Alpha not “dead” – just not always better than beta (as long as you’re sure about the future direction of markets of course)

CAPM / Alpha Theory 01 May 2011

When you shop for orange juice at your local grocery store, you have surely faced the following conundrum.  You have essentially two choices:  frozen concentrated orange juice or orange juice in a jug (often made from frozen concentrate).  Both products are roughly the same price even though the jug contains several times the volume of the concentrate.  But you’re not fooled.  The only difference, of course, is that the jug of orange juice contains a couple of litres of additional water.  Both contain exactly the same amount of orange juice.  The concentrated orange juice contains vitamins vital for your long term health.  The water – although cheap and plentiful – is equally important for overall health, albeit with more immediate benefits (especially if you’re lost in the Sahara Desert).

In many ways, an actively managed investment portfolio (hedge or traditional) is a combination of alpha – critical for long-term growth and development of a portfolio, and beta – cheap and plentiful.  Pure alpha can be a little sour and hard for some to swallow while pure beta is bland and provides little nutritional value.  But like water, the beta in a portfolio can sometimes be more immediately beneficial than alpha.  Our Sahara Desert wanderer would surely prefer a cup of water to a cup of concentrated orange juice.  Similarly, alpha may not always be the best (immediate) choice for a portfolio.

That’s essentially the argument made by this recent research note called “Is Alpha Dead?” by Andreas Steiner Consulting, a firm outside of Zurich.  The firm argues that…

…alpha does not automatically result in superior risk-adjusted returns and is not a suitable performance metric except for investors with an unlimited appetite for leverage. (our emphasis)

But one could argue that if only a tiny alpha was possible in a given market, it wouldn’t make it to the radar screens of most investors anyway.  In other words, the raw unlevered alpha would have to be large enough to attract the interest of investors who could conceivably lever it up into something substantial.  If the requisite leverage was not possible, most investors would likely identify that up front and steer clear.

“Most” investors.  But not all.  It appears the paper’s real targets are highly leveraged hedge funds, a small subset of the global hedge fund industry.  The firm continues…

“…Alpha cannot distinguish skill from leverage. Therefore, Alpha on a standalone basis is a misleading performance measure for risk-averse investors.”

In other words, if you know the market will deliver you the Sharpe ratio you need, then why waste your time with alpha?  That’s a fair question.  But we feel it’s a bit of a leap for the paper to make the following claim:

“…Alpha is in a very critical condition in the most optimistic interpretation of the arguments. A more realistic assessment of the conclusions would be that Alpha is dead.” (our emphasis)

“Sharpe Ratio Attribution”

Regardless of your views on the true fate of alpha, you might be interested in the way the firm decomposes the common Sharpe ratio to make its point

Starting with the CAPM, the divide everything by the standard deviation of the portfolio…

Then they replace the beta term with its constituent parts – portfolio-benchmark correlation times the ratio of portfolio volatility to benchmark volatility – and eventually get a portfolio Sharpe ratio

Put another way, the Sharpe ratio of a portfolio is the sum of two things:  its alpha and the benchmark’s Sharpe ratio grossed down by the portfolio/benchmark correlation (which is, of course, -1 to +1).

In a sense, this constriction is like a volatility-agnostic CAPM.  The returns of a portfolio are made up of systematic returns plus idiosyncratic returns.  Likewise, the Sharpe ratio of a portfolio is made up of a benchmark-derived portion and a skill-based portion.

So what?  Well, in order for an investment to add to the portfolio’s Sharpe ratio, it’s alpha therefore needs to meet the following criteria (what the paper calls the “lower bound for alpha”):

Clearly, as the paper says, “[T]he value of alpha is not ‘absolute’ but can only be assessed relative to a benchmark.”

Similarly, the value of concentrated orange juice can only be assessed after you determine if you’re dying of thirst at the moment. When you’re sure that water will deliver what you need, not concentrated O.J., then you should indeed go for the water…

But usually we can’t predict the direction of benchmark beta.  If you’re nervous about the direction of markets, then you may not want to invest in equity markets based on historical Sharpe ratio.  But assuming an appropriate time horizon, alpha may well be more consistent and less cyclical and betting on the market.

The paper goes on to criticize the use of inappropriate benchmarks to goose alphas and the tendency for some to turn a blind eye to “hidden betas”.  These, plus the arguments listed above lead the authors of this research note to unequivocally conclude that:

Alpha should not be used for performance evaluation purposes because it does not necessarily result in superior risk-adjusted returns.

Yet alpha seems to live on in what the authors call an “alpha-centric world.”  Why?  Perhaps like Churchill’s observation about democracy, alpha is the worst form of measurement except for all the others than have been tried.

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One Comment

  1. John R. Graham
    May 18, 2011 at 6:47 pm

    I like this a lot. It is simple because it uses one factor (i.e. CAPM) but it also rips the beta out of the alpha very elegantly. According to this formula, if there’s zero correlation between the portfolio and the benchmark, all of the alpha “counts”. If there’s perfect correlation between the portfolio and the benchmark, none of the alpha counts. That makes sense for alternatives.

    However, this measurement loses the benefit of having different measures of upside risk vs. downside risk.

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