Return arithmetic on election week

Nifty closed at 23,263.90 on 3 Jun 2024, 21,884.50 on 4 Jun and 22,620.35 on 5 Jun. (a) Compute the simple and log returns for 4 Jun and 5 Jun. (b) Compute the two-day simple and log returns from 3 Jun to 5 Jun directly, and check them against the aggregation rules of Proposition 2.1(a). (c) An investor held 60% in a Nifty ETF and 40% in a gold ETF on 3 Jun. On 4 Jun the gold ETF returned +1.2% (assume this figure). Compute the portfolio's simple return and its log return. Compare the log return with the weighted average of the two assets' log returns and explain the sign of the difference.