Tracking difference

A Nifty 50 index fund has an expense ratio of 0.30%, keeps an average 2% of assets in cash, and over a year the index earns 14% while cash earns 6.5%. Trading costs from flows are 0.08%, securities-lending income 0.03% and the dividend-timing loss 0.03% (illustrative). (a) Compute the expected tracking difference from (6B.25). (b) With index volatility of 16%, compute the tracking error contributed by cash. Add an independent 0.10% from sampling and compute the total tracking error. (c) Compare your answers with SEBI's 2% tracking-error limit for equity index funds. Which number should an investor use to compare two index funds, and why? (d) Derive (6B.25) and state where the first-order approximation could fail.