There has been an ongoing debate in the finance world about whether sigma or alpha is the better metric for measuring investment performance. Both sigma and alpha aim to quantify how much excess return an investment strategy achieves over a benchmark, but they go about it in different ways. This article will examine the key differences between sigma and alpha, look at the advantages and criticisms of each, and provide an overview of the sigma vs alpha debate.
What is Sigma?
Sigma, also known as excess return, measures the volatility-adjusted return of an investment strategy relative to a benchmark. It accounts for both the excess returns generated by the strategy, as well as the volatility or risk taken to achieve those returns. Sigma is calculated as:
Sigma = (Portfolio Return – Risk-Free Return) / Volatility
Where portfolio return is the actual return of the investment strategy, risk-free return is the return that could be earned on a risk-free investment like Treasury bills, and volatility is the standard deviation of the investment strategy’s returns. A higher sigma indicates that a strategy is generating higher excess returns per unit of volatility.
Advantages of Sigma
There are several potential benefits to using sigma rather than alpha as an investment performance metric:
- Accounts for risk – Since sigma adjusts for volatility, it measures the excess return earned per unit of risk taken. Strategies with high returns but even higher volatility may have lower sigma.
- Easier comparison – Sigma provides a volatility-adjusted metric that allows for easier performance comparison across strategies with different risk profiles.
- Benchmark agnostic – Sigma does not depend on a specific benchmark, only a risk-free rate. This avoids issues with benchmark mismatch that can affect alpha.
- Preferable for hedge funds – Many hedge fund strategies aim for absolute returns uncorrelated to market benchmarks. Sigma may be a more suitable performance metric than alpha for such strategies.
Criticisms of Sigma
Some of the main criticisms leveled against using sigma include:
- No skill measure – Sigma does not isolate manager skill, since volatility is largely driven by strategy/asset class rather than active decisions.
- Rewards volatility – Sigma may incentivize unnecessary risk-taking, as higher volatility mechanically boosts sigma.
- No benchmark context – Without a benchmark, sigma does not give context on whether performance is good or bad for a given strategy.
- Difficult comparison – Comparing sigma across different assets or strategies remains challenging due to differences in risk-free rates.
What is Alpha?
Alpha measures the excess return generated by an investment strategy relative to a market benchmark. It is calculated as:
Alpha = Portfolio Return ??? Benchmark Return
Where portfolio return is the actual return of the investment strategy and benchmark return is the return of the relevant market benchmark over the same period. A positive alpha indicates the strategy has outperformed its benchmark, while a negative alpha means it has underperformed.
Advantages of Alpha
Some key benefits of using alpha as a performance metric are:
- Measures skill – Alpha aims to isolate manager skill by measuring excess returns versus a benchmark that represents the general market.
- Benchmark context – Alpha provides context on performance relative to the investor’s benchmark to determine if value is being added.
- Intuitive – The concept of outperforming a benchmark is relatively simple to explain and understand.
- Universal – Alpha allows comparing performance across diverse strategies by normalizing to each one’s benchmark.
Criticisms of Alpha
Some common criticisms of using alpha include:
- Benchmark dependent – Alpha is tied to a specific benchmark, which may not be relevant or investable for all strategies.
- No risk adjustment – Simply comparing returns does not account for the amount of risk taken to generate alpha.
- Mean reversion – Alpha tends to regress over time as outperforming managers attract more assets.
- False outperformance – Benchmark misfit, leverage, or other factors can artificially inflate alpha without skill.
Sigma vs. Alpha Comparison
Here is a summary comparing sigma and alpha as performance metrics:
| Sigma | Alpha | |
|---|---|---|
| Definition | Volatility-adjusted excess return vs. risk-free rate | Excess return vs. benchmark |
| Accounts for risk | Yes, adjusts for volatility | No, only compares returns |
| Measures skill | No, volatility more dependent on strategy than manager skill | Yes, measures outperformance of benchmark |
| Benchmark dependence | No, benchmark not required | Yes, requires specifying relevant benchmark |
| Intuitive concept | No, volatility adjustment more complex | Yes, beating a benchmark is straightforward |
When is Sigma Preferable to Alpha?
Sigma may be more appropriate than alpha in cases such as:
- Hedge funds – Many hedge fund strategies aim for absolute returns uncorrelated with markets. Sigma better suits their goals than alpha.
- Illiquid assets – Some investments like private equity have no clear benchmarks. Sigma avoids the need to construct hypothetical benchmarks.
- Risk parity – These strategies target a volatility level across assets. Sigma aligns better with risk parity’s volatility-based approach.
- Tactical allocation – Sigma can evaluate market timing decisions based on volatility rather than benchmark outperformance.
In general, sigma has more utility for measuring performance when no natural or investable benchmark exists for the strategy in question.
When is Alpha Preferable to Sigma?
Alpha may be more suitable than sigma when:
- Evaluating active management – Alpha helps answer whether an active manager is adding value relative to the market.
- Asset class strategies – Traditional long-only equity or fixed income strategies are readily benchmarked to market indexes.
- Manager skill – Alpha aims to isolate manager skill more directly compared to volatility-driven sigma.
- Manager selection – Comparing alphas helps identify managers with consistency in outperforming relevant benchmarks.
Alpha tends to have more relevance for traditional benchmarked strategies where isolating manager skill and adding value over a market index are key objectives.
Conclusion
There is no definitive verdict on whether sigma or alpha is “better,” since each metric has merits depending on the strategy and investor goals. Sigma accounts for risk-taking and avoids benchmark mismatch issues but does not isolate skill. Alpha measures excess returns versus a relevant benchmark to evaluate skill, but does not adjust for risk. Sigma suits hedge funds and other unbenchmarked strategies, while alpha aligns better with traditional active management. Rather than debating sigma vs alpha, investors may be best served by considering which metric is most appropriate given their specific objectives and situation.