Hi, I have created several long only and long/short strategies using stocks from the S&P 500. To evaluate the performance I regressed the returns of the strategies on the returns from the S&P 500. But especially for the long/short strategies, I get a low R^2 and a negative beta, resulting in a highly positive alpha. Some strategies have a strong alpha, even though they completly underperforme the market based on sharpe ratio and raw returns. How do I interpret the alpha for these strategies? I know a low R^2 usually speaks for a wrong benchmark, but these are stocks that are all in the S&P500. How can that be the wrong benchmark?
Does your long/short strategy have a target ‘net long’ positioning? There’s a big difference in benchmarking a 15% net-long strategy vs. a 90% net long strategy. If your getting below 25% the strategy would be better classified as a market neutral strategy. With a negative beta I’m wondering if that might be the case.
If it is a market neutral strategy then the benchmark should be the short term ‘risk free’ rate, since theoretically you have no market risk and all returns are driven by alpha. If it is a long/short strategy then maybe you use a custom benchmark to target the allocation that is net long. For example, if you are 75% net long then your benchmark could be 25% tbill index, 75% S&P 500.
Whatever you decide, don’t use any of the hedge fund indexes like HFRI because they carry all sorts of survivorship biases and crap like that.
When you say there is a strong alpha but they “completely underperform the market,” do you still get positive absolute returns? If so, then it means that your strategy is not optimal as a stand-alone strategy, but that it can provide value if added to a portfolio that includes the market portfolio. If not, then forget about it. You can’t eat relative returns for dinner.
Also realize that the recent performance of the stock market since 2009 outperforms just about everything, so even if you get a fair amount of alpha, it’s hard to compete with just buying SPY and hanging tight. However, that can’t last forever, so the big question is whether your long-short strategy will remain uncorrelated with the S&P 500 in a downturn. If the next downturn is a credit crunch, you may find your longs going down in value and your shorts going up in value because other long/short funds are reducing total exposure by selling their longs and covering their shorts. So you will want to do what you can to judge how vulnerable you are to an event like that.
From a marketing point of view, you may still want to provide the pure strategy because your clients may decide to do the mixing with the S&P 500 themselves.
Finally, a lot of people report alpha but forget to check if it is significantly different from zero. If your alpha is large, then it’s more likely to be significant, but sometimes the standard errors are large. Alpha really isn’t at all reliable if it’s not statistically siginificant, but that doesn’t stop people from reporting it anyway.
I think he is blindly applying the CAPM formula:
r_portfolio = r_f + Beta*(r_market - r_f) + r_alpha
Negative Beta and positive market risk premium means that r_alpha will become more positive. This is not a good application of the formula, since Beta here is meant to be a scale of volatility, and negative volatility has no meaning.
It would be better to use another metric, like (absolute return minus risk free rate)/volatility, or something like that.
“these are stocks that are all in the S&P500. How can that be the wrong benchmark?”
Well, it’s because the L/S strategy has no market risk premium. It has zero Beta. Use the investor’s cost of capital or something else as the benchmark.
The Long Only strategy can be indexed to SPX if it has a decent sampling of stocks from all sectors, or if you intend for the “alpha” to come from sector selection. Otherwise, weighted sector indexes could be a better benchmark.
Remember also that there are two uses of alpha in equity portfolios. (This is related to Ohai’s comment about the use of CAPM)
There is stock alpha, which compares the stock’s performance to a benchmark, and in this case, the S&P 500 is a fine one to use, although if you are specifically targetting a sector or a capitalization, you may want to target a benchmark that is a passive index for that stock type.
The stock alpha is useful for figuring out whether you want the stock to be in the long portfolio or the short portfolio.
At some level, the portfolio alpha is a weighted average of all the stock alphas, at least if you are using the same benchmark as you were using to examine the stocks. But depending on what the portfolio strategy is, you may not want to use the S&P as your benchmark.
However, in this case, you generally want to consider how the portfolio compares to other portfolios that have the same strategy. In a market-neutral case where you expect to have 0 or close to 0 beta, then a sensible benchmark is cash, or possibly some other portfolio composite that is also 0 beta.