The Revealed Preference of Sophisticated Investors

• Author: Marat Molyboga,Jesse Blocher
• Published date: 01 October 2017

Berk and van Binsbergen () claim to show that among several popular asset pricing models, the Capital Asset Pricing Model (CAPM) most closely matches the one that mutual fund investors use. They claim that their finding applies to anyone who can invest in a mutual fund, not just mutual fund investors. This claim is based on the idea that a positive net present value opportunity in mutual funds would be recognised by these investors and competed away. Virtually all investors can invest in mutual funds, so Berk and van Binsbergen's result implies that the CAPM is the model used by all investors across all asset classes.

This comprehensive claim seems unlikely, and the literature in other asset classes contradicts it. Szymanowska et al. () identify common risk factors in commodities markets. Asness et al. () identify value and momentum factors in multiple asset classes, Koijen et al. () do the same with a carry factor. In light of these findings, how can the CAPM be the best asset pricing model for all types of investors across all asset classes?

To investigate this claim, we apply Berk and van Binsbergen (2016)'s methodology to a new set of multi‐factor models in a setting dominated by sophisticated investors who have access to all of these asset classes: hedge funds. The advantage of using hedge funds over mutual funds is that hedge fund investors, by SEC rule, must be sophisticated or have high net worth, and thus they are well‐attuned to risk adjustments and diversification. Hedge funds have no restrictions on asset classes or short selling. From early on, hedge funds have been modeled using multiple asset class factors (Fung and Hsieh, ), and the number of possible risk factors to consider has since multiplied, such that we consider 43 of them.

We also find that the asset pricing model that best predicts hedge fund investors flow is the CAPM. This finding is surprising, given the diversity of risk faced by hedge fund investors and the well‐documented failure of the CAPM to price the cross‐section of assets (e.g., Fama and French, ). Sophisticated, professional and institutional investors dominate equity markets (Gompers and Metrick, ; French, ). So, how can equity market investors rely on the CAPM if average stock returns are not related to beta? Our findings amplify this puzzle.

Hedge fund data present unique challenges. One such challenge, quite relevant to our study, is restrictions on flows commonly employed by hedge funds. One restriction on fund flows is a lockup period, which is a minimum investment time for cash invested (e.g., 180 days). There are also separate limits on withdrawals, such as redemption notices (e.g., 30 days) and infrequent redemption dates (e.g., twice per year). To address these combined challenges, we always measure flows over a 12 month horizon following a 24 month evaluation period. The 24 month evaluation period is chosen because 99% of our sample has lockup periods of less than two years. We measure fund flows over the subsequent 12 months to account for the combination of the redemption notice duration and redemption frequency. For instance, if a 30 day notice period causes you to miss the semi‐annual redemption date, you would have to wait more than 6 months to withdraw funds. In our sample, 97.7% of funds have both redemption notices periods of less than 180 days and redemption frequencies of less than 180 days. Thus, for almost our entire sample, an investor can effectively evaluate fund performance over a two year period, decide to withdraw funds, and successfully do so over the subsequent 12 months.

A second challenge is that hedge funds voluntarily contribute to datasets, thus some hedge funds are missing from our analysis. However, for the same reasons explained in Berk and van Binsbergen (), our results are not isolated to our sample: if we find in our sample that the CAPM is the most likely risk model, then it must be that any investor who can invest in these hedge funds also uses the same model. Thus, our result extends even to the hedge funds not in the sample, because those investors also can invest in the funds we analyse.

However, voluntary reporting by hedge funds could also lead to bias. We use the most representative hedge fund data available, and we correct for known biases using the most effective methods in the literature. However, we cannot guarantee that the data are unbiased, nor are there any hedge fund data we can acquire that can be reasonably declared unbiased. The question is rather: how does that bias affect our results?

The bias that remains in our data is ‘non‐reporting bias’, which occurs when funds either stop reporting (but continue normal operations) or never report to a dataset. The datasets used for hedge fund research are marketing tools, which means that there are two types of funds to which this bias pertains: poorly performing funds that never report and fail, and top performing funds that never begin reporting or that stop reporting because word of mouth publicity is sufficient.

Given the statistical strength of our results, the omitted funds would have to exhibit a strong flow‐performance relationship coordinated on a single non‐CAPM model to overturn our findings. The most popular multi‐factor model in the literature (Fung and Hsieh, ) is strongly rejected in our data. However, if it were the case that the omitted funds strongly rejected the CAPM for a different model, can one hedge fund sample strongly support the CAPM while another strongly supports a different model when the investor set has significant overlap between the two samples? We think that is highly unlikely.

As a further robustness check, we also analyse funds of hedge funds and find again that the CAPM dominates. Funds of hedge funds are themselves hedge funds that invest in other hedge funds. The benefit of analysing these funds is that it indirectly mitigates ‘non‐reporting bias’, because these funds of hedge funds have access to the entire universe of hedge funds, whether they report or not (Fung and Hsieh, , Jorion and Schwarz, ).

Our data come from BarclayHedge. BarclayHedge has the most complete coverage of assets under management (AUM) of any dataset and thus is optimal for our methodology, which requires fund flows. Joenväärä et al. () analyse the most commonly used hedge fund data available, and find that idiosyncratic biases across hedge fund datasets have mostly disappeared. This finding means that complicated multi‐dataset merges (as in Titman and Tiu, ) are no longer necessary to obtain representative data. We adjust for known biases using the best methods available. We require the first reported date to correct for incubation bias as recommended by Bhardwaj et al. (), who show that other commonly used methods are insufficient. Bhardwaj et al. () also identify a ‘graveyard bias’, in which funds request histories to be deleted from graveyard databases that researchers use to control for survivorship bias. We have confirmed with our vendor that this bias is not present in our data, and we further validate this confirmation with a separate dataset on commodity trading advisors (CTAs) from the same vendor.

A final concern about hedge fund data is fund pricing. Because hedge fund investments are often illiquid and over‐the‐counter, they are harder to price. In contrast, equities are publicly traded and marked‐to‐market daily. This illiquidity presents as autocorrelation, so we include models that adjust for autocorrelated returns as measured by Getmansky et al. () and Asness et al. (). Our results are robust to this adjustment. First, we find little statistical difference between adjusted and unadjusted models when measured by revealed preference. Second, adjusting for autocorrelation does not substantially alter performance rankings. Adjusted and unadjusted models are correlated between 87%–93%.

Equilibrium assumptions in Berk and Green () do not hold as strictly among hedge funds. Their key assumption is a competitive capital market in which quantities, not prices, adjust. However, successful hedge fund managers do not only manage larger funds; they also get call option‐shaped incentives that gives them a percentage of fund performance (Goetzmann et al. ). Performance persistence also occurs among hedge funds (e.g., Kosowski et al. , Jagannathan et al. ), which implies that managers do not capture all of the rents. Finally, despite disagreement as to the exact shape of the flow‐performance relationship, it is commonly agreed that it is monotonically increasing (Getmansky et al. ). To account for this mismatch, we show that hedge fund managers are skilled at using the value‐added performance measure from Berk and van Binsbergen (). We also show that this skill is correlated with fund performance, as identified by the CAPM, but not by other multi‐factor models. Thus, the necessary link between performance and fund flows exists, but it is noisier than in mutual fund data.

Our analysis is comprehensive. In addition to the CAPM, we analyse 42 factors derived from the literature on hedge fund performance assessment and characterisation. We include these 43 factors in a stepwise regression following Titman and Tiu () and Liang (). Stepwise regressions use a statistical test across combinations of the input set of factors to identify the most parsimonious and best‐fitting multi‐factor model, by individual hedge fund. We also test the popular seven‐ and eight‐factor models of Fung and Hsieh (). We find that the CAPM dominates all of them.

Building on this finding, we show that the market return used in the CAPM analysis is of minor importance. We test models with four proxies for the market return: the S&P 500, the CRSP value‐weighted market index, and both value‐ and equal‐weighted hedge fund of funds benchmarks. The statistical differences between flow‐performance betas in the revealed‐preference test is insignificant among the four models...