Statistical alpha can be divided into fake alpha, which is a premium for non-directional systematic risk, and true alpha, which reflects the quality of the investment process. Fake alpha arises from exposure to conventional factors that are not correlated with the market portfolio. Failing to distinguish fake and true alpha can be costly for investors and strategy developers. Fake alpha is easy and cheap to produce and after periods of high risk premia on conventional factors it can post impressive performance statistics (or backtests). Subsequently, investors overload on managers or strategies that use these factors and related performance inevitably deteriorates. This goes some way in explaining the negative historic alpha on actively managed funds.

Müller, Marcel, Tobias Rosenberger and Marliese Uhrig-Homburg (2017), “Fake Alpha”, SFB 649 Discussion Paper 2017-001.

The post ties in with this site’s lecture on information inefficiency, particularly the consequences of information cost, and the lecture on implicit subsidies, particularly the importance of distinguishing implicit subsidies from non-directional systematic risk premia.

The below are excerpts from the paper. Emphasis and cursive text have been added.

What is fake alpha?

“We decompose the CAPM alpha in two components: First, the fake alpha component, which accounts for the beyond-market-risk premia part. We obtain it by using multi-factor models [that are standard in the equity space] …and then estimate the part of the CAPM alpha which is linked to loadings on factors other than the market factor. Second, the True Alpha component, which is equal to the difference between the CAPM alpha and the Fake alpha, and henceforth represents the part of the CAPM alpha not linked to any beyond-market-factor risk premia.”

“Our results are in line with an attenuated version of a thesis stated by John Cochrane (2010), who claims that ‘There is no alpha. There is just beta you understand and beta you do not understand…’, as it seems, like the only beta an average mutual fund investor understands is the market beta. Within our model, even if the managers didn’t have any skill at all, investors would still provide flows to their funds in the long-run equilibrium, since they confuse skill with risk premia on omitted factors.”

Why is fake alpha a common phenomenon?

Investors chase CAPM alphas [returns that exceed the premium paid for taking systematic market risk, based on the Capital Asset Pricing Model]… Empirical findings…show that of all major assets pricing models the CAPM is the one that is most likely used by investors of equity mutual funds to determine their investment decision…Investors not only chase CAPM alphas, but they are also unaware of any beyond-market factor risk. This enables a manager to easily generate CAPM alphas by loading on beyond-market-risk factors.”

“The [investment] manager can choose to invest the provided funds in either a true active strategy, a factor strategy, or the market portfolio… Capital flows in and out of a fund are linked to the fund’s past net performance measured against the CAPM. As compensation for the management services the manager charges a fix proportional fee on the total assets under management.”

“Whenever industry size and hence competitiveness rises it gets relatively expensive for the managers to generate true alpha. In this situation, fund managers seem to increase their exposures towards the beyond-market-risk factors to generate fake alpha instead. This relationship is also confirmed the other way around, meaning whenever risk premia on beyond-market risk factors increase and hence it gets relatively cheap to generate fake alpha, the managers excessively load on the beyond-market-risk factors. At the same time, they focus less on the true alpha part. This could be suggestive of managers being aware about the investors’ coarser information set, but since being rewarded proportional to the managers’ assets under management their behavior is perfectly rational.”

What are the consequences of investing in fake alpha?

“Ultimately, investors’ ignorance of factor strategies leads them to overestimate manager’s skill, and eventually, to overinvest into the fund in equilibrium.”

“[The present and previous studies] empirically observe negative risk adjusted average net returns to investors for active managed mutual equity…[If] investors…have a coarser information set compared to fund managers and are therefore unable to correctly quantify risk, …net returns to investors in equilibrium might be simply a result of all agents behaving rational under these circumstances.”

What is the quantitative empirical evidence?

“We use data provided by the Center for Research in Security Prices (CRSP) and Morningstar. Our sample contains 3,292 actively managed mutual funds from the United States that primarily invest in domestic equity (>95% AUM invested in domestic stocks), covering the period from March 1993 to December 2014 on a monthly grid.”

“We estimate true alpha in the same manner as investors’ alpha but instead of using the one factor CAPM as risk adjustment model, we use either the three factor model by Fama and French (1993) or the four factor model by Carhart (1997)…The fake alphas are calculated by simply taking the difference between investors’ alpha and the net true alpha. Depending upon the risk adjustment model the average true alpha lies between 1 bp and 2 bp per month whereas the average Fake alpha ranges from 3 bp to 5 bp per month.”

“[In an equilibrium model] ex-post expected investors’ Alpha should be negative but not exceeding the level of the management fee in the long-run equilibrium states. This is due to the outcome that under the imposed restrictions investors overinvest into the funds in the long-run equilibrium…In line with the model, we empirically find that the average net alpha measured against the CAPM is significantly negative in equilibrium states.”

“We show that on average investors do not learn about the structural mistake they are making, but we are able to identify a small group of investors that seems to learn.”

“[In an equilibrium model] investors’ alpha, true alpha, fake alpha, as well as the operating costs should all be inversely related to the fund’s size…We [indeed] obtain a significant negative relationship between a fund’s size and the net alpha to investors… A fund’s size measured in end-of 2014 inflated dollars…where we [adjust] the fund’s AUM by the total market capitalization…We account for variations in overall equity-market size that might be mirrored in a fund’s AUM as well….We find strong empirical evidence for decreasing excess returns to scale on the fund level…Looking at the standardized size of a fund instead of the absolute (deflated) assets under management we find robust decreasing returns to scale.”

“As a fund grows from zero (0%) to its mean size (100%) the investors’ alpha on average declines by 26 bp per month…The negative relation is statistically significant. The decreasing returns to scale relation is not only statistically but also economically significant. For example, a one-standard-deviation increase in the standard size leads to a sizable decline in investors’ alpha of about 16 bp per month.”


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