# How to calculate "Differential Sharpe ratio"?

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?

• 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/… Nov 16, 2018 at 15:32
• 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 Nov 19, 2018 at 4:05
• In fact, the whole thing would fail whenever (A_(t))^(2) > B_(t) so I assume you can't just initialize with any values Nov 19, 2018 at 4:06
• 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). Nov 20, 2018 at 13:26