Imagine you are a provider of portfolio insurance. You are establishing a four-y

Question

Imagine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $70 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 6.2% per year. Assume for simplicity that the portfolio pays no dividends (or that all dividends are reinvested). What percentage of the portfolio should be placed in bills? What percentage of the portfolio should be placed in equity? Calculate the put delta and the amount held in bills if the stock portfolio falls by 3% on the first day of trading? What action should the manager take?

Explanation / Answer

Answer: N(d 1 ) – 1 = 0.7422 – 1 = –0.2578.

Place 25.78% of the portfolio in bills,

74.22% in equity ($51.954 million)

At the new portfolio value, the put delta becomes –0.2779, so that the amount held in bills should be: ($67.9 million * 0.2779) = $18.87 million. The manager must sell $0.826 million of equity and use the proceeds to buy bills.

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