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You need to hedge the risk in a stock portfolio that yourcompany owns in it's pension plan using the E-mini S&P500futures contracts (that has a multiplier of 50). The current valueof the portfolio is $325 million and the S&P500 is currently at2637.72 while the futures price for the next month delivery is at2643.25. You estimate that the beta of this portfolio is 1.1 whilethe beta of the S&P500 is 1. What position do you take infutures. You need to round to the nearest contract.

How would you change your answer if you decided to tailthe hedge?

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Nestor Rutherford
Nestor RutherfordLv2
28 Sep 2019

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Part 1. Suppose you need to hedge the risk in a stock portfoliothat your company owns in it's pension plan using the E-miniS&P500 futures contracts (which has a multiplier of 50). Thecurrent value of the portfolio is $325 million and the S&P500is currently at 2637.72 while the futures price (for next monthdelivery) is at 2643.25. You estimate that the "beta" of thisportfolio is 1.1 while the beta of the S&P500 is 1. Whatposition do you take in futures?

Part 2. In the above question suppose you want a tailed hedge.Now what position do you take in futures?

Part 3. In part 1 above suppose it is 1 month (1/12 of a year)until delivery of the futures and the 1-month interest rate is 3.5%per annum. Using the S&P500 index level and the futures pricewhat must the dividend yield on the S&P500 be in order topreclude arbitrage?

5. In early April, an insurance company portfolio manager has a stock portfolio of $200 million with a portfolio beta of 1.15. The portfolio manager plans on selling the stocks in the portfolio in June to be able to pay out funds to policyholders for annuities, and is worried about a fall in the stock market. In April, the CME Group S&P 500 Futures contract index is 2340.40 for a June futures contract ($250 multiplier for the contract).

a.What type of futures position should be taken to hedge against the stock market going down and how many future contracts are needed for this hedge?

[Hint: # contracts = [Amount Hedged / Futures Index Price x Multiplier] x Beta Portfolio

Type of Position _____________

Explain why ________________________________________

# of Contracts_____________

b. Suppose in June the stock market (S&P500 index) falls by 10% and the S&P500 futures index falls by 10% as well, what is the portfolio manager’s opportunity loss (gain) on his portfolio, and his futures gain (loss) and the net hedging result?

Spot Gain or Loss ____________ Futures Gain or Loss ___________

Net Hedging Result _____________

9. A portfolio manager has an equity portfolio that is valued at$75 million. The Portfolio has a current beta of .9 and a dividendyield of 1%. It is currently August 15 and the manager is concernedthat markets are volatile and the portfolio could lose value, sothey decide to hedge.

a. The manager will use the S&P 500 index contracts tohedge. The contract is settled n cash at $250 times the contractprice. The current S&P index value is 1484.43 and a DecemberS&P 500 index contract has a price of 1517.20?

b. Based on these expectations, should they take a short or longfuture position and why?

c. An optimal number of contract is N*=( Dollar value of theportfolio/dollar value of one future contract)X Portfolio beta?

d. Based on ( c ) Above compute N* and set up the appropriatehedge ?

e. On December 15 the position will be closed. The currentS&P 500 Index is 1410.20 and the current contract matures, soconvergence takes place. Compute the percentage loss in the S&Pindex and the percentage loss in the portfolio which will be ( %loss in market X Portfolio beta) ?

f. Compute the dollar loss on the portfolio the dollar change inthe future position and they dividend earned on the portfolio ( 3Months). Add these up to get the total hedge portfolio value?

g. How good was the hedge? Answer this by comparing the changein the market value of the portfolio to the change in the futuresposition?

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