20 February 2012 at 13:11 GMT
Introductory words on alpha
In our little series on US sectors (part 1 and part 2) we examined the returns of US sectors since 1993 and tried to answer if investors are better off without financials in their portfolios. The conclusion was that a portfolio excluding financials, under the assumptions highlighted in part 2, did not perform significantly better when measured by Information Ratio, as the annualised alpha was only 0.5 percentage points.
Even more impressive was our analysis of the best portfolio (equally weighted portfolio consisting of energy, consumer staples and health care) as measured against the S&P 500. Despite an annualised 3.2 percentage point higher return over an almost 19-year period it was not statistically significant!
So what kind of performance does it take to eliminate the possibility that your excess performance is purely due to luck?
It takes Warren Buffett performance to statiscally beat the market
One of the best investment performances of all time is surely in the hands of Warren Buffet which has turned one US dollar invested in 1964 into almost 5,000 US dollars as of 2010, corresponding to an annualised return of 20.3 percent (see chart below). The S&P 500 has returned 6.7 percent annualised in the same period. Warren Buffet's investment company, Berkshire Hathaway, has produced an alpha of 13.6 percent annualised. This is a spectacular run, but is it enough to be validated as skill and not just luck?
In order to answer that question we did a two sample t-test on the annual returns of Berkshire Hathaway and S&P 500. The result is a t statistic of 3.93 and a p-value of 0.0002. In other words, we can easily reject the null hypothesis at 1 percent significance level and accept the alternative hypothesis, namely that the true difference in means is not equal to zero. Our statistical analysis also shows that Berkshire's Information Ratio is 0.96 for the period; given 0.5 has been found as the threshold for the top quartile of portfolio managers Warren Buffett's performance is truly incredible. Overall, Buffett's performance seems to be due to skill and not luck.
Another way to look at it is by observing the chart below, showing the annual excess return (alpha) between Berkshire Hathaway and the S&P 500. The orange dotted line shows the mean of annual alpha and it is clear that it is far above zero and only seven out of 46 years have seen a negative alpha.
How do you create alpha?
The key ingredients to superior active performance (defined by the Fundamental Law of Active Management) are skills (the correlation of forecast with realised returns), breadth (number of independent, skillful bets per year) and efficiency (the correlation of the manager's portfolio with an idealised paper portfolio in the absence of constraints and costs).
If we assume that efficiency is 1 or in other words that the portfolio implementation reflects the ideal portfolio (not possible in true investing), then we can reduce alpha generation as the product of skill and breadth.
This leads us to the obvious conclusion that two generic strategies exist for capturing alpha.
1) Few concentrated bets with a high edge (skill)
2) Many bets with a small edge
The first strategy is the one conducted by Warren Buffett. He believes in his edge and thinks that it is big and thus only places concentrated bets; at least that was how he used to invest before getting really big. It is only strategy implemented by many macro hedge funds which lead to their success around the financial crisis (mostly due to shorts on housing and financials). This kind of investing is very difficult and thus consistency is rarely found among this breed.
The other strategy is to place many bets with a small edge which is what high frequency trading firms and statistical arbitrage strategies (pair trading, sector trading etc.) do. This strategy is normally driven by computers and factor models which leads to high consistency, as long as the model works, but can lead to spectacular returns through the many bets.