Question

1. You are a portfolio manager with $10 million in stocks. You like the stocks you own, but the portfolio beta is 1.2 and you are concerned about a market decline. Your investors expect you to be “fully invested”, so you do not want to eliminate risk entirely. You decide that you would like to reduce the portfolio’s beta using futures, but only for the next 3 months. You know that the spot S&P index is at 1900. The dividend rate on the stocks in the index is 2.2%/year. The 3-month risk-free rate is .36%. At what price do you expect the 3-month futures to be trading? The value of one mini S&P contract is $50 times the index. How many contracts do you need to reduce portfolio beta to 1.0? Are you long or short?

2. You have a portfolio of Treasury notes. You have a report that shows the change in price of your portfolio from yesterday to today. You also know how much the 5-year Treasury benchmark yield changed. Estimate the duration of your portfolio using only the following info. Assume no accrued interest from yesterday, and no portfolio purchases or sales.

                               8/26/2017     8/27/2017

                           Portfolio value in millions at the close of the market         $50.125     $50.250

5-year Treasury benchmark yield to maturity     1.46%                 1.41%

                           Next, you would like to reduce the duration of your portfolio by 1.0 years, but do not want to sell any of your bonds. The 5-year Treasury note futures trade at 118.50. The contract is for $100,000 par amount of underlying notes. (That means that the value of one contract is 118.50*100,000/100=$118,500.) The duration of the futures underlying is 4.7 years. How many futures contracts do you need to short to reduce the combined duration by 1.0 years?

3. Today is Jan 27, 2016. You are negotiating with a bank to borrow $3 million for 90 days     at a rate of 3-month LIBOR plus 1.00%. You are confident they will approve you, but their credit process takes 30-45 days. You are worried that LIBOR will rise from today’s level, and would like to “lock in” today’s rate level. Eurodollar futures are trading at :

Bid     Ask

Feb 2016     99.3775     99.3800

Mar 2016     99.3450     99.3500

Apr 2016     99.3100     99.325

Last day of trading for each month is about the 15th. What action could you take? Ignore margin. Recall that the rate implied by the Eurodollar contract is 3-month LIBOR. Contract size is $1,000,000 notional.

4. BMW expects to sell an average of 2,000 autos each month for the next 3 years in the U.S. They build the cars in Germany; therefore, their costs are incurred in euros. The average sale price in the U.S. is $50,000/auto. They expect prices to stay at that level over the next several years. They would like to hedge so that their revenue is very predictable (in euros) from their U.S. sales. U.S. and German interest rates are flat for all maturities through 3 years at 2% in the U.S., and -0.35% in Germany. The current spot exchange rate is $1.12/euro. What should their hedge be?

Answer 1

1. (i) 3 months S&P future contract ( 1 contract ) would trade at approximately $ 1918.053

(ii) Theoretical contracts to be traded are 126 or 127 to bring down the portfolio beta to 1. ( basing on below calculation )

(iii) As portfolio of stocks are in LONG , Futures contract position should be SHORT to get perfectly hedged portfolio