Only through measures of performance may investors and portfolio managers know if the combination of management techniques and the type of information used resulted in abnormal returns. Furthermore, it is important to determine if that performance is a result of pure luck or of management skill. Several measures have been proposed in the literature on mutual fund performance evaluation, but there is (still) a large controversy around them.
The concern with the performance evaluation of investment portfolios is prior to the Modern Portfolio Theory (MPT) introduced by Markowitz (1952). For example, Cowles (1933) compared the average return of a set of active portfolios with the return of a passive portfolio and concluded that the active portfolios had inferior performance.
Cowles, however, only analysed the portfolios’ return, ignoring risk. MPT has taught us that risk is an essential parameter when we wish to evaluate performance. The question is: what is risk and how should it be measured? If, relatively to return, there is a general consensus, the same is not true relatively to risk.
Markowitz formulated the investor’s portfolio selection problem in terms of these two key parameters: return and risk (as measured by the variance or its square root, the standard deviation). Investors would optimally hold a portfolio with the highest expected return for a given level of risk and the minimum level of risk for a given level of expected return, a mean-variance efficient portfolio. His contribution was later important for the distinction between the variability of returns from an individual security (the overall risk) and its contribution to the risk of a portfolio (the systematic risk)12. The importance of diversifying a portfolio consists of reducing risk without
12 The overall or total risk from an individual security has two components: specific risk, which can be reduced through diversification, and systematic risk, which cannot be diversified away.
giving up return and this can be achieved not only by investing in many securities but by investing in securities with low covariances among themselves. By introducing the possibility of investing in a risk-free asset, Tobin (1958) extended Markowitz’s analysis. As such, the optimal portfolio results from a combination between the risk-free asset and one risky portfolio, with the latter being independent of investors’ risk preferences.
Building on Markowitz’s work, Sharpe (1964), Lintner (1965) and Mossin (1966) develop the Capital Asset Pricing Model (CAPM), an equilibrium model that describes the relationship between return and risk. Since specific risk can be reduced or eliminated through diversification, only systematic risk is relevant. The CAPM implies that the expected return of an asset must be linearly related to the covariance of its returns with the return of the market portfolio, as measured by beta. So, according to this model only one risk factor, the market portfolio, is sufficient to explain expected returns.
As theoretical and empirical arguments suggest that more than one factor may be required, some alternative asset pricing theories have been developed, for example: the Arbitrage Pricing Theory (APT), based on arbitrage arguments and the Intertemporal Asset Pricing Model (ICAPM), based on equilibrium arguments. The APT was introduced by Ross (1976) as an alternative to the CAPM. It is more general in the sense that it allows for multiple risk factors and it overcomes one of the major limitations of CAPM as it does not require the identification of the market portfolio. However, both the (standard) CAPM and the APT are single-period models and, therefore, assume that expected returns are identically and independently distributed. Alternatively, the
ICAPM, proposed by Merton (1973), as a continuous time model13, allows for time- varying risk premiums. In this model the market portfolio is one of the factors and state variables emerge as additional factors. These additional factors represent investors’
demand to hedge uncertainty about future investment opportunities.
Conditional models in which stock and bond returns are assumed to be predictable on the basis of lagged instrumental variables (such as public information), are another approach that allows for time-varying expected returns and risk. The information given by those variables may be correlated but is not necessarily equivalent to the state variables in the ICAPM.
Empirical tests of all these models are not conclusive, and if in theory they are distinct, in practice it is hard to distinguish them (Connor and Korajczyk, 1989). A multi-factor model may be a better model not because the correct model is the APT or the ICAPM but because it is a better candidate for a mean-variance efficient benchmark than the market portfolio. While in the earlier years, after its development, the CAPM seemed to be a good model in explaining asset returns, in more recent years several studies have identified empirical anomalies, with the most widely cited study being that of Fama and French (1992). If conditional versions of the CAPM (e.g.: Jagannathan and Wang, 1996) or the multiple factor models of the APT or ICAPM are better is still awaiting further empirical confirmation.
Thus, the sources of risk affecting security returns are still an issue in debate. As a consequence of these developments in the measurement of risk, different approaches for evaluating performance have been proposed in the financial literature. Several non- parametric measures, which have the advantage of being independent of any asset
13 Among others, Long (1974), and more recently Fama (1996), have provided a discrete time version of the ICAPM.
pricing model, have also been developed (e.g.: Chen and Knez, 1996). The application of new econometric techniques and the growth in academic research added new dimensions to performance evaluation. Topics such as performance attribution, investment styles, survivorship bias, persistence of performance and more recently conditional performance evaluation have been the focus of the majority of the studies on mutual fund performance.
The use of conditioning information is one of the most recent developments on mutual fund performance. As there is now widespread empirical evidence suggesting that predetermined information variables (related to economic conditions) are useful in predicting stock and bond returns, then measures of performance should incorporate this evidence and, consequently, assume that expected returns and risks are time-varying (conditional) instead of constant (unconditional). Previous empirical findings on fund performance and on the persistence of performance, which are based on unconditional measures, may be biased due to the covariance between expected market returns and the conditional measure of risk. In fact, recent studies suggest that funds’ performance is enhanced by applying conditional performance measures (e.g.: Ferson and Schadt, 1996; Chen and Knez, 1996; Dahlquist and Söderlind, 1999) and are also better able to detect persistence of performance (e.g.: Christopherson, Ferson and Glassman, 1998;
and Christopherson, Ferson and Turner, 1999). Given its important implications for questions related to market efficiency and its economic significance for investors, the subject of conditional performance evaluation is perhaps one of the most interesting in current mutual fund research, and it is the main focus of this study.
On the other hand, the majority of the empirical studies have restricted the application of those performance measures to stock funds, in spite of the great importance that bond funds assume in some markets. The application of these same
measures to evaluate bond portfolios is not, however, straightforward. Several methodological issues arise when analysing bond funds: there is less agreement on the validity of the equilibrium pricing models for bonds; fixed interest instruments are characterised by a variety of market segments, maturities and issuers that cause problems of coverage by available indices; and the fact that fixed interest securities often exhibit non-normal and autocorrelated returns thus making statistical tests more ambiguous. Hence, bond fund performance evaluation is a topic clearly in need of more research and that we propose to analyse.
In this chapter, given that the main subject of this study is the conditional performance evaluation of bond funds, we will start by briefly reviewing some of the most relevant methodologies for evaluating their performance, giving particular attention to the benchmark problem, which is a major source of debate and criticisms and can be even more critical in the context of bond portfolios. We will then review and discuss the conditional performance evaluation approach. Since this approach is based on the assumption that stock and bond returns are predictable, we also review the literature in the area of return predictability. Finally, we will review and discuss the topic of performance persistence focusing particularly, and for reasons just mentioned above, on the literature on bond fund performance persistence.
3.2. PERFORMANCE EVALUATION IN THE CONTEXT OF ASSET PRICING