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> > Sharpe Ratio
>>
>> Japanese Yen only 0.94
>> 3 Commodity (Optimal weighting) 1.76
>> 15 Commodity (Optimal weighting) 2.20
>> 15 Commodity (Equal Weighting) 1.36
>
>Bob, you said you'd expect an N-commodity portfolio to have a Sharpe
>ratio sqrt(N) larger than a 1-commodity portfolio. Obviously the Yen
>has a higher Sharpe than the average. But shouldn't the optimal 15
>portfolio be sqrt(15)/sqrt(3) = 2.24x better than the optimal 3? But
>in reality it's 1.25. Why the discrepancy?
Congratulations! I wondered if anybody would notice that...
The improvement from JY to 3-commodity should have been sqrt(3) = 1.73. It was 1.87. The discrepancy is due to the fact that the returns on the three were not quite equal so the optimum mix was not quite equal - but it was close. I made sure those three were not correlated to check the theory.
But when I got to 15 commodities, lots of them were partially correlated so the improvement was less than it would have been if they had been uncorrelated.
Bob Fulks
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