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发表于 2012-4-2 14:08
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George Kaufman, portfolio manager and CEO of Kaufman Co., is extremely busy. He has a number of important issues that must be dealt with before the end of the week.
The portfolio Kaufman manages consists of $40 million in bonds and $60 million in equities. The modified duration of the bond portfolio is 6.3. The beta of the equity portfolio is 1.25. The holding period for each is 1 year. Kaufman also has the authority to borrow up to $25 million which may be invested on a short-term basis to earn the spread between the borrowing rate and the investing rate.
Kaufman is afraid that interest rates will rise 25 basis points in the near future and would like to decrease the duration of the bond portion of the portfolio to 5.0 for a short period of time. He prefers to use futures contracts to do this since it is a temporary change and he does not want to actually sell bonds in the portfolio. Kaufman is considering using a Treasury bond futures contract that has a modified duration of 4.2, a yield beta of 1.1, and a price (including the multiplier) of $245,000.
Kaufman would like to borrow money three months from today so he can invest at the expected higher interest rates. However, he would like to lock in today’s interest rates for the loan. To do this he is considering locking in a loan rate using a forward rate agreement (FRA). A cash settlement will be made based on the actual interest rate three months from now, relative to the FRA interest rate. If Kaufman decides on this strategy, he would borrow $20 million at 5 percent for 9 months. The loan date would start three months from today.
The equity portion of the portfolio has performed extremely well over the recent past and Kaufman must decide on one of the following two strategies:
Equity Strategy 1: Kaufman could hold on to his current profits for the next six months which should make the reported annual return rank in the top one percentile of similar portfolios. Again, Kaufman prefers to use futures contracts instead of selling stocks to lock in the profits. The portfolio is composed of the same stocks and sector weightings as the S&P 500. The contract on the index is at 2000 (with a multiplier of 250), and it expires in 6 months. The risk free rate is 2 percent and the dividend yield on the index is 3 percent.
Equity Strategy 2: Kaufman believes there is a chance the market may move significantly over the next six months. To benefit from the expected move in the market, Kaufman could increase the equity portion of the portfolio from its current beta of 1.25 to 1.4 by using equity index futures. The appropriate equity index futures contract that Kaufman is considering using has a beta of 0.90 and a price (including the multiplier) of $335,000.
Finally, Kaufman Co. is expecting a $6 million cash inflow in 4 months and would like to pre-invest the funds to create the same exposure to the bond and stock market that is found in the original portfolio. The most appropriate stock index futures contract for accomplishing this has a total price (including the multiplier) of $315,650 and a beta of 1.10. The most appropriate bond index futures contract has a total price of $115,460, a yield beta of 1.05 and an effective duration of 6.2.
Assume Kaufman Co. uses a FRA to hedge the loan rate. If interest rates are 4.85 percent at expiration of the FRA, the settlement payment is closest to: A)
| $21,710, with the bank paying Kaufman the settlement. |
| B)
| $21,710, with Kaufman paying the bank the settlement. |
| C)
| $28,739, with Kaufman paying the bank the settlement. |
|
| Settlement payment | = 20,000,000 × [(0.0485 – 0.05) × (270 / 360)] / [1 + ((0.0485)(270 / 360)] | | = 20,000,000 × (-0.001125 / 1.036375) = $21,710.29 |
Since the realized rate at the time of the loan, 4.85%, is lower than the contract rate of 5%, Kaufman would want to pay to get out of the FRA so that he can borrow at the prevailing lower rate. (Study Session 14, LOS 34.i)
The value of the bond portfolio given a 25 basis point increase is closest to:
In this case use the modified duration of the bond portfolio, 6.3 to find the value of the portfolio given a 25 basis point increase in rates:
New value = $40,000,000 × (1 - (6.3 × 0.0025)) = $39,370,000 (Study Session 9, LOS 23.g)
The number of Treasury bond futures contracts that Kaufman would need to reduce the duration of the bonds in the portfolio is closest to:
Contracts = (Yield Beta) [(MDTarget – MDP) / MDF][VP / (Pf(Multiplier))]
Contracts = 1.1 × [(5 – 6.3) / 4.2] × ($40,000,000 / $245,000) = -55.59
To reduce the duration of the portfolio, take a short position in the futures contract. Note that we must round the number of contracts up to 56 since partial contracts cannot be traded. (Study Session 15, LOS 36.d)
Kaufman is interested in increasing the beta of the equity portfolio to 1.4 for a brief period of time. Kaufman is expecting a(n): A)
| increase in the market; a long position in approximately 27 contracts will accomplish this target. |
| B)
| decrease in the market; a short position in approximately 72 contracts will accomplish this target. |
| C)
| increase in the market; a long position in approximately 30 contracts will accomplish this target. |
|
Number of Contracts = (Target Beta – Portfolio Beta / Beta on Futures) × (Value of the portfolio / Price of the futures × the multiplier).
Number of Contracts = [(1.4 – 1.25) / 0.90] × ($60,000,000 / $335,000) = 29.85 contracts.
The positive sign indicates that we should take a long position in the futures to “leverage up” the position. If that is Kaufman’s goal, he must be expecting an increase in the market. (Study Session 15, LOS 36.a)
How many S&P index futures contracts would Kaufman need to buy or sell to create a six-month synthetic cash position? A)
| Sell approximately 121 contracts. |
| B)
| Buy approximately 121 contracts. |
| C)
| Sell approximately 400 contracts. |
|
[$60,000,000 × (1.02)0.50] / (2000 × $250) = 121.19 contractsKaufman would need to sell the contracts to create the synthetic cash (zero equity) position. If he were converting cash to a synthetic equity position, he would of course buy contracts. (Study Session 15, LOS 36.c)
The most appropriate strategy to pre-invest the anticipated $6 million inflow would be to: A)
| buy 21 bond futures contracts and buy 35 stock futures contracts. |
| B)
| buy 22 bond futures contracts and sell 13 stock futures contracts. |
| C)
| buy 22 bond futures contracts and buy 13 stock futures contracts. |
|
Take the existing portfolio weights, 40% debt and 60% equity and apply them to the new money that is coming in. Also, “mirror” the duration and beta of the original portfolios.
Number of bond futures = 1.05 × [(6.3 - 0) / 6.2] × [(6,000,000 × 0.40) / 115,460] = 22.18 contracts
Number of stock futures = [(1.25 – 0) / 1.10] × [(6,000,000 × 0.60) / 315,650] = 12.96
Kaufman Co. would take a long position in both the stock index and bond futures contracts because it is synthetically creating an existing portfolio until the actual $6 million is received and can be invested. (Study Session 15, LOS 36.e) |
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