Good and Bad Properties of the Kelly Formula

Introduction (Via Ziemba)

This issue I would like to discuss good and bad properties of the Kelly expected log capital growth criterion and in the process lead into the next columns on hedge funds by discussing two of the great traders who ran unofficial hedge funds. The main advantages are that if your horizon is long enough then the Kelly criterion is the road, however bumpy, to the most wealth at the end and the fastest path to a given rather large fortune.

Thorp (1997) has shown that the great investor Warren BuffettÕs Berkshire Hathaway actually has had a growth path quite similar to full Kelly betting. Figure 1 shows this performance from 1985 to 2000 in comparison with other great funds. Buffett also had a great record from 1977 to 1985 turning 100 into 1429.87, and 65,852.40 in April 2000.

Keynes was another Kelly-type bettor. His record running KingÕs College CambridgeÕs Chest Fund is shown in Figure 2 versus the British market index for 1927 to 1945, data from Chua and Woodward (1983). Notice how much Keynes lost the first few years; obviously his academic brilliance and the recognition that he was facing a rather tough market kept him in this job. In total his geometric mean return beat the index by 10.01 per cent. Keynes was an aggressive investor with a beta of 1.78 versus the benchmark United Kingdom market return, a Sharpe ratio of 0.385, geometric mean returns of 9.12 per cent per year versus Ð0.89 per cent for the benchmark. Keynes had a yearly standard deviation of 29.28 per cent versus 12.55 per cent for the benchmark. These returns do not include KeynesÕ (or the benchmarkÕs) dividends and interest, which he used to pay the college expenses. These were 3 per cent per year. Kelly cowboys have their great returns and losses and embarrassments. Not covering a grain contract in time led to Keynes taking delivery and filling up the famous chapel. Fortunately it was big enough to fit in the grain and store it safely until it could be sold.

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30. January 2010 by Miguel Barbosa
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