P1.T4. Problem 18.16 Portfolio insurance with future

[eszaknyugat]

Hi David,

Problem 18.16 d) (p.100) Portfolio insurance with 9-month index future.
There are 2 aspects I do not understand:
1. Why we use 119,7 M for calculating short position and not the original 360 M value? We hedge the S&P500 with the future contracts. How short put came into the picture?
2. Why we adjust with 250 (trading days i guess)? Spot delta of future (1.023) is expressed in 9 months, isn't it?

Thank you for your guidance!
eszaknyugat

 

[David Harper CFA FRM]

Hi @eszaknyugat FYI, the source question is here, it's a Hull question (not mine) FWIW. This isn't a hedge but rather, per 18.13 Portfolio Insurance in Hull, this is creating a synthetic put option as insurance. You will notice that answer (C) gives "(c) Delta of one put = -0.3327 such that 33.27% of portfolio ($119.77 million) should be sold." That is, 119.7 is what would could call "delta dollars" (delta of -0.3327 is also called a percentage Greek, it is dimensionless by itself). So you are absolutely correct, we'd hedge this with futures contracts. But this is not a hedge, it's synthetic option to provide insurance. Under this approach of using index future to synthesize put options, we need to short futures contracts with 119.7 delta dollars. The resulting answer of 390 contracts gives the correct delta dollars: 390 futures contracts * 1200 index value * 250 multiplier * 1.022755 = $119.784 million (just working backwards from the solution, which I find much easier). So the solution for the number of contracts gets 390 contracts = $119.784 million / (1200 index value * 250 multiplier * 1.022755), effectively. So 250 is not trading days, 250 is the multiplier on the S&P index, it's a contract feature. See contract feature (near the top) at http://www.cmegroup.com/trading/equity-index/us-index/sandp-500_contract_specifications.html. Finally, yes delta of contract is nine-months per exp[(riskfree - dividend yield)*T] = exp[(6% - 3%)*0.75] = exp[3%*0.75] = 1.022755. I hope that helps,