FIN 550 Week 9
21-3
| FIN 550: Corporate Investment Analysis | ||||
| Week 9 Homework | ||||
| Andrea Bryant | ||||
| Chapter 21 | ||||
| 3.) | June Klein, CFA, manages a $100 million (market value) U.S. government bond portfolio for an institution. She anticipates a small parallel shift in the yield curve and wants to fully hedge the portfolio against any such change. | |||
| Conversion Factor for | Portfolio Value/ | |||
| Security | Modified Duration | Basis Points Values | Cheapest to Deliver Bond | Future Contract Price |
| Portfolio | 10 years | $100,000 | Not Applicable | $1,000,000,000 |
| U.S. Treasury bond | 8 years | $75.32 | 1 | 94-05 |
| futures contract | ||||
| a. | Discuss two reasons for using futures rather than selling bonds to hedge a bond portfolio. No calculations required. | |||
| First, futures enable hedging of the portfolio against any parallel shift during selling of the portfolio. | ||||
| Also, the manager can maintain liquid cash which may held in case of a future gain when selling. | ||||
| b. | Formulate Klein's hedging strategy using only the futures contract shown. Calculate the number of futures contracts to implement the strategy. Show all calculations. | |||
| No. of futures | = (10000000*10) / [(94+5/32)*75.32*8] | |||
| 17625.8694180414 | ||||
| c. | Determine how each of the following would change in value if interest rates increase by 10 basis points as anticipated. Show all calculations. | |||
| (1) | The original portfolio | |||
| (2) | The Treasury bond futures position | |||
| (3) | The newly hedged portfolio | |||
| Increase 0.001 | ||||
| Change in portfolio -0.001 x 10 x 10,000,000 | ||||
| -100000 | ||||
| Change in T bond position 17,625.87*94.15625*75.32*0.001 | ||||
| 125000.004127162 | ||||
| Newly Hedge Portfolio | 225000.004127162 | |||
| d. | State three reasons why Klein's hedging strategy might not fully protect the portfolio against interest rate risk. | |||
| It does not protect the portfolio fully since the number of futures may be adjusted when the cheapest bond value changes. | ||||
| e. | Describe a zero-duration hedging strategy using only the government bond portfolio and options on U.S. Treasury bond futures contracts. No calculations required. | |||
| The options are used to hedge against downward risk while on the upside the portfolio has limited potential. | ||||
21-4
| 4.) | A bond speculator currently has positions in two separate corporate bond portfolios: a long holding in Portfolio 1 and a short holding in Portfolio 2. All the bonds have the same credit quality. Other relevant information on these positions includes: | |||||
| Portfolio | Bond | Market Value (Mil.) | Coupon Rate | Compounding Frequency | Maturity | Yield to maturity |
| 1 | A | $6.00 | 0.0% | Annual | 3 years | 7.31% |
| B | 4 | 0.0 | Annual | 14 years | 7.31 | |
| 2 | C | 11.5 | 4.6 | Annual | 9 years | 7.31 |
| Treasury bond futures (based on $100,000 face value of 20-year T-bonds having an 8 percent semi-annual coupon) with a maturity exactly six months from now are currently priced at 109–24 with a corresponding yield to maturity of 7.081 percent. The “yield betas” between the futures contract and Bonds A, B, and C are 1.13, 1.03, and 1.01, respectively. Finally, the modified duration for the T-bond underlying the futures contract is 10.355 years. | ||||||
| a. | Calculate the modified duration (expressed in years) for each of the two bond portfolios. What will be the approximate percentage change in the value of each if all yields increase by 60 basis points on an annual basis? | |||||
| Modified Duration = (1/1+10.355) *100 | ||||||
| 8.81 | ||||||
| b. | Without performing the calculations, explain which of the portfolios will actually have its value impacted to the greatest extent (in absolute terms) by the shift yields. (Hint: This explanation requires knowledge of the concept of bond convexity.) | |||||
| The modified duration shows that a yield shift results to a 8.81% shift in the bond value | ||||||
| c. | Assuming the bond speculator wants to hedge her net bond position, what is the optimal number of futures contracts that must be bought or sold? Start by calculating the optimal hedge ratio between the futures contract and the two bond portfolios separately and then combine them. | |||||
| Based on the assumption that interest rates would increase sharply in the next year, the TD team recommended “plain vanilla” interest rate swaps as the most attractive hedging mechanism. Interest rate swaps would effectively lock in a fixed rate on CRP’s floating rate bank debt at interest rate levels that were attractive to the company. Andrew and Sara had certainly heard of interest rate swaps, but to this point CRP had never borrowed money at floating rates and had no real need for hedging products. Even the LIBOR floating rate borrowing option was a new concept to the company. | ||||||
21-6
| 6.) | As a relationship officer for a money-center commercial bank, one of your corporate accounts has just approached you about a one-year loan for $1,000,000. The customer would pay a quarterly interest expense based on the prevailing level of LIBOR at the beginning of each three-month period. As is the bank's convention on all such loans, the amount of the interest payment would then be paid at the end of the quarterly cycle when the new rate for the next cycle is determined. You observe the following LIBOR yield curve in the cash market: | |
| 90-day LIBOR | 4.60% | |
| 180-day LIBOR | 4.75 | |
| 270-day LIBOR | 5 | |
| 360-day LIBOR | 5.3 | |
| a. | If 90-day LIBOR rises to the levels “predicted” by the implied forward rates, what will the dollar level of the bank's interest receipt be at the end of each quarter during the one-year loan period? | |
| Rate | Interest | |
| 1st Quarter | 4.60% | $15,333.33 |
| 2nd quarter | 4.75% | $15,833.33 |
| 3rd quarter | 5% | $16,666.67 |
| 4th quarter | 5.30% | $17,666.67 |
| b. | If the bank wanted to hedge its exposure to failing LIBOR on this loan commitment, describe the sequence of transactions in the futures markets it could undertake. | |
| The bank may take advantage of interest rate swaps. | ||
| c. | Assuming the yields inferred from the Eurodollar futures contract prices for the next three settlement periods are equal to the implied forward rates, calculate the annuity value that would leave the bank indifferent between making the floating-rate loan and hedging it in the futures market and making a one-year fixed-rate loan. Express this annuity value in both dollar and annual (360-day) percentage terms. | |
| Rate | Interest | |
| 1st Quarter | 4.60% | $15,333.33 |
| 2nd quarter | 4.75% | $15,833.33 |
| 3rd quarter | 5% | $16,666.67 |
| 4th quarter | 5.30% | $17,666.67 |
| Total Interest Earned | $65,500.00 | |
| Interest Rate % | 6.55% | |
21-9
| 9.) | Alex Andrew, who manages a $95 million large-capitalization U.S. equity portfolio, currently forecasts that equity markets will decline soon. Andrew prefers to avoid the transaction costs of making sales but wants to hedge $15 million of the portfolio's current value using S&P 500 futures. |
| Because Andrew realizes that his portfolio will not track the S&P 500 Index exactly, he performs a regression analysis on his actual portfolio returns versus the S&P futures returns over the past year. The regression analysis indicates a risk-minimizing beta of 0.88 with an R2 of 0.92. | |
| Futures Contract Data | |
| S&P 500 futures price | 1,000 |
| S&P 500 index | 999 |
| S&P 500 index multiplier | 250 |
| a. | Calculate the number of futures contracts required to hedge $15 million of Andrew's portfolio, using the data shown. State whether the hedge is long or short. Show all calculations. |
| The number of future contracts required is | |
| (value of the portfolio / value of the index futures) x beta of the portfolio = [15,000,000/ (1,000 * 250)] * 0.88 | |
| 52.8 | (Short) |
| b. | Identify two alternative methods (other than selling securities from the portfolio or using futures) that replicate the strategy in Part a. Contract each of these methods with the futures strategy. First, shortening of the SPDRS may be more expensive than the futures in trading due to liquidity and transaction costs. Also, there might be a higher tracking error for futures compared to the SPDRs since the S&P 500 futures which can close under and over a fair value. The SPDRs do not have a cost of rolling over in which a future short position may incur if held longer than the expiration date. Also shortening a forward contract on the S&P forward index in which the price of this transaction is negotiable between either party. Forwards are less liquid therefore it may be difficult to reverse. It may also involve a counterparty risk. It however has an advantage of customization. |
21-10
| FIN 550: Corporate Investment Analysis | ||
| Week 9 Homework | ||
| Chapter 21 | ||
| Chapter 21: Problems 3(a-e), 4(a-c), 6(a-c), 9(a-b), 10(a-c), and 11(a-c) | ||
| Problem 10 | The treasurer of a middle market, import-export company has approached you for advice on how to best invest some of the firm's short-term cash balances. The company, which has been a client of the bank that employs you for a few years, has $250,000 that it is able to commit for a one-year holding period. The treasurer is currently considering two alternatives: (1) invest all the funds in a one-year U.S. Treasury bill offering a bond equivalent yield of 4.25 percent, and (2) invest all the funds in a Swiss government security over the same horizon, locking in the spot and forward currency exchanges in the FX market. A quick call to the bank's FX desk gives you the following two-way currency exchange quotes. | |
| Swiss Francs per U.S. Dollar | U.S. Dollar per Swiss Francs (CHF) | |
| Spot | 1.5035 | 0.6651 |
| 1 year CHF Futures | - | 0.6586 |
| a. | Calculate the one-year bond equivalent yield for the Swiss government security that would support the interest rate parity condition. | |
| ($1/0.6651) * (1 + R) * 0.6586 = 1.0425 0.990 = 0.990 R = 1.0425 R= 5.28% | ||
| b. | Assuming the actual yield on a one-year Swiss government bond is 5.50 percent, which strategy would leave the treasurer with the greatest return after one year? | |
| The return on the CHF would be greater. If the actual rate is 5.5% for a one year Swiss government bond, then the return on CHF investment would be greater since ($1 / 0.6651) * (1 + R) * 0.6586 ($1 / 0.6651) * (1 + 0.55) * 0.6586 = 1.0447 | ||
| c. | Describe the transactions that an arbitrageur could use to take advantage of this apparent mispricing, and calculate what the profit would be for a $250,000 transaction. | |
| First, he could borrow the $250, 000 domestically at 4.25 $% and convert it to $375883.33 CHF. Then he can buy Swiss government bonds and engage in a forward contract in order to reconvert the proceeds after a year. The money should then be invested at 5.5% where the arbitrageaur may have $ 396556.91 which he can convert into dollars at a forward rate of 0.6586 $/CHF. He would therefore make a profit of $547.38 before commissions. | ||
| Solution | ||
| a. | ||
| b. | ||
21-11
| 11.) | Bonita Singer is a hedge fund manager specializing in futures arbitrage involving stock index contracts. She is investigating potential trading opportunities in S&P 500 stock index futures to see if there are any inefficiencies that she can exploit. She knows that the S&P 500 stock index is currently trading at 1,100. | |
| a. | Assume that the Treasury yield curve is flat at 3.2 percent and the annualized dividend yield on the S&P index is 1.8 percent. Using the cost of carry model, demonstrate what the theoretical contract price should be for a futures position expiring six months from now. | |
| b. | Describe the set of transactions that Bonita would have to undertake to take advantage of an actual futures contract price that was (1) substantially higher or (2) substantially lower than the theoretical value you established in Part a. | |
| c. | Assuming that total round-trip arbitrage transaction costs are $20 for the set trades described in Part b, calculate the upper and lower bounds for the theoretical contract price such that arbitrage trading would not be profitable. | |
| a) | Future contract price using cost of carry method | |
| FO,T = SO + SO(RFRT - dt) | ||
| Where, | ||
| FO,T is the future price | ||
| So is the spot price of index | 1100 | |
| RFR is the risk-free rate | 3.20% | |
| dt is the dividend yield | 1.80% | |
| Placing the values in formula we get, | ||
| FO,T = | =1100+1100*((3.2%/2)-(1.8%/2)) | |
| Contract price for 6 month future contract = | 1107.7 | |
| b) | Spot Price = | 1100 |
| Future Price = | 1107.7 | |
| It means she buys index at 1100 and short futures at 1107.70 | ||
| If actual future contract price is subatantially higher: | ||
| Suppose that actual future contract price is 1120 | ||
| The profit will be: | ||
| Profit will be | =(1107.7-1120)+(1120-1100) | |
| 7.7 | ||
| If actual future contract price is subatantially lower: | ||
| Suppose that actual future contract price is 1080 | ||
| Profit will be | =(1107.7-1080)+(1080-1100) | |
| 7.7 | ||
| The above calculation shows that the profit will be same irrespective of index value. | ||
| The lossrs of index will be offset from gain that will arise from future. | ||
| c) | If total round-trip arbitrage transaction costs are $20 the upper and lower bounds | |
| for the theoretical contract price will be 1120 and 1080 | ||