Consider a portfolio of 20,000 shares in Company A. The shares are currently priced at $100 each. You want to use portfolio insurance (a synthetic put), to protect the value of the portfolio from falling below $92 per share over the next 12 months. No dividends are expected over the period. Assume a two period binomial model, a continuously compounded risk free rate of 12% p.a and that prices will move +/- 10% each 6 months. You are required to construct the synthetic put so that the cost of insurance is incurred now.

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 (synthetic put) in total and per share. How does this compare to the price of an equivalent put obtained via the two-period binomial model? Show all workings.

c)  Calculate the value of the portfolio per share in 12 months’ time assuming the stock price decreases in both periods. Did the portfolio insurance meet its objective with respect to protecting the value of the portfolio? Why/why not? Show all workings.

d)  Briefly comment on two sources of risk associated with the strategy.