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 portfoliois3.3%perannumwithsimplecompounding.Theclientisconcernedaboutafurther downturn in the market as she thinks the recent bull market rally does not truly reflect the underlyingeconomicreality.Shehasthereforerequestedyouradviceonhowbesttoprotect 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 continuouscompoundingforallmaturities.Availableindexoptionsarequotedinincrements of 25 index points and the multiplier (per point) for each option contract is equal to10.

(a)Describe the options portfolio insurance strategy that would insure against your client's portfolio falling below 70 million over the next three months. Explain why this strategy fulfils the client's request and why hedging with index futures does notsuffice.

(b)Calculatethegains/lossesonthestrategyiftheleveloftheFTSE100indexinthreemonths iseither(i)5,250,or(ii)6,250,andprepareashortsummaryforyourclienttodiscussthe outcome of the insurance strategy in these two scenarios. (Note you do not need to calculate the insurancepremium).

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 Excel's GoalSeek (or otherwise) to estimate the implied volatility of the index, based onmarketpricesofthreemonthEuropeancallandputoptionsontheindex.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 dothis:

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