Introduction

Investors are constantly on the hunt to find managers that will deliver “alpha.” But what is alpha? People define it in different ways. It could simply mean the excess return over some benchmark. It could also mean the excess return after controlling for exposure to certain risk factors.


What is considered alpha to one investor may be risk to be hedged away by another investor with a more advanced risk model.


As Larry Swedroe and Andrew Berkin stated in their history of asset pricing models, the alpha of a manager can vary depending on the sophistication and extensiveness of your risk model.1 In this post, we’ll use an illustrative example to demonstrate that the “alpha” of a manager may be lower than initially expected once we control for its benchmark return or the returns of common risk factors. 


Body 

Say a U.S. equity manager delivered a 10% return over the past year. There was a time when all of this return would be considered “alpha” or thought to be directly attributed to that manager’s skill.2


Alpha1

The advent of market indexes, however, helped investors measure performance against a benchmark. Say that over this same year, the S&P 500 index yielded a 6% return. If we used the S&P 500 to benchmark the performance of the manager, then perhaps it’s not fair to attribute all of the 10% return to that manager’s skill. One could have earned 6% by just investing in the S&P 500.3 The added value of the manager could, therefore, be seen as only 4%.


Formula1

The introduction of the Capital Asset Pricing Model (CAPM) in the 1960s went a step further by arguing that it’s not just about the difference in the levels of returns between a manager and the equity market.4 One should also consider the amount of equity market risk the manager takes. 

A manager that has higher exposure to equity market fluctuations may earn a higher return, however that extra return may simply be compensation for assuming additional equity market risk. This risk can be measured by beta, or the manager’s sensitivity to moves in the equity market. 

Using the same manager and benchmark from the example above, the excess return of 4% still holds if the manager exhibited a beta of 1.0 to the S&P 500 index. However, what if the manager simply had a greater exposure to the S&P 500, e.g., exhibiting a beta of 1.2 to the index? This means that the manager historically delivers a 1.2% return for every 1% return the index delivers. That extra 0.2% is not necessarily attributable to alpha, rather it’s reward for taking additional exposure to the index. In this case, the alpha is actually lower than 4%:


Formula2

This is quite important because the CAPM is able to break down the manager’s returns into alpha and beta components. The beta component should be easy and relatively low cost to access. The alpha component is the unique return the manager delivered to the investor. This helped frame how investors think about the returns they are getting, where the returns are coming from, and what investors should be paying for those returns. Continuing with our example:


AlphandBeta

In the 1990s, Eugene Fama and Kenneth French expanded on the CAPM by adding two new variables to the model – size and value.6 These two factors were meant to capture exposure to strategies that are now well-known to have compensated investors historically – that is, investing in small-cap and high-value stocks (the latter defined as stocks with high accounting book value relative to market price). This model can be seen as further explaining alpha by attributing some of the excess returns that managers earned relative to the equity market to these two factors. 

Say the manager we’ve been analyzing was implementing a strategy that exhibited betas to the small cap and value factors of 0.2 and 0.5, respectively. What happens to its 2.8% CAPM alpha?


Formula3

Assuming that the Fama-French small cap and value factors returned 1% and 2% respectively over the year, we end up with a 1.6% unique alpha:


Formula

As the collection of explanatory factors expands, more of what was previously described as the “unique” return is explained by the investor’s exposure to well-known factors. What was once considered entirely alpha can now be partially attributed to familiar active investment strategies, like investing in small-cap and value stocks. Over the years, more of these strategies have been identified, such as quality and low risk, and modern risk factor models include tens, or even hundreds, of factors. In the future, it’s possible that even more factors will be identified that attribute returns to explainable factors instead of unique alpha.


Conclusion

In summary, an investment can have different amounts of alpha depending on what it is measured against. To try and better understand the “unique” return that a certain investment provides, consider the benchmark and/or risk factors used in your evaluation. 

Stay tuned for a follow-up post that will discuss how the concepts described above impact investors in practical terms.


References
1 Berkin, Andrew and Larry Swedroe. Is Outperforming the Market Alpha or Beta? American Association of Individual Investors. https://www.aaii.com/journal/article/is-outperforming-the-market-alpha-or-beta.touch
2 Before the introduction of the first major market index, the Dow Jones Industrial Average, in May 1896, investors may have considered investment returns to be all attributable to “alpha.”
3 An investor might not earn 6% after the consideration of fees and transaction costs.
4 Sharpe, William F. (September 1964). “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk”. The Journal of Finance.
5 The illustrative example above assumes that the risk-free rate equals zero.
6 Fama, Eugene F. and Kenneth R. French (June 1992). “The Cross-Section of Expected Stock Returns”. The Journal of Finance.
7 The illustrative example above assumes that the risk-free rate equals zero.

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