(a) (3 minutes) We wish to compare the performance of 2 executing brokers, A and B, and divide our order flow randomly and equally between them. We observe that out of 400 orders, 175 orders are sent to broker A. Should we be concerned? Why or why not? (b) (10 minutes) Assume normally-distributed returns with mean, 0, and variance, 1, and a signal which forecasts the sign of the returns perfectly. (Hence the signal has values of +1, 0 or -1.): i. What is the correlation between the signal and the returns? ii. What would the correlation be if the variance is o2? iii. How, if at all, would the correlation change if the mean increases? What happens to the correlation if the mean decreases? Prove your answers mathematically and/or graphically. (a) (3 minutes) We wish to compare the performance of 2 executing brokers, A and B, and divide our order flow randomly and equally between them. We observe that out of 400 orders, 175 orders are sent to broker A. Should we be concerned? Why or why not? (b) (10 minutes) Assume normally-distributed returns with mean, 0, and variance, 1, and a signal which forecasts the sign of the returns perfectly. (Hence the signal has values of +1, 0 or -1.): i. What is the correlation between the signal and the returns? ii. What would the correlation be if the variance is o2? iii. How, if at all, would the correlation change if the mean increases? What happens to the correlation if the mean decreases? Prove your answers mathematically and/or graphically