The Importance Of Ii (As Sharpe Ratio)

A reader ezbentley late pointed out a little-noticed fact inward the derivation of Kelly's formula: if nosotros utilise the optimal Kelly leverage, together with thus the measure divergence of the annualized compounded growth charge per unit of measurement of your equity is none other than the Sharpe ratio (Sdev=S). This fact is of mild involvement inward itself, but its implication has relevance to around other interesting fact of behavioral finance, thus I volition reproduce our discussions here.

Suppose our strategy has an annualized Sharpe ratio of 2. According to the inward a higher house result, Sdev=2 every bit well. This may startle around of us: a measure divergence of 200% of our compounded increment charge per unit of measurement g - wouldn't ruin live on real likely? But banking corporation check out g itself: g=S^2/2, thus g=2 when S=2, which agency that g itself is just 200%. Influenza A virus subtype H5N1 Sdev of 200% hither agency that if the increment charge per unit of measurement drops ane measure divergence below its mean, nosotros volition withal deal non to lose coin for the year. Another mode to pose this is that in that place is a 84.1% lead chances that our annual supply volition live on greater than 0, based on the Gaussian distribution.

It gets ameliorate if southward goes inward a higher house 2. For example, at S=3, g=4.5, but Sdev is simply 3. So you lot tin dismiss come across that every bit southward goes inward a higher house 2, a 1 measure divergence fluctuation of g below the hateful volition withal acquire you lot a positive number: profitable for the year.

This is a real interesting result: this agency that S=2 is actually an of import threshold inward to a greater extent than ways that I realized. From behavioral finance experiments, nosotros already know that humans demands $2 profits for $1 risk. Given the universal wish of portfolio managers non to lose coin on the year, it turns out that the need of a Sharpe ratio of at to the lowest degree two is quite rational!

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