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A few years back in an interview I remember being asked to derive the Sharpe ratio from the correlation between a pre-open daily signal and the open-close returns. I think you had to make some assumptions regarding the risk/reward and accuracy but you could start with a correlation of say 0.05 and back out a sharpe ratio.

I'm interested in revisiting this and can't seem to find anything similar online. Anyone know of any resources?

Update: Happy with comment answer, thanks!

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  • $\begingroup$ The 'correlation profile' exercise in Short Sharpe Course does this computation, finding that the Sharpe is approximately equal to the correlation under a 'small angle approximation'. $\endgroup$ – steveo'america Sep 17 '20 at 22:27
  • $\begingroup$ Thank you! So we have the optimal allocation being $c \frac{\mu + \rho \sigma f_t}{(\mu + \rho \sigma f_t)^2 + (1 - \rho^2) \sigma^2}$, from the next page I use $c = \rho$ and that's the sharpe? Testing for $\rho = 0.1$, $\mu = 0$, $\sigma = 0.01$, $f_t = 1$, $c = \rho$ gives a sharpe of 1 which seems reasonable. Is that correct? $\endgroup$ – Quantoisseur Sep 18 '20 at 12:15
  • $\begingroup$ $c$ is a positive constant which adjusts the allocation to reach a desired level of volatility. The (optimal) signal-noise ratio is $\zeta_*$ and that's approximately equal to $|\rho|$. $\endgroup$ – steveo'america Sep 18 '20 at 22:41
  • $\begingroup$ Okay, so then I'm confused at how to arrive at the Sharpe ratio which shouldn't be scalable. $\endgroup$ – Quantoisseur Sep 18 '20 at 23:11
  • $\begingroup$ It's a small angle approximation, so the Sharpe is only approximately $|\rho|$ when that number is small. That's a reasonable assumption when looking at a daily signal, and the kind of alpha available to mere mortals. $\endgroup$ – steveo'america Sep 19 '20 at 5:13

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