Alpha and Sailing
Jul 21st, 2006 | Filed under: CAPM / Alpha TheoryBy: Alpha Male
This article (”Portable Alpha: Beta & Alpha, Both Important, Totally Different & Great Together“, July 2005) on combining non-correlated assets will resonate with sailors. Ferrell and Podewils propose a method of analysing the benefits of diversification using vector analysis. While they don’t specifically make reference to sailing, they use many of the same concepts.
“Risk vectors are a helpful tool in measuring Beta and Alpha risks and correlations. The length of each line shows the amount of expected volatility. The angle created by the intersection of the two lines shows the correlation of their risks. If we observe the risk of a portfolio comprised of a combination of two perfectly correlated risks that are both long investments, the combined vectors are double the original volatility. Returns are also doubled, in both positive and negative directions.”
For sailors, one way of looking at Ferrell and Podewils’ approach is to view the volatility of the equity market as the wind direction where the length of the vector represents the annualized standard deviation of the market (e.g. S&P500) rather than the wind speed. Let’s say the annualized standard deviation of the S&P500 was 20% and that your whole portfolio was made up of the S&P500 (e.g. via SPDRs). Then let’s say you replaced half of your holdings with a fund that had a 1.0 correlation to the market. Since the correlation is one, the volatilities would be purely additive and your overall portfolio volatility would remain 20%. With a correlation of 1.0, you can never lower your volatility from 20%. You are essentially on a “run” with the market. This is illustrated in the chart at left. (sailors: remember to flip the arrow directions to understand chart) On a run, your complex and expensive sailboat is unable to add any value beyond a leaf being blown across the water.
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