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The Investment Committee of UoM has suggested that it may be time to take some "insurance" on the U.S. equity portfolio, given "rich valuations" in the U.S. Equity markets.
As the CRO, they suggest that you look into designing this "insurance" program for the U.S. Equity Portfolio, leaving the mechanics and logistics up to you. Excited about this project, you initially think about purchasing Put Options on the several different stock positions in the portfolio (over 300 individual securities in multiple industries). Though, you realize various complexities with this approach: (1) Various securities have thinly traded options, and some don't have any at all; (2) Option expirations are dissimilar for dissimilar securities; (3) Some options can only be purchased in the OTC market (dealing with the OTC market brings many more complexities, such as paperwork and credit risk); and (4) Even if options were available for all the underlying securities, buying, selling and monitoring all those option positions could be a recipe for a serious headache.
Explain the appropriate number of option contracts to purchase, and run a scenario analysis to explain what the net payoff of the U.S. Equity Portfolio given the following market scenarios:
(i) Calculate the unweighted average daily variance for the time series. Explain any assumptions or simplifications you have made, and the working for each step.
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