If the probability distribution of returns develops throughout time in relative harmony with economic variables, it seems reasonable that investors consider this information when making investment decisions relative to portfolios. Thus, these variables should play an important role in the formulation of the model. The importance of using variables representative of public information and of time variation of risk premiums has been recognised, having allowed for important developments both at the level of equilibrium models and at the level of performance evaluation. These approaches, still considered a relatively new area of research, are expected to substantially contribute to knowledge.
Conditional performance evaluation consists of measuring a portfolio’s performance taking into consideration the public information that is available to investors at the moment the return is generated, that is, it admits that the expected return and risk vary throughout time as public information changes and, thus, controls for common variation. As stated before, unconditional measures may attribute superior performance to managers that follow dynamic strategies using only available public information. Since this may be accomplished by any investor, because the information is public, it would be incorrect to call it superior performance. Conditional performance evaluation is, therefore, consistent with a version of market efficiency, in the semi- strong form sense of Fama (1970). Only managers who correctly use more information than is generally available to the public, are considered to have potentially superior ability.
As mentioned in the previous section, recent empirical studies have shown that public information variables, related to economic conditions, are predictors of returns on stocks and bonds. The conditional performance evaluation approach extends these developments to the problem of evaluating portfolio performance. Ferson and Schadt
(1996) adjust Jensen’s (1968) alpha and two simple market-timing models (Treynor and Mazuy, 1966; and Merton and Henriksson, 1981) to incorporate conditioning information. Following Shanken (1990), they assume that the conditional beta is a linear function30 of a vector zt−1 of variables of information (for further details on this matter see section 5.2 of Chapter 5).
The cross products of the market’s excess return and the predetermined information variables capture the covariance between the conditional beta and the conditional expected market return. Ferson and Shadt (1996) found that this covariance is the major source of bias in the traditional unconditional Jensen’s alpha. These additional factors can be interpreted as the returns to dynamic strategies, which hold
1
zt− units of the market index, financed by borrowing or selling zt−1 in Treasury bills.
It is easy to extend this analysis to models with multiple factors (and to an APT framework), by including the cross products of each factor with the information variables.
Ferson and Schadt (1996) conclude that the inclusion of conditioning information causes a shift in the distribution of alphas to the right region of superior performance.
Using the unconditional Jensen’s alpha, either in the context of the CAPM or in the context of a multi-factor model, the funds of their sample (67 equity funds over the period of 1968 to 1990) tend to have negative performances. The incorporation of
30 Two alternatives have been used in modelling time-varying returns and risk: through betas in models that admit unspecified heteroscedasticity (beta is assumed to have a specific functional relation to the lagged variables as in Shanken, 1990) and betas that specify time-varying second moments (ARCH and GARCH models). According to Ghysels (1998), assuming a functional form for betas can lead to misspecification which may bias test results.
predetermined information variables31 enhances funds’ performance. The conditioning information seems to have a greater impact on the measure of performance than moving from a single-factor to a multi-factor model. The negative bias of the unconditional measure is due to a negative covariance between fund betas and the conditional expected market return.32 Furthermore, they find that the conditional versions of the Treynor and Mazuy (1966) and Merton and Henriksson (1981) models represent an improvement, as the evidence of perverse market timing is removed.
Kryzanowski, Lalancette and To (1997), investigated a sample of 130 Canadian equity funds over the period 1981 to 1988, using an APT model with prespecified macrofactors and with time-varying risk premiums and betas, where the time variation of betas was captured by variables similar to those of Ferson and Schadt’s (1996) for the Canadian market. Consistent with Ferson and Schadt, the inclusion of time-varying betas led to an increase of Jensen’s alpha. The same type of evidence was found by Sawicki and Ong (2000) for managed fund performance in the Australian market, over the period 1983-1995.
Christopherson, Ferson and Glassman (1998) extended the model of Ferson and Schadt (1996) by allowing the conditional alpha to vary with the information variables in the same way as beta. They assume that managers’ abnormal returns vary over time and they track their variation as a function of the conditioning information. When
31 Five information variables are used: the lagged (previous month) level of the one-month treasury bill yield, the dividend yield at the end of the previous month, a term spread, a corporate bond default-related yield and a dummy variable for the month of January.
32 This negative covariance implies that funds have lower market betas when the expected market return, given the information variables, is relatively high, and higher market betas when expected market returns are relatively low. One of the possible explanations for this relies on the flow of money into the funds. If more money flows into funds when market returns are expected to be high and if managers take some time to allocate that money according to their usual styles, then funds, at some times, would have larger cash holdings and, consequently, lower betas (see Ferson and Warther, 1996).
applying their model, to a sample of pension funds using the same information variables as Ferson and Schadt (1996), the distribution of the unconditional and conditional alphas, whatever benchmark used (a market index, a style index or multiple style indices), appears quite similar, contrasting with the findings of Ferson and Schadt.33 Similar results were also obtained by Cai, Chan and Yamada (1997), in a study on the performance of a sample of Japanese mutual funds over the period 1981 to 1992. The Jensen alphas did not improve with the conditional model. Indeed, both the unconditional and conditional alphas were skewed to the left.
Cortez and Silva (2002) obtained distinct results. In their study, the conditional Jensen’s alpha, applied to a sample of Portuguese equity funds (over the period April 1994 to March 1998) worsened funds’ performance: conditioning information eliminated the evidence of superior performance.
Although reaching different conclusions about the impact of conditioning information, most of the previously mentioned studies conducted performance evaluation in the context of asset pricing models. Other alternative conditional performance measures have also been developed and analysed. Chen and Knez (1996), following Hansen and Jagannathan (1991), extend the performance evaluation theory to the case of general evaluation models. Modern evaluation theory identifies models based on the stochastic discount factors (SDF)34 that they imply. For any evaluation model, the SDF is a m scalar random variable, so that for any asset that affords a t
33 Unlike mutual funds, pension funds are not subject to high frequency flows of public money.
34 The term “stochastic discount factor” is usually ascribed to Hansen and Richard (1987). Stochastic Discount Factors can be viewed as a unified framework to represent any asset pricing model. A regression approach, with a beta pricing formulation, and the Generalized Method of Moments (GMM) approach with a SDF formulation, may be considered as competing paradigms for empirical work. However, under the same distributional assumptions, and when the same moments are estimated, the two approaches are essentially equivalent (Cochrane, 2001; Jagannathan and Wang, 2002). For a review in this subject see Ferson (2003).
certain random payoff (V ) at time t, the price at time t-1 is given by: t
) V m ( E
Pt−1 = t t Ωt−1 [3.1]
where Ωt−1 represents the information set available at time t-1. Supposing that there are N assets available to investors and the prices are different from zero, and since m is t the same for all assets, it follows that:
1 ) R
m (
E t t Ωt−1 = [3.2]
where R represents the gross returns vector (payoff divided by the price) of N assets t and 1 is a N-vector of ones. If R is equal to the return of a portfolio made up of the N p assets, and R is replaced by xR, where x represents the portfolio’s weights vector. p These portfolio weights may change over time according to the information available to the portfolio manager. Assuming that the manager holds only public information:
1 1 ) ( x ) R ) ( x m (
E t Ωt−1 ' t Ωt-1 = Ωt−1 ' = [3.3]
where )x(Ωt−1 indicates the dependence in relation to public information, x depends only on Ωt−1 and ∑x=1.
Performance evaluation consists of identifying managers that set up portfolios using private information (that does not exist in Ωt−1) for which there will be higher performance when facing situations in which [3.3] does not occur, that is, we may define alpha as:
1 ) R
m (
E t p,t t 1
t ,
p = Ω −
α − [3.4]
Assuming a conditional setting, the public information set Ωt−1 is replaced by a set of predetermined information variables Zt−1. It follows from the law of iterated expectations that the measure of performance is:35
1 ) Z R m (
E t p,t t 1
t ,
p = −
α − [3.5]
The SDF in the approach of Chen and Knez (1996) does not rely on a specific asset pricing model and, hence, on its accuracy. It is efficient by construction and requires only the returns on benchmark assets. For a sample of 68 US equity funds, over the period 1968 to 1989, Chen and Knez, using both unconditional and conditional36 measures, did not reject the hypothesis of no abnormal performance. However, as in Ferson and Schadt (1996), they also found that the conditional measures tend to increase performance estimates.
Dahlquist and Söderlind (1999) followed the same approach of Chen and Knez (1996) to evaluate the performance of a sample of 24 Swedish equity funds over the period 1991 to 1995. They considered three different measures: an unconditional measure resulting from “fixed-weight benchmark portfolios”, an unconditional measure resulting from “dynamic benchmark portfolios” (which corresponds to the conditional
35 It should be noted that Rp,t refers to raw returns. When excess returns are used, the performance measure becomes: αp,t =E(mtrp,t Zt−1) where rp,t is the excess return of portfolio p.
36 For the conditional model, Chen and Knez (1996) used 3 information variables: the nominal 1-month Treasury bill rate, the dividend yield on the CRSP value-weighted stock index and the difference in yield- to-maturity between bonds with greater than 15 years to maturity and bonds with 5 to 15 years to maturity (a term spread).
measure proposed by Ferson and Schadt, 1996)37 and a conditional measure (which is similar to the conditional model with time-varying alphas of Christopherson, Ferson and Glassman, 1998)38. Relatively to the unconditional measures, Dahlquist and Söderlind (1999) do not find significant evidence of abnormal performance. When the conditional measure was used, the results indicate a tendency toward positive performance.
Farnsworth, Ferson, Jackson and Todd (2002) also studied the use of SDF models in evaluating the investment performance of portfolio managers. They investigated several conditional formulations of m , including a SDF version of the CAPM, several t versions of multi-factor models, where the factors are specified as economic variables (designated as non-traded factors) and, as traded factors, the numeraire portfolio of Long (1990)39, a SDF that is a payoff of a portfolio constructed to be mean-variance efficient, as in Chen and Knez (1996) and, based in the model of Bakshi and Chen (1998), a SDF which is an exponential of a linear function of the log returns on the primitive assets.The results show that no model clearly dominates, but some models were clearly inferior. The worst performing models were the numeraire portfolio and a linear factor model with four non-traded economic factors. Moreover, “conditional models can deliver smaller average pricing errors for dynamic strategies and control better the predictability in pricing errors, but at the cost of larger variance of the pricing errors on the primitive assets of the model” (Farnsworth, Ferson, Jackson and Todd, 2002, p. 499). The models were evaluated using artificial mutual funds that control for market timing or security selection ability. They found that the measured performance is
37 The information variables used in this study were: two variables to capture the shape of the yield curve (a level variable and a slope variable) and the lagged return on the general stock portfolio.
38 The conditional alpha model can be viewed as a linearized version of the conditional measure proposed in Dahlquist and Söderlind (1999) (see Söderlind, 1999).
39 The numeraire portfolio approach to evaluate the performance of bond funds was used by Kang (1997) and Hentschel, Kang and Long (2000).
not highly sensitive to the choice of the SDF, excluding the few that perform poorly on their test assets. Also, many of the SDF models presented a bias, producing small negative alphas when true performance was neutral: around –0.19 percent per month for unconditional models and –0.12 percent for conditional models (this is less than two standard errors, as a typical standard error is 0.1 percent per month). When applied to evaluate the performance of a sample of equity mutual funds (over the period 1977 to 1993), once more they found that the measured performance is not highly sensitive to the SDF model and the overall conclusion is that the average fund performance is consistent with the null hypothesis of neutral performance.
Ferson and Khang (2002) developed a conditional version of the Grinblatt and Titman (1993) weight-based approach to measure performance. The previously discussed performance techniques are all returns-based and, consequently, they ignore potentially useful information that is often available: the composition of the managed portfolio. Ferson and Khang (2002) argue that the use of portfolio weights may be especially important when expected returns are time-varying and managers trade between return observation dates (interim trading bias). Under this scenario, returns- based approaches are likely to be biased. Using a small sample of equity pension funds for the period 1985-1994, Ferson and Khang found that unconditional weight-based measures are affected by the interim trading bias and by combining conditioning information with portfolio weights, it is possible to obtain relatively precise and reliable estimates of performance. Under unconditional weight-based measures, some funds appeared to outperform. However, this evidence disappeared when the conditional weight-based measure was used: abnormal performance of pension funds was no longer significant.
The main problem of the conditional performance evaluation approach is related to the assumed functional form for time-varying betas. According to Ghysels (1998, p.
550) “if beta risk is misspecified, there is a real possibility that we commit serious pricing errors that potentially could be bigger than a constant beta model”. Considering several conditional CAPM and APT dynamic asset pricing models, this research revealed that, in many cases, the pricing errors on the primitive assets resulting from constant beta models are smaller than those with time-varying beta models. Farnsworth, Ferson, Jackson and Todd (2002) found similar evidence, although their results suggest a “refinement” of those of Ghysels (1998) as they found, as we mentioned above, that conditional models have smaller pricing errors on the dynamic strategy returns and control better for the predictable components of primitive asset returns. This implies that particular attention should be given to the specification of the functional form of betas and that the subject related to the out-of-sample performance of conditional and unconditional models is still an evolving issue.
In conclusion, although empirical evidence shows that conditional models make a difference, there is no general consensus on the sign of the impact of incorporating conditioning information. The majority of the studies find that conditional performance measures make the managed fund performance look better, while a few others find no impact or even a negative impact. Notwithstanding, in most of the cases, empirical evidence suggests that abnormal performance, after controlling for public information, is rare. Moreover, despite the problem of the assumed functional form of time-varying betas, it seems clear that as conditional performance evaluation uses more information than traditional models, it has the potential to provide more accurate performance measures. However, previous studies have used a standard set of information variables without previously analysing their predictive ability and independently of the type of
funds being evaluated. Consequently, there has been scarce analysis of how sensitive conditional performance measures are to the selected conditioning information variables.