor indicator of long-term arithmetic return. Since long-term arithmetic return is equivalent to long-term average continuous return, the relevant mean-variance frontier replaces expected arithmetic return with expected continuous return. The article shows that, for the continuous return mean-variance frontier, expected return initially rises, then declines and becomes negative as risk increases.

“The Behavior of Equity and Debt Risk Premiums”: Reply to Comment

University. n their comment on our 1993 article in this Journal, Ibbotson and Lummer question our conclusion that the stochastic processes generating the I equity and horizon risk premiums are generally mean-reverting and downward-trending. They do not question our results concerning the default and smallstock risk premiums. They also assert that the equity and horizon stochastic processes are stationary. As we note in our article (see endnote 2), stationarity requires a constant mean and a constant variance. In our regression models, the lag coefficient would have to be zero in order for the mean to be constant. Therefore, a lag coefficient significantly different from zero would indicate that the stochastic process is not stationary. The empirical results reported in Exhibit 1 of our 1993 article indicate sigdcantly positive lag coefficients for the income equity risk premium, horizon risk premium, income horizon risk premium, and capital gains horizon risk premium for the 1926-1989 time period. (All subsequent references to numbered exhibits refer to our Summer 1993 article.) The lag coefficients for the income equity and income horizon risk premiums were also si@cantly positive in both the 1926-1957 subperiod (see Exhibit 2A) and the 1958-1989 subperiod (see Exhibit 2B). In addition, to show that there is mean reversion, we also need to show that the lag coefficient is significantly less than one. We used the Dickey-Fuller test for this purpose. The empirical results reported in

A Continuous Return Model for the Low-Volatility andLow-Beta Anomalies

This study shows that a “rational,” capital asset pricing model (CAPM) type of positive relationship between short-horizon expected arithmetic return and risk can lead to a negative long-horizon relationship between compound annual return and risk (whether risk is measured by volatility or beta). This result follows from the stochastic portfolio theory relationship that a stock’s growth rate is less than its expected arithmetic return by approximately one-half its variance of return. The negative long-horizon relationships between return mean and volatility/beta often have been noted and characterized as the low-volatility and low-beta anomalies. Thus, these characterizations may be problematic.

Carry Costs and Futures Hedge Calculations

This paper calculates carry costs directly and focuses on the effect that carry cost lumpiness has on hedge variables. It shows that carry cost adjusted price changes should be used to reduce errors in the calculated hedge: ratio, profit, and effectiveness. Results demonstrate that the errors can be both statistically and economically significant and tend to be more significant if the asset’s carry costs are lumpier (that is, larger and less frequent). We study the traditional regression (TR), carry cost adjusted regression (CCAR), and error correction (EC) hedge ratio calculation approaches. Unlike the CCAR method, the TR and EC approaches err by using the spot price change to represent spot profit. When the payout dates are included in the analysis, the CCAR in-sample hedge effectiveness is statistically significantly higher than it is for the TR and EC approaches. Furthermore, when payout dates are excluded, their hedge effectiveness results converge toward those for the CCAR method. The CCAR approach provides out-of-sample hedge effectiveness that is higher than that for either of the other approaches. Additionally, the (in-sample to out-of-sample) hedge effectiveness slippage is about half as much for the TR and CCAR approaches as it is for the EC approach. Finally, though the hedge ratios are similar across methods, the hedge profits of the assets studied are significantly mismeasured because the TR and EC methods ignore carry costs.

Valuing Investment Management Fees, Active Portfolio Management, and Closed-End Fund Discounts

Risk-neutral valuation is used to value a portfolio and decompose it into the components accruing to its stakeholders. The analysis incorporates managers’ expected performance and contract renewal issues. A managed portfolio’s economic value is shown to differ from its net asset value. A better foundation for computing fair closed-end fund discounts and a partial explanation of equilibrium in the markets for open and closed-end mutual funds are provided. Tests on the behavior of net redemptions following closed-end fund open-endings and the relation between premiums and investment performance around IPOs strongly support the paper’s theory.