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- 1/25/10
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I'm reading a book called "Quantitative Trading: How to build your own algorithmic trading business" but Ernest P. Chan. In one of the chapters the author demonstrates that taking SPY over a period of nearly 14 years produces mean return of 0.1123 (11.23%) with stddev of 0.1691. assuming market rate of 4% we get mean excess return of 7.23%.
Then by Kelly's formula we get that the leverage factor should be ~2.52, hence the author concludes that the leveraged return is 0.04+(2.52^2)/2 = 0.13138.
Everything makes sense according to the formulas but something still bothers me: say that I make, on average, 11.23% per year on the SPY. If I invest $100K at the beginning of a "typical" year, I's earn $11,230 by the end of the year. If I leverage with the above factor then I'd earn, on average, 2.52*11,230 = $28,300 but since I only have $100K I'd have some financing costs which are, if I'm not mistaken, in the order of 0.04*152,000 = $6,080. So on average I's be making more than $22K on my $100K... which is much more than the 13.138% of the "correct" calculation. Can someone please help me understand why the naive calculation is wrong?
Then by Kelly's formula we get that the leverage factor should be ~2.52, hence the author concludes that the leveraged return is 0.04+(2.52^2)/2 = 0.13138.
Everything makes sense according to the formulas but something still bothers me: say that I make, on average, 11.23% per year on the SPY. If I invest $100K at the beginning of a "typical" year, I's earn $11,230 by the end of the year. If I leverage with the above factor then I'd earn, on average, 2.52*11,230 = $28,300 but since I only have $100K I'd have some financing costs which are, if I'm not mistaken, in the order of 0.04*152,000 = $6,080. So on average I's be making more than $22K on my $100K... which is much more than the 13.138% of the "correct" calculation. Can someone please help me understand why the naive calculation is wrong?
