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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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Bunny Greenfelder
Bunny GreenfelderLv2
28 Sep 2019

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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 _____________

A fund manager has a portfolio worth $50 million with a beta of 0.95. The manager is concerned

about the performance of the market over the next 2 months and plans to use 3-month futures

contracts on the S&P 500 to hedge the risk. The current level of the index is 2,300, one contract is on

250 times the index, the risk-free rate is 5% per annum, and the dividend yield on the index is 2%

per annum.

a) Calculate the theoretical futures price of a 3-month S&P 500 futures price.

b) How many futures contracts should the manager buy or sell to hedge the exposure to the

market over the next 2 months?

c) Calculate the value of the hedged position (stock and futures) if the index in 2 months is 2000.

2. An equity portfolio manager rarely if fully invested in thefund but will have some funds in cash. Unfortunate, this createswhat is called a cash drag on the portfolio due to the low returnon cash funds. On way to deal with this is called neutralizingcash. It involves using stock index futures to synthetically raisethe equity position of the portfolio to overcome the cash drag. Theportfolio currently has an asset value of $500 million. 95% of itis invested in a stock portfolio that has an average beta=1.0. Thereaming 5% is in a cash fun. In a six month period the broad market(s&p) rise by 11.50% while the cash fund rises by 2.5%.

a. Based on the portfolio weight, compute the portfolio weightaverage over the six month period. Compare this return to the boardmarket return. How much did the portfoliounderperform the market?

b. One way to add return is to synthetically add stock exposurewith stock index futures. We want to have a synthetically portfoliothat has 100% stock exposure so we need to add 5% of the portfoliovalue in stock index future? The current index future price is 1200and the contract size is $250 times the index. This is differentthan hedge in that we want the additional stock exposure so wewould take a long position inn future. The chosen contract willmature three months from today?

c. In three months the following changes have taken place: TheS&P 5 has gone from 1120 to 1220 and the contract matures soconvergence taken place. Based on portfolio these parameters,analyze the performance of the futures position. How much portfoliovalue did the extra equity exposure add?

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