...RSM332 - Final Exam - Winter 2011 - solutions 120 marks Stocks a) $208.33 million (2 marks) b) NPV of project = $8.1 million (3 marks), new price per share = $21.64 (3 marks) c) any good 3, examples listed (2 marks each, 6 marks total) d) any three listed (2 marks each, 6 marks total) Bonds a) strip coupons payments from 18,000 of the 10 year 4% coupon bonds (4 marks), strip the $12,000,000 par payment from the year-7 coupons of 300,000 10-year bonds (4 marks), sell off all the remaining cash flows as zero coupon bonds (or keep them in inventory) (4 marks) b) the return on the coupon is greater than the capital loss (2 marks) c) reduced risk means a reduced YTM (3 marks) d) Rogers is at a higher risk of default that the Canadian Government and thus has a higher YTM (2 marks), a higher YTM means a lower Duration (1 mark) Portfolios 1 a) WB = 1-WA (2 marks), solved portfolio vol up to quadratic equation (2 marks), WA = 0.79762 or 0.05413 (2 marks), WA = 0.79762 (2 marks) b) E(rp) 14.19% (4 marks), give full marks in follow-through errors from a, or if a rate is assumed and calculate E(rp) c) country specific risks can be diversified away (4 marks) d) Overweighing of home country (2 marks), more risk, no extra return (2 marks) Portfolios 2 a) correlation = -1 (3 marks) b) solved portfolio vol up to quadratic equation (3 marks), WA = 0.375 (3 marks), E(rp) = 18.25% (2 marks) c) arithmetic mean does not consider...
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...Exam 1998--Question 17 A bond is trading at a price of 100 with a yield of 8%. If the yield increases by 1 basis point. the price of the bond will decrease to 99.95. If the yield decreases by 1 basis point. the price of the bond will increase to 100.04. What is the modified duration of the bond? a) 5.0 b) -5.0 c) 4.5 d) -4.5 Example 1-6: FRl\1 Exam 1998--Question 22 What is the price impact of a 10-basis-point increase in yield on a 10-year par bond with a modified duration of 7 and convexity of 50? a) -0.705 b) -0.700 c) -0.698 d) -0.690 Example 1-8: FRl\1 Exam 1998--Question 20 Coupon curve duration is a useful method for estimating duration from market prices of a mortgage-backed security (MBS). Assume the coupon curve of prices for Ginnie Maes in June 2001 is as follows: 6% at 92. 7% at 94. and 8% at 96.5. What is the estimated duration of the 7s? a) 2.45 b) 2.40 c) 2.33 d) 2.25 Example 1-9: FRl\'1 Exam 1998--Question 21 Coupon curve duration is a useful method for estimating convexity from market prices of an MBS. Assume the coupon curve of prices for Ginnie Maes in June 2001 is as follows: 6% at 92. 7% at 94. and 8% at 96.5. What is the estimated convexity of the 7s? a) 53 b)26 c) 13 d) -53 Example 1-10: FRM Exam 2001-Question 71 Calculate the modified duration of a bond with a Macauley duration of 13.083 years. Assume market interest rates are 11.5% and the coupon on the bond is paid semiannually. a)...
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...$100 to be received on 12/31/92 and purchased on 9/17/92 is available either in the form of $100 par amount of the 12/31/92 bill or in the form of $100/(1+.09125/2) par amount of the 9 1/8’s of 12/31/92. (Indeed, since $100 par of the 9 1/8’s will pay off $(100 + 9.125/2) on 12/31/92, $100/(1 + .09125/2) par amount of the 9 1/8’s will pay off $100.) Can we buy this cash flow low through one instrument and sell it high through the other? We must see if the asked price of one of the instruments is lower than the bid price of the other. For the T -bill, we have computed from Example 14 the asked price: A PBILL ≈ 99.17 . B PBILL = 100 1 − d nSM 360 = 100 1 − .0288 105 360 ≈ 99.15 . 3. Part a. Settlement is 9/17/92, the next coupon date is 12/31 the last coupon date is 6/30/92, therefore nSN = 105, nLS = 79, and nLN = 184. In addition, c = .09125. Accrued interest is...
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...6954 2 Table 1- Zero option prices A. Given the current term structure of interest rates, we can easily derive the prices of zero-coupon bonds. As the interest rates are continuously compounded, the formulas used to calculate the discount factors and the zero prices are: ������(������, ������) = ������ −������(������,������)(������− ������) ������������ (������, ������) = 100 × ������(������, ������) B. Assuming Ɵi=1% and σ=1.50%, we can set up the Ho-Lee model, which implies the following 3-step interest rate tree (where each step is = 0.5): 1 1.20% 2.76% 0.64% 2 4.32% 2.20% 0.08% Table 2- Ho-Lee interest rate tree 3 5.88% 3.76% 1.64% -0.48% At each node, the interest rate was calculated using ������������+1,������ = ������������,������ + ������������ × ∆ + ������ × √∆ For upward movements, and ������������+1,������+1 = ������������,������ + ������������ × ∆ − ������ × √∆ For downward movements. The risk neutral probability of an upward or downward movement is set at p*=1/2. The model implied zero-coupon prices are then computed using the different step bond trees (Table 14 in the Appendix). The following table shows the comparison between the implied and the term structure zero-coupon prices for each maturity: the Check row contains the difference between the two. 1 Term structure Implied Check 99.4018 99.4018 0.0000 2 98.4127 98.5618 -0.1491 3 97.0446 97.4891 -0.4445 4 95.6954 96.1940 -0.4986 Table 3 - Comparison on bond prices We can see...
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...Topic 1: Financial Markets 1. You are among the OTC marketmakers in the stock of BioEngineering, Inc. and quote a bid of $102.25 and an ask of $102.50. Suppose that you have a zero inventory. (a) On Day 1 you receive market buy orders for 10,000 shares and market sell orders for 4,000 shares. How much do you earn on the 4,000 shares that you bought and sold? What is the value of your inventory at the end of the day? (Hints: It is possible to have negative inventory. Further, there is more than one correct way to value an inventory, but please state what assumption your valuation is based on.) You have sold 10,000 shares at the ask price of $102.50. You bought 4,000 shares at a bid price $102.25. Thus, 6,000 shares are sold short (sold without already owning the security). Your revenue from the 4,000 “round trip” purchase and sale produces a profit equal to the bid minus the ask times the volume done. Hence, the profit on the round trip trades is $0.25 × 4, 000 = $1, 000. The value of your inventory is equal to the value of your short position of 6,000 shares. Since there is both a bid and an ask price, this question can answered is various ways depending on what you assume: The “conservative” valuation is to value your position at the ask price of $102.50. Then, you have a position of -$615,000. This conservative valuation is useful because, if you cover your short position by buying from another dealer at his ask price of $102.50, you would have to pay $615,000. (Also, in...
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...Bankruptcy and Restructuring at Marvel Entertainment Group 1. Why did Marvel file for Chapter 11? Were the problems caused by bad luck, bad strategy, or bad execution? What is the amount of debt of MEG (the operating company) and the Marvel Holding Companies (Marvel owners)? The Chapter 11 bankruptcy provided an opportunity for all the major stakeholders to evaluate their options regarding their investment and control of Marvel. Bankruptcy alleviated Marvel’s immediate cash shortage, protected it from creditors and some litigation, and provided Marvel with a ‘fresh start.’ Bad strategy: Diversified youth Entertainment Company Bad execution: Overpaying for acquisitions There’s a combination of bad strategy and bad execution caused the problem. First, Perelman attempted to “expand the industry pie” and decrease marginal costs, which instead only worked to distract Marvel from producing quality product. Besides, Perelman showed a poor judgment in several acquisitions aimed at building Marvel into an entertainment empire but which only further distracted the company and paid more than he could earn from the acquisitions At the year 1996, there are more than 70% debts at Marvel entertainment group. The public debts issued by Marvel Holding Companies are 47.2% of the old shares and 9.1% new shares by the time reorganization plan 2. Describe and evaluate the proposed restructuring plan. Will it solve the problems that caused Marvel to file for chapter 11? The...
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... E. none of the above. 2. The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000. What is, according to the expectations theory, the expected forward rate in the third year? A. 7.00% B. 7.33% C. 9.00% D. 11.19% E. none of the above 3. An inverted yield curve implies that: A. Long-term interest rates are lower than short-term interest rates. B. Long-term interest rates are higher than short-term interest rates. C. Long-term interest rates are the same as short-term interest rates. D. Intermediate term interest rates are higher than either short- or long-term interest rates. E. none of the above. 4.. A bond will sell at a discount when __________. A. the coupon rate is greater than the current yield and the current yield is greater than yield to maturity B. the coupon rate is greater than yield to maturity C. the coupon rate is less than the current yield and the current yield is greater than the yield to maturity D. the coupon rate is less than the current yield and the current yield is less than yield to maturity E. none of the above are true. 5. A coupon bond that pays interest semi-annually is selling at par value of $1,000, matures in 7 years, and has a coupon rate of 8.6%. The yield to maturity on this bond is: A. 8.0% B. 8.6% C. 9.0% D. 10.0% E. none of the above 6.. You have just purchased a 7-year zero-coupon bond with a yield to maturity of 11% and a...
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...Answers to Practice Questions 1. Downward sloping. This is because high coupon bonds provide a greater proportion of their cash flows in the early years. In essence, a high coupon bond is a ‘shorter’ bond than a low coupon bond of the same maturity. 2. The key here is to find a combination of these two bonds (i.e., a portfolio of bonds) that has a cash flow only at t = 6. Then, knowing the price of the portfolio and the cash flow at t = 6, we can calculate the 6-year spot rate. We begin by specifying the cash flows of each bond and using these and their yields to calculate their current prices: Investment Yield C1 . . . C5 C6 Price 6% bond 12% 60 . . . 60 1,060 $753.32 10% bond 8% 100 . . . 100 1,100 $1,092.46 From the cash flows in years one through five, it is clear that the required portfolio consists of one 6% bond minus 60% of one 10% bond, i.e., we should buy the equivalent of one 6% bond and sell the equivalent of 60% of one 10% bond. This portfolio costs: $753.32 – (0.6 $1,092.46) = $97.84 The cash flow for this portfolio is equal to zero for years one through five and, for year 6, is equal to: $1,060 – (0.6 1,100) = $400 Thus: $97.84 (1 + r6)6 = 400 r6 = 0.2645 = 26.45% 3. Using the general relationship between spot and forward rates, we have: (1 + r2)2 = (1 + r1) (1 + f2) = 1.0600 1.0640 r2 = 0.0620 = 6.20% (1 + r3)3 = (1 + r2)2 (1 + f3) = (1.0620)2 1.0710 r3 = 0.0650 = 6.50% (1 + r4)4 = (1 + r3)3 (1 + f4) = (1...
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...10: DURATION BONDS III FIN300 (Matt Marcinkowski, Fall '13) DURATION • Consider two bonds with 10 years to maturity and $1,000 face value (assume annual coupons/compounding): • Bond A: Coupon rate = 10% • Bond B: Coupon rate = 0% (discount paper) Yield Bond 8% A B $1,134.20 (+13.4%) $463.19 (+20%) 10% $1,000 $385.54 12% 887.00 (-11.3%) $321.97 (-16.5%) FIN300 (Matt Marcinkowski, Fall '13) DURATION • Now, consider two bonds with 10 percent coupon rate and $1,000 face value (assume annual coupons/compounding): • Bond C: Time to maturity = 5 years • Bond D: Time to maturity = 25 years Yield Bond 8% C D $1,079.85 (+8%) $1,213.50 (+21.4%) 10% $1,000 $1,000 12% $927.90 (-7.2%) $843.14 (-15.7%) FIN300 (Matt Marcinkowski, Fall '13) DURATION • We have observed the following: • The price of Bond A is less sensitive (in relative terms) to interest rate changes than the price of Bond B. • This is due to the fact that Bond A has a higher coupon rate (10%) than Bond B (0%) • We have also observed that: • The price of Bond C is less sensitive (in relative terms) to interest rate changes than the price of Bond D. • This is due to the fact that Bond D has a longer time to maturity than Bond C. FIN300 (Matt Marcinkowski, Fall '13) DURATION • Bond prices are more sensitive in relative terms to interest rate changes if the coupon rate is lower and if the time to maturity is longer. • To compare interest rate sensitivity of bonds with different coupon rates and times...
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...Chapter Nine Interest Rate Risk II Chapter Outline Introduction Duration: A Simple Introduction A General Formula for Duration • The Duration of Interest Bearing Bonds • The Duration of a Zero-Coupon Bond • The Duration of a Consol Bond (Perpetuities) Features of Duration • Duration and Maturity • Duration and Yield • Duration and Coupon Interest The Economic Meaning of Duration • Semiannual Coupon Bonds Duration and Interest Rate Risk • Duration and Interest Rate Risk Management on a Single Security • Duration and Interest Rate Risk Management on the Whole Balance Sheet of an FI Immunization and Regulatory Considerations Difficulties in Applying the Duration Model • Duration Matching can be Costly • Immunization is a Dynamic Problem • Large Interest Rate Changes and Convexity Summary Appendix 9A: The Basics of Bond Valuation Appendix 9B: Incorporating Convexity into the Duration Model • The Problem of the Flat Term Structure • The Problem of Default Risk • Floating-Rate Loans and Bonds • Demand Deposits and Passbook Savings • Mortgages and Mortgage-Backed Securities • Futures, Options, Swaps, Caps, and Other Contingent Claims Solutions for End-of-Chapter Questions and Problems: Chapter Nine ***signed to the questions 2 3 16 20 1. What is the difference between book value accounting and market value accounting? How do interest rate changes...
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...Chapter 11 Managing Bond Portfolios 1. Duration can be thought of as a weighted average of the ‘maturities’ of the cash flows paid to holders of the perpetuity, where the weight for each cash flow is equal to the present value of that cash flow divided by the total present value of all cash flows. For cash flows in the distant future, present value approaches zero (i.e., the weight becomes very small) so that these distant cash flows have little impact, and eventually, virtually no impact on the weighted average. 2. A low coupon, long maturity bond will have the highest duration and will, therefore, produce the largest price change when interest rates change. 3. An intermarket spread swap should work. The trade would be to long the corporate bonds and short the treasuries. A relative gain will be realized when the rate spreads return to normal. 4. Change in Price = – (Modified Duration Change in YTM) Price = -Macaulay's Duration1+ YTM Change in YTM Price Given the current bond price is $1,050, yield to maturity is 6%, and the increase in YTM and new price, we can calculate D: $1,025 – $1,050 = – Macaulay's Duration1+ 0.06 0.0025 $1,050 D = 10.0952 5. d. None of the above. 6. The increase will be larger than the decrease in price. 7. While it is true that short-term rates are more volatile than long-term rates, the longer duration of the longer-term bonds makes their rates of return more volatile. The higher duration...
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...Solutions to Homework 3, FINC-UB.0002.02 Xuyang Ma Topic 6: Equity Valuation 1. Suppose that the consensus forecast of security analysts of your favorite company is that earnings next year will be E1 = $5.00 per share. Sup- pose that the company tends to plow back 50% of its earnings and pay the rest as dividends. If the Chief Financial O cer (CFO) estimates that the company's growth rate will be 8% from now onwards, answer the following questions. (a) If your estimate of the company's required rate of return on its stock is 10%, what is the equilibrium price of the stock? The equilibrium price of a stock can be determined using Gordon's growth formula as follows: P0 = where E1 (1 − b) R−g b = .5 the plow back ratio, R = .10 the required rate of return, and g = .08 is the growth rate. Thus, the price should be: P0 = $5(1 − .5) = $125 .10 − .08 1 (b) Suppose you observe that the stock is selling for $50.00 per share, and that this is the best estimate of its equilibrium price. What would you conclude about either required rate of return; or pany's future growth rate? Recall from the formula above, that a higher required rate of return implies a lower equilibrium price of the stock. On the other hand, a higher growth rate implies a higher stock price. a lower equilibrium stock price ($50 either: Thus, (i) your estimate of the stock's (ii) the CFO's estimate of the com- < $125) could indicate that (1) the required rate of return...
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...week's lecture is on Bonds, from Chapters 14, 15, and 16 You are to work on 10 problems. Due date: Saturday, July 12, by 11:59 pm Chapter 14: 10, 11, 12, 14, 16 Chapter 15: 7, 11, 14 Chapter 16: 8 and 12 SOLUTIONS Chapter 14: 10. a. | Zero coupon | 8% coupon | 10% coupon | Current prices | $463.19 | $1,000.00 | $1,134.20 | | | | | b. Price 1 year from now | $500.25 | $1,000.00 | $1,124.94 | Price increase | $ 37.06 | $ 0.00 | − $ 9.26 | Coupon income | $ 0.00 | $ 80.00 | $100.00 | Pre-tax income | $ 37.06 | $ 80.00 | $ 90.74 | Pre-tax rate of return | 8.00% | 8.00% | 8.00% | Taxes* | $ 11.12 | $ 24.00 | $ 28.15 | After-tax income | $ 25.94 | $ 56.00 | $ 62.59 | After-tax rate of return | 5.60% | 5.60% | 5.52% | | | | | c. Price 1 year from now | $543.93 | $1,065.15 | $1,195.46 | Price increase | $ 80.74 | $ 65.15 | $ 61.26 | Coupon income | $ 0.00 | $ 80.00 | $100.00 | Pre-tax income | $ 80.74 | $145.15 | $161.26 | Pre-tax rate of return | 17.43% | 14.52% | 14.22% | Taxes** | $ 19.86 | $ 37.03 | $ 42.25 | After-tax income | $ 60.88 | $108.12 | $119.01 | After-tax rate of return | 13.14% | 10.81% | 10.49% | * In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year end is treated as a capital loss and therefore is not treated as an offset to ordinary income. ** In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary...
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...PRICING W HAT IS A BOND? A bond is a claim on some fixed future cash flows. A commonwealth government bond (CGB) is a bond which pays semi-annual coupons, in which the maturity date/ coupon payment date is on the 15th of every month. A zero coupon bond is a bond with no coupons. The important information of a bond: 1. 2. 3. 4. 5. 6. Transaction date: T Settlement date:T+2 Coupon payment dates Maturity date YTM Coupon rate • 1. 2. Cum-interest or Ex-interest? If ex-interest If> 7 days to the next coupon payment-----> cum-interest Y IELD TO MATURITY The Yield to Maturity (YTM) of a bond is: Interest rate that makes the present value of the bond’s payments equal to its price. Determined by the market, reflecting annual rate of return required by market. The Relationship between YTM and Bond Price: YTM = Price AND Price Sensitivity YTM = Price AND Price Sensitivity When YTM = C = 10%, P = FV = $100 o C = YTM, P = FV – Par Bond o C < YTM, P < FV – Discount Bond o C > YTM, P > FV – Premium Bond N O ARBITRAGE PRINCIPLE An arbitrage is a set of trades that generate zero cash flows in the future, but a positive and risk free cash flow today. This is done through the violation of law of one price. An arbitrage trade is done by selling the real instrument, and buying a synthetic instrument (replicating strategies or portfolios). By constructing a synthetic bond and buy the under-priced real bond and selling 1 ...
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...as bonds with higher durations (given equal credit, inflation and reinvestment risk) may have greater price volatility than bonds with lower durations. It is an important tool in structuring and managing a fixed-income portfolio based on selected investment objectives. Investment theory tells us that the value of a fixed-income investment is the sum of all of its cash flows discounted at an interest rate that reflects the inherent investment risk. In addition, due to the time value of money, it assumes that cash flows returned earlier are worth more than cash flows returned later. In its most basic form, duration measures the weighted average of the present value of the cash flows of a fixed-income investment. All of the components of a bond—price, coupon, maturity, and interest rates—are used in the calculation of its duration. Although a bond’s price is dependent on many variables apart from duration, duration can be used to determine how the bond’s price may react to changes in interest rates. This issue brief will provide the following information: < A basic overview of bond math and the components of a bond that will affect its volatility. < The different types of duration and how they are calculated. < Why duration is an important measure when comparing individual bonds and constructing bond portfolios. < An explanation of the concept of convexity and how it is used in conjunction with the duration measure. January 2007 issue brief Basic Bond Math...
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