Consider a portfolio of 10,000 shares currently priced at $50 each. You want to use portfolio insurance to protect the value of the portfolio from falling below $44 per share over the next 12 months. No dividends are expected over the period. Assume a two-period binomial model, a risk-free rate of 2% p.a. continuously compounded and stock volatility of 25% p.a. You are required to construct the portfolio so that the cost of insurance is incurred now.
Mean 0.03
Median 0.05
Standard deviation 0.99
Skewness -3.66
Kurtosis 93.93

a) What steps are required to protect the portfolio? Show the cashflows now, in 6 months and 12 months’ time assuming the stock price decreases in both periods. Show all workings.
b) Calculate the cost of the insurance. How does this compare to the price of an equivalent put? Show all workings.
c) Calculate the value of the portfolio per share in 12 months’ time. Did the portfolio insurance meet its objective with respect to protecting the value of the portfolio? Why/why not? Show all workings.