Fixed Income Midterm
Fixed Income代写 1. ____ All else equal (credit risk, coupon, YTM, timing of cash flows) a bond with a longer maturity will have a larger MacCauley’s duration
This is a take-home exam. You can use any classroom materials at your disposal to solve the problems.
1.(10 points).
Please answer true or false to the following questions
1. ____ All else equal (credit risk, coupon, YTM, timing of cash flows) a bond with a longer maturity will have a larger MacCauley’s duration.
2. ____ Properly executed, a long/short arbitrage trade can make money when the YTMs on both bonds in the trade go down.
3. ____ If I calculate duration using the duration formula and a change of 10bp to recalculate bond prices, and then calculate duration using the duration formula again using a change of 20bp to recalculate prices, the two answers that I get will be approximately the same.
4.____ All else equal (credit risk, YTM, cash flow timing, and maturity), a bond with a lower coupon rate will have less interest rate risk (i.e. price sensitivity).
5.____ The Federal Reserve Board directly sets the discount rate.
6. ____ For the holder of a fixed-rate coupon bond, reinvestment risk is a bigger problem during a period of falling interest rates than during a period of rising interest rates.
7.____ If I believe that interest rates are going down in the future, I would purchase bonds with a very short duration to profit from this idea.
8. ____ If the yield curve is upward sloping, the 6-month forward rate will be greater than the 6-month spot rate and lower than 1-year spot rate. (Assume all rates are stated as bond equivalent yields.)
9. ____ When the perception in the economy is that credit risk is getting worse/higher, the spread between YTMs on corporate and Treasury bonds will likely narrow.
10.______ Off-the-run bonds tend to be less liquid, and therefore have lower yields to maturity.
2.(10 points). Fixed Income代写
You are given the following data. All forward rates are expected future six-month rates. All rates are stated annually, as BEYs. If in doubt as to how a rate is defined, read the Definition column! J
| Rate | Definition (please read!!) |
| Six month spot rate, stated as BEY= 5% | Zero coupon rate for a six month zero coupon bond, stated as BEY |
| One year spot rate, stated as BEY = 5.3% | Zero coupon rate for a one year zero coupon bond, stated as BEY |
| Six month forward rate, stated as BEY = 5.6% | Expected six-month rate six months from now (stated as BEY) |
| One year forward rate, stated as BEY = 6.083% | Expected six-month rate one year from now (stated as BEY) |
| 1.5 year forward rate, stated as BEY = 6.601% | Expected six-month rate 1.5 years from now (stated as BEY) |
| 2 year forward rate, stated as BEY = 7.141% | Expected six-month rate 2 years from now (stated as BEY) |
| 2.5 year forward rate, stated as BEY = 7.695% | Expected six-month rate 2.5 years from now (stated as BEY) |
| 3 year forward rate, stated as BEY = 8.266% | Expected six-month rate 3 years from now (stated as BEY) |
Q: What is the price of a 2-year zero coupon bond with semi-annual compounding and a par value of $100?
Round your answer to three decimal places. As always, assume semi-annual compounding. Show all your work for full credit. (If you show the correct answer without showing your work, you will not get any credit).
3.(8 points). Fixed Income代写
Assume that you are given the following discount factors, related to bootstrapping the yield curve.
| Time in Years | Time in Periods | Coupon Rate | Discount Factor |
| 0.5 | 1 | 0.00% | 0.97895 |
| 1 | 2 | 0.00% | 0.95694 |
| 1.5 | 3 | 6.00% | 0.93256 |
| 2 | 4 | 6.25% | 0.90650 |
| 2.5 | 5 | 6.50% | 0.87886 |
Q: Price a 2.5 year coupon bond with a par value of $100, a coupon rate of 5%, and semi-annual interest payments.
Round to two decimal places. Show all your work for full credit (If you show the correct answer without showing your work, you will not get any credit).
4. (15 pts.) Fixed Income代写
Assume that you purchase the following semi-annual pay corporate bond with a par value of $100. The settlement date is 5/28/09.
| Par Value: | $100 |
| Coupon (%): | 5.000% |
| Maturity Date: | 1-Feb-2015 |
| Yield to Maturity (%): | 14.964% |
(2 pts.) a. What is the semi-annual coupon payment for this bond? Round to two digits (e.g. 4.30) and show your work for full credit.
(3 pts.) b. What is the w for this bond (the first “time” exponent when you discount the cash flows)? Round to four digits (e.g. 0.4361). Please show your work for full credit.
(3 pts.) c. What is the present value of the first cash flow for this bond? For the calculation, please do not round the “time” exponent to fewer than 4 decimal places. Show your work for full credit and round to four decimal places; e.g. $10.5426.
(5 pts.) d. What is the present value of the final cash flow for this bond? For the calculation, please do not round the “time” exponent to fewer than 4 decimal places. Show your work for full credit and round to four decimal places; e.g. $10.5426.
(2 pts.) 5e. Calculate the accrued interest for this bond. Show your work and round to four decimal places; e.g. $0.5426.
5.(15 points total, 3 pts each part) Fixed Income代写
Assume that you own 10,000 semi-annual pay $100 par value bonds with a coupon rate of 7%, a YTM of 5%, and a maturity of 10 years. Assume that you are concerned about rates rising in the future and you want to protect (hedge) the value of your portfolio from this situation. For your hedging bond, you choose a semi-annual pay 10-year maturity, 10% coupon bond with the same credit quality as your long position.
a.Calculate the DV01 of each bond, rounding to 4 digits, e.g. $0.1426. Show your work for partial credit.
7% bond DV01:
10% bond DV01:
b. What is the hedge ratio?
c. State your balance sheet at the moment you do the hedge. Round the bond prices to the nearest dollar, and round the number of bonds used for the hedge to the nearest bond. Also assume that when you short-sell a bond you do not earn interest on the cash that the short sale generates.
d. Assume that YTMs on these bonds rises to 6% in two weeks. Restate your balance sheet, by actually repricing the bonds, assuming that no coupons were paid during the 2-week period.Also ignore the fact that the maturity of your bonds has changed by 2 weeks — assume that the maturity is still 10 years, for simplicity.
e. Was your hedge successful?Why or why not?
6.(6 pts, 3 pts each) Fixed Income代写
Assume that I think the spread between the 5 year and 10 year Treasury bonds is going to narrow (shrink). Which bond will I buy (go long) and which bond will I sell short, and why?
7.(6 pts.)
A quote from Bloomberg news October 6, 2013: “The yield on 10-year U.S. bonds dropped to a two-month low of 2.58 percent on Oct. 3, after Treasury Secretary Jacob J. Lew said the government won’t be able to pay its debts in 14 days unless Congress raises the $16.7 trillion borrowing ceiling. While short-term bill rates and the cost to insure against a default have risen, volatility in Treasuries has fallen.”
Q: Does this situation reflect a steepening or flattening of the Treasury yield curve and how can you tell?
8.(10 points)
Assume that a bond has a price of $123.3837. You calculate the price if the bond’s YTM goes up by 20 basis points, and this answer is $121.6201. Your calculation of the price if the bond’s YTM goes down by 20 basis points is $125.1799.
Q: What is your estimate of the convexity measure? (round to 4 digits for example: 35.3382, and show your work).
9.(10 points) Fixed Income代写
Assume that the duration for a bond is 8.25 and its convexity measure is 42.31. Assume that the initial price of the bond is $102.
Q: Estimate the bond’s new price, assuming that the bond’s YTM goes down by 35 basis points.
Use both the duration and convexity percentage adjustments in your calculation.
Round each of the duration and convexity percent change estimates to 6 decimal places which is 4 percentage points; for example, if you get 0.07252153, use .072521 or 7.2521%
Round your final bond price to four digits (e.g.: $105.6839)
Duration percent change estimate (rounded to six digits):
Convexity adjustment (percent change estimate, rounded to six digits):
New price (rounded to four digits; initial price is $102, as stated above):
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