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Instead of using the "sliding the time window" method of calculating the sharpe ratio under online framework, they've defined "differential sharpe ratio" as such

But under equation 5, you can recursively calculate At and Bt given the current return and previous values of A and B But when t = 1, what are the initial values of At and Bt?

  • $\begingroup$ It is OK to start $A_t$ and $B_t$ at zero since they are moments. Further discussion of the Differential Sharpe Ratio is here quant.stackexchange.com/questions/37969/… $\endgroup$ – noob2 Nov 16 '18 at 15:32
  • $\begingroup$ If you initialize such that A_(t) and B_(t) are zeroes, then if you look at the denominator for equation 4, you would get zero as your denominator $\endgroup$ – Kevvy Kim Nov 19 '18 at 4:05
  • $\begingroup$ In fact, the whole thing would fail whenever (A_(t))^(2) > B_(t) so I assume you can't just initialize with any values $\endgroup$ – Kevvy Kim Nov 19 '18 at 4:06
  • $\begingroup$ You have to wait until $A_t,B_t$ stabilize to meaningful non-zero values before you plug them into the expression for $D_t$ obviously. To compute $D_t$ today if you use a month's worth of prior $R_t$ values you will have meaningful nonzero $A_t,B_t$ to compute today's $D_t$. Then tomorrow you just update them with equation (5) and then (4). $\endgroup$ – noob2 Nov 20 '18 at 13:26

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