What $R^2$ does an intraday signal need?

(a) Prove (5.24) and show that a position proportional to the predictor, $w = x/\sigma_x$, earns $E[wy] = \rho\sigma_y$. (b) For a Nifty-futures signal predicting a half-hour return with $\sigma_y = 0.30\%$, and an all-in round-trip cost of 8 bp, what correlation and what $R^2$ does the sign strategy need to break even?