Son-Nan Chen

An Examination of Risk-Return Relationship in Bull and Bear Markets Using Time-Varying Betas

Security behavior in bull and bear markets has received some attention in recent years. Fabozzi and Francis [5] first documented evidence that security betas are not influenced by the alternating forces of bull and bear markets. Their subsequent study of mutual fund betas also indicated that mutual funds generally respond indifferently to bull and bear market conditions. Using the concept of bull and bear market variations, Kim and Zumwa1t [9] developed and tested the risk premiums associated with the upside and the downside portions of returns variation. They concluded that investors expect to receive a risk premium for downside risk and pay a premium for upside variation of returns. From their results, Kim and Zumwalt [9] suggested that the down-market beta measuring downside risk (downside variation of returns) may be a more appropriate measure of portfolio risk than the single beta in the market model.

Beta Nonstationarity, Portfolio Residual Risk and Diversification

Over the past years the beta coefficient has been widely used as a measure of systematic risk in investment and portfolio analysis. The validity of using the beta coefficient as the proper measure of systematic risk is dependent upon the assumption that the beta coefficient is stationary over time. Unfortunately, this assumption has been challenged by a number of empirical studies which have found the beta coefficient to be unstable over time. Examples of such empirical investigations are those documented by Blume [4], Levy [12], Levitz [11], Baesel [2], Altman, Jacquillat, and Levasseur [1], and Roenfelt, Griepentrong, and Pflaum [16]. Most recently, Fabozzi and Francis [9] reported that some security beta coefficients tend to be random over time. Their findings also support the regression tendency of the beta coefficients towards the mean over time, as found by Blume [4]. Thus, because the beta coefficient is changing over time, the use of the ordinary least-squares (OLS) method in investment and portfolio analysis will yield an inefficient estimate of systematic risk. Furthermore, the OLS estimates of security and portfolio residual risks will be influenced by the variability of beta coefficient. Therefore, the purpose of this paper is to investigate the relationship between the variability of the beta coefficient and portfolio residual risk, and hence to provide a real picture of the process of portfolio diversification under the condition of beta nonstationarity. It is shown that the use of the OLS method to estimate security and portfolio residual risks will produce an incorrect conclusion that larger residual risks tend to be associated with higher variability in the beta coefficient.

Information effects of earnings and dividend announcements on common stock returns: Are they interactive?

Abstract This article reexamines the interaction effect between the concurrently released earnings and divided announcement on common stock returns. On the basis of a synthesis of two models that separately identify the effects of earnings and dividend surprises, it is hypothesized that the total effect of two types of signals should explain the total changes in stock prices without any interaction between them, regardless of their release time. In the ensuing attempt to test this hypothesis, we find that an analysis of this nature is very sensitive to the interval between the two signals and the specified test period surrounding the announcements. The overall test results are not supportive of a corroborative effect between earnings and dividend announcements. This is consistent with our a priori presumption and the observed corporate practice of information disclosures, but not with the findings of an earlier study.

Investment Decisions under Uncertainty: Application of Estimation Risk in the Hillier Approach

In a seminal paper in 1963, Frederick S. Hillier alerted the finance community to the importance of including probabilistic information in the process of investment decision-making [4]. The method proposed and demonstrated by Hillier introduced the use of additional information regarding the probability distributions governing three measures of investment merit: present worth; internal rate of return; and uniform annual cost. He showed that by assessing investment merit only on the basis of a measure of central tendency, crucial information regarding dispersion, hence risk, was ignored and investments were not evaluated accurately. By incorporating the amount of risk involved in terms of the probability distribution of the present worth, the internal rate of return, or uniform annual cost, a firms management can make more sound decisions regarding risky investment proposals. Since this important paper was published, a virtual revolution has occurred in finance, particularly in the area of risk assessment. Indeed, under modern capital asset pricing theory, the dispersion in the probability distribution of future cash flows is an irrelevant statistic. Instead, as the theory goes, a projects systematic risk, as indexed by its “beta,†is the only relevant measure of risk. This disparity between modern capital asset pricing theory and the type of analysis that follows from the Hillier approach will be addressed in detail in Section III. We will show that under conditions in which dispersion is regarded as the relevant measure of risk, the Hillier approach provides a reasonable approximation of the dispersion arising from the multiperiod framework.

Valuation of Interest Rate Spread Options in a Multifactor LIBOR Market Model

Within the multifactor LIBOR market model, the authors examine three types of interest rate spread options: LIBOR vs. LIBOR, LIBOR vs. swap rate, and swap rate vs. swap rate. These financial products are widely traded in the marketplace or are embedded in structured notes, such as CMS range accruals and steepeners. In the first case, the authors show that the drift has an impact on the pricing which differs from the results of previous research. The authors also present a new approach to approximating the distribution of a forward swap rate under the LIBOR market model and then employ it to price CMS spread options. The numerical examples show that the approximate pricing formulas are robustly accurate as compared with Monte Carlo simulation using recent two-year data.

Estimation risk and optimal portfolios

; A recent article by Elton, Gruber, and Padberg (EGP) [6] advocated the use of an elegant yet simple technique for finding efficient portfolios. Unlike traditional portfolio selection models, their procedure did not require the estimation of security covariance structures or the use of quadratic programming to find an optimal portfolio. Instead, the simple ranking devices developed by EGP can be implemented with the use of a programmable calculator and a modest set of security inputs provided by the analyst. One of the key inputs to the simple ranking procedure is a security’s systematic risk or beta coefficient. The other required inputs are expected return and variance. Unfortunately, security analysts never know the true values of a security’s beta coefficient, expected return, or variance and must therefore rely on estimates based upon historical data. These sample estimates, like any estimate, are subject to ”estimation risk.” Intuitively, one can think of estimation risk as the presence of uncertainty surrounding an analyst’s estimates of the required pieces of information. In statistics, the precision or accuracy of a sample estimate is gauged by the size of the estimator’s standard error: the smaller this standard error, the more reliable the sample estimate. Since we occupy a world of uncertainty, it is important to develop decision models that reflect all available information, including the amount of estimation risk facing the security analyst. The procedure developed by EGP does not consider this potentially important problem facing the portfolio manager. Further, when investors ignore estimation risk, they are essentially treating the sample estimates as the true parameter values. Consequently, as Bawa, Brown, and Klein [2] have shown, a portfolio select.ion rule that omits estimation risk can lead to the selection of suboptimal portfolios. In order to enharice the accuracy of this procedure, we also use the “new beta” introduced by Carve11 and Strebel [4] in the Fall 1984 issue of this Journal. Their modification derives ex ante betas from historical betas by incorporating into the beta estimates I:he dispersion of analysts’ earnings forecasts. Thus, the procedure we present reflects the uncertainty in beta and the expected return for a security. All proofs are omitted and the interested reader is referred to Chen and Brown [5], Alexander and Resnick [l], and Strebel [7]. ‘The presentation is organized as follows. First, we discuss the relationship of our procedure to the ranking devices derived by EGP. Second, we will assert, without proof, the new ranking devices and then provide an example for implementing this approach

Cross-Currency Equity Swaps in the BGM Model

n equity swap entails a sequence of exchanges of the return on a specified equity portfolio against a payment computed in a different way on the same notional principal. Valuation models exist, but those with a floating leg tied to a short-term interest rate are not so easy to use. The BGM (Brace-Gatarek-Musiela) model is a useful way to model short-rate dynamics for this purpose. Further complications occur when the swap legs are denominated in different currencies and/or notional principal varies over time. In this article, the authors develop very general valuation models for multi-currency equity swaps with floating-leg payoffs based on BGM short rates, as well as possible amortization of notional principal.

Mean reversion behavior of the returns on currency assets

Abstract Using the variance ratio and the regression test, we examine whether there exist a random walk component and a transitory component in the returns on currency assets and real exchange rates. The test results have shown that both the returns on currency assets and real exchange rates exhibit a random walk component and a transitory component, and thereby indicating mean-reverting behavior. Possible economic interpretations are provided.

On selectivity and market timing ability of U.S.-based international mutual funds: Using refined Jensen's measure

This paper evaluates the performance of 15 U.S.-based international mutual funds for the period 1980-89. Selectivity and timing skills of mutual fund managers are the primary criteria for performance evaluation. The technique used here is the one developed by Treynor and Mazuy and refined by Lee and Rahman. We find that many of the international mutual funds outperformed the U.S. market benchmark, perhaps due to the expanded diversification opportunities that they provide. When a world market index is used as the benchmark, fund managers show relatively poor performance in terms of selectivity skills. However, there is strong evidence that some managers rely rather heavily on timing skills in international capital markets.

Pricing derivatives with modeling CO2 emission allowance using a regime-switching jump diffusion model: with regime-switching risk premium

Carbon markets trade the spot European Union Allowance (EUA), with one EUA providing the right to emit one tone of carbon dioxide (CO2). We examine the spot EUA returns in BlueNext that exhibit jumps and a volatility clustering feature. We propose a regime-switching jump diffusion model (RSJM) with a hidden Markov chain to capture not only a volatility clustering feature, but also the dynamics of the spot EUA returns that are influenced by change in the CO2 emission economic conditions. In addition, the switching jump intensities of the RSJM are shown to be affected by change in the carbon-market macroeconomic environment. We further derive the theoretical futures-option prices with a constant convenience yield under the RSJM via the generalized Esscher transform where regime-switching risk is priced with a risk premium. The empirical study shows that the derived futures-option pricing model under the RSJM with regime-switching risk is a more complete model than a jump diffusion model for pricing CO2 options.