How Positive Alpha Can Coexist with Benchmark Underperformance
Summary
The document explores how a strategy can have positive estimated alpha while its cumulative return trails the benchmark. It explains the distinction through a factor model: alpha measures performance unexplained by market exposure, while realized total return also reflects beta and the benchmark’s direction. A portfolio with weak or negative market exposure can lag a rising index even if it earns gains that are independent of that index.
Two examples illustrate this point. One combines a flawed index-tracking sleeve with a manager whose returns are uncorrelated with the S&P 500; the portfolio may underperform during market rises while retaining alpha. Another describes insurance as a strategy with negative expected return and negative beta but potentially high alpha because it diversifies market risk. These are conceptual examples, not empirical verification of the reported pyfolio result. The document does not inspect the program’s calculation or the supplied return data, and statistical alpha estimates still depend on the model, measurement period, and data quality.
Key ideas
- Alpha measures return unexplained by modeled market exposure, not cumulative outperformance by itself.
- A strategy with low or negative beta can lag a rising benchmark while earning positive alpha.
- Diversifying or insurance-like returns can have negative expected returns and still provide portfolio value.
- An alpha estimate depends on its factor model, sample period, and input data.
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Full text
# Can alpha be positive if cumulative returns underperform the benchmark? # Can alpha be positive if cumulative returns underperform the benchmark? According to my portfolio analysis program (pyfolio), the alpha of the following strategy is .17 (I am assuming 17%). [Based on pyfolio documentation, alpha here is the "annualized alpha".] However, the cumulative returns of the benchmark are about 10-fold higher than that of the strategy (~12% vs ~125%), see graph. To me this is non-intuitive, and I was wondering if someone had a good explanation. Does beta (negative in this case) have something to do with it? Of course, it is also possible that I am not using the software correctly, or misinterpreting its output. I will go into its source code to try and figure out the calculation it performs. But I hoped someone knows what might be going on here. Thanks! UPDATE: Here's a link to a csv file with returns: https://drive.google.com/file/d/1m04SfUPzYdB9fPPSLMHbNq5iM0LWf3fc/view?usp=sharing ## Answer by kurtosis (score 2) https://quant.stackexchange.com/a/55996 Yes, this is absolutely possible. Here is a simple thought experiment to show how. We want to benchmark to the S&P 500. We allocate 90% of our capital to an index tracking strategy and 10% to some new portfolio manager with a good track record. (We'll call the new PM "Rumplestiltskin," for ease of reference.) Unfortunately, there is a bug in our index tracking strategy and it ends up being mostly mean-zero noise with an S&P 500 beta of 0.1. (This may sound implausible. Check the returns of some hedge funds and you will see it is very plausible.) On the other hand, Rumplestiltskin turns everything to gold: he makes consistent gains uncorrelated with the S&P 500. If Rumplestiltskin's gains are small, we will likely underperform the S&P 500 when it rises; however, we will have alpha that will be shown to be significant with enough data. ## Answer by phdstudent (score 2) https://quant.stackexchange.com/a/63586 The best example of an underperforming strategy with big alpha, is insurance. Every year you pay a premium to insure your house. That strategy has negative expected return, negative beta, but super high alpha (as it is uncorrelated with the market and diversifies well your portfolio).
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