A UK based client holds a welldiversified equity portfolio which has finally regained all the value it lost during the recent COVID19 related crash. The portfolio is currently worth 75 million and has a market beta of 1.5. Moreover, the expected dividend yield on the equity portfolio is 3.3% per annum with simple compounding. The client is concerned about a further downturn in the market as she thinks the recent bull market rally does not truly reflect the underlying economic reality. She has therefore requested your advice on how best to protect the value of her portfolio going forward, while still benefitting if the bull market continues. The FTSE100 index is currently at 5,969 and the dividend yield of the FTSE100 index is 2.1% per annum with simple compounding. The riskfree interest rate is 0.3% per annum with continuous compounding for all maturities. Available index options are quoted in increments of 25 index points and the multiplier (per point) for each option contract is equal to 10.

1. (a) Describe the options portfolio insurance strategy that would insure against your clients portfolio falling below 70 million over the next three months. Explain why this strategy fulfils the clients request and why hedging with index futures does not suffice.

2. (b) Calculate the gains/losses on the strategy if the level of the FTSE100 index in three months is either (i) 5,250, or (ii) 6,250, and prepare a short summary for your client to discuss the outcome of the insurance strategy in these two scenarios. (Note you do not need to calculate the insurance premium).

Your client is impressed by the proposed strategy, but she is surprised by how expensive the insurance premium is. You state that this is due to an increased market volatility brought about by the uncertainty over the future impact of COVID19. To explain things further you decide to investigate the implied volatility of the FTSE100 index using market option prices.

(c) Use Excels GoalSeek (or otherwise) to estimate the implied volatility of the index, based on market prices of threemonth European call and put options on the index. Specifically, complete the following table with the estimated implied volatilities (to 3 significant figures). Note you will need information stated earlier in the question to do this:

Strike	Call price	Call implied volatility	Put price	Put implied volatility
K = 5,400	589		112
K = 5,600	432		153
K = 5,800	292		213
K = 6,000	176		297
K = 6,200	91		412
K = 6,400	38		552

You should also answer the following questions:

1. Plot the implied volatility as a function of the strike price.

2. Are the option prices consistent with the assumptions underlying the BlackScholes model? Does the implied volatility depend on the moneyness of the option? Explain.

3. Is the implied volatility of one option class higher than the other? If so, explain why.