Let's start with something you've described earlier already: Why is Alpha a bad guideline for portfolio optimization?
Levy: Investors care about the expected return and the risk of their entire portfolio. This is captured by the portfolio’s Sharpe Ratio. The alpha of an asset with respect to a given benchmark measures the change in the portfolio’s Sharpe Ratio driven by a marginal increase in the asset’s weight. Thus, alpha indicates which assets should be marginally over- or underweighted relative to the benchmark weights. But for larger changes , which are those relevant to investors, the optimal weight adjustments are almost unrelated to the alphas. In fact, in many cases the optimal adjustment is in the opposite direction of alpha – it may be optimal to reduce the weight of an asset with a positive alpha, and vice versa. Investors who hold a single mutual fund should select the fund by its Sharpe Ratio – alpha is completely irrelevant for them.
That's counterintuitive. Can you give an example, please?
Levy: Suppose that fund A has an expected return of 7%, a standard deviation of 20%, and a beta of 0.5, and that fund B has an expected return of 9%, a standard deviation of 20%, and a beta of 0.9. Assume that the market portfolio’s expected return is 11%, its standard deviation is 20%, and the risk-free interest rate is 1%. This implies that fund A has a correlation of 0.5 with the market, and fund B has a correlation of 0.9 with the market. So fund A has an alpha of 1% (calculation: 7 – [1 + 0,5(11 – 1)]), while fund B has an alpha of –1% (calculation: 9 – [1 + 0,9(11 – 1)]).
Thus, ranking funds according to their alphas leads to the incorrect conclusion that fund A is better.
Levy: Yes. The conclusion is incorrect because the Sharpe Ratio of fund A is only 0,3 (calculation: [7 – 1] / 20), compared to fund B with a Sharpe ratio of 0,4 (calculation: [9 – 1] / 20). Thus, investors are better off with fund B, or combinations of fund B and the risk-free asset. In this specific example it is even better to hold the market portfolio, which has a Sharpe Ratio of 0.5, but this need not necessarily be the case in general.
So investors should not use alphas to select assets to be included in their portfolio?
Levy: There is a big difference depending on whether the investor constructs her own portfolio, and is selecting the individual stocks to be included in the portfolio, or the investor is selecting a mutual fund, which is already well-diversified. In both cases the investor’s ultimate goal is maximizing her portfolio’s Sharpe Ratio. But Alpha is certainly irrelevant in the second situation. In a different study me and my co-author argue that alpha is practically irrelevant in the first situation as well.
But alpha is popular as a measure of the performance of fund managers.
Levy: Its appeal is that it provides a measure of excess return after controlling for various systematic risk factors. This may be a good measure of a fund manager’s ability to generate excess return relative to systematic risk-exposure. But it is not a relevant measure for the investor selecting a single mutual fund, who cares about the fund’s risk, including its non-systematic risk.
Why is the Sharpe ratio the relevant performance measure for most investors?
Levy: In the standard Mean-Variance framework for which Harry Markowitz and William Sharpe have received the Nobel prize, return distributions are assumed to be normal, and the investor can borrow or lend at the risk-free rate. In this setting, there is a single stock portfolio that is optimal for all investors – this is the portfolio with the maximal Sharpe Ratio, also called „the tangency portfolio“. For any other portfolio, there is a dominant combination of the risk-free asset and the tangency portfolio in the sense that all investors are better off. This is true not only for risk-averse investors, but in fact, for any investor who prefers more rather than less money.
In the new study, what did you analyse in particular?
Levy: The main question that we ask is whether the active equity mutual fund industry on aggregate creates or destroys value for investors, and how much. This is very different than the question of whether fund managers are talented and create value. For example, if a manager creates an annual value of $10 million, but extracts $15 million as fees, the manager is talented, but the net effect for his investors is negative.
You estimate the aggregate annual loss to investors in U.S. active equity funds at $235 Billion. How do you arrive at such an incredible number?
Levy: The natural alternative for investing in an active US equity fund is a „passive“ investment in the S&P 500 index via ETFs, for example. Thus, we compare each fund with the passive market index. A fund that yields a higher Sharpe Ratio than the market, after fees, creates value for investors. A fund that yields a Sharpe Ratio lower than the market destroys value. By adjusting for risk we can translate differences in Sharpe Ratios into differences in returns (see figure below). Multiplying this return difference by the amount of money each fund manages we arrive at a Dollar estimate of the value each fund creates or destroys.
However, the aggregate loss is a hypothetical number, is it? As it represents the loss based on the theoretical average return of funds in order to equate their Sharpe Ratios with that of the S&P 500?
Levy: It is an estimate based on the empirical data. Of course, no one can know the exact true aggregate loss. But the fact that the $235 Billion a year estimate is robust to various estimation methods, increases my confidence that this is close to the true aggregate loss.
You write that the loss can be decomposed into two components: A wealth destruction of $186 Billion, and a $49 Billion wealth transfer from investors to funds. How do you arrive at these numbers?
Levy: The $49 Billion figure is a direct transfer from investors to funds via fees. But most of the loss is due to the fact that most funds underperform the index even before fees. In other words, even if all funds would have charged zero fees, investors would still suffer an aggregate loss of $189 Billion relative to the alternative of investing in the market index.
Why do investors still put their money in mostly underperforming active funds?
Levy: Investors are human, and like most humans many of them suffer from a variety of systematic cognitive biases. Active mutual funds are highly motivated and efficient in exploiting this when marketing their products. For example, they tend to advertise their performance only when it was good; which may lead to the wrong impression that funds are much better than they actually are. Another approach is the „incubation strategy“: privately starting several new funds and after a few years making public only those who did well. This presents investors with a very biased track record.
Do you have any idea of what a fair amount of activeness could be in the markets to avoid excess but still make sure price efficiency more or less stays in place?
Levy: The well-known scientist Richard Roll explains the equilibrium between active and passive investing by a beautiful analogue from biology: the hawk-dove equilibrium. The hawk strategy is conducting security analysis and being active, while the dove strategy consists of passive investing. Clearly, if everyone analyses securities, the benefits will be less than the costs. But if everyone is passive, the benefits of analysis will be tremendous. The equilibrium is where it is not worthwhile for the marginal passive investor to begin analyzing, nor for the marginal active investor to become passive. The fact that active funds on average underperform relative to being passive indicates that currently there is too much active investing (too many hawks). So what is the equilibrium amount of active investing? I don’t really know, but my guess is that we are pretty far from equilibrium. My guess is that if one half of the money invested in active funds moves to passive funds the market would become more efficient, not less. But this is only a guess.
Why do you think the market would become more efficient with less money in active funds?
Levy: One reason is that currently there are too many resources allocated to security analysis, so the costs are greater than the benefits. Another reason is the misalignment of incentives: Fund managers typically want to increase assets under management. So if an investment strategy on average underperforms, but once every few years yields very good performance, then from the point of view of the manager, following this strategy, and advertising a lot after the rare outperformance makes sense. Of course, this is not so good for investors.
Other than one might think in terms of public perception, active funds are still larger than passive funds, and there is probably quite a long way to go until equilibrium.
Levy: Indeed. As of 2021, active funds manage about six times as much money as passive funds. Active U.S. Domestic equity funds managed about $2 Trillion in 2000, and this value has grown to $10 Trillion in 2021. So yes, I agree that there is a long way to go.
Finally, what do you think can be done to reduce the inefficiency implied by the excessive amount of active management?
Levy: I would suggest three ways. The first is mechanism design: Make passive investing the default choice in pension plans in which the investor has to choose among several alternative portfolios. The second is regulatory: When funds advertise returns, it should include the fund’s returns as well as the market index returns in all of the past five years. The third and the most important way is the dissemination of knowledge accumulated through scientific research. I hope that this interview helps in this endeavour!