Question
This question has a lot of parts. I only need answers to K-U but I included all of them for reference. Consider the prices of
This question has a lot of parts. I only need answers to K-U but I included all of them for reference.
Consider the prices of bonds, as shown below. All bonds have a face value of $1000 (as is the norm). TTM = Time to Maturity.
TTM | Coupon | Price |
(years) | Rate | |
0.5 | 0 | $991.12 |
1 | 0 | $978.47 |
1.5 | 0 | $963.64 |
2 | 0 | $942.60 |
2.5 | 0 | $906.60 |
3 | 0 | $871.28 |
3.5 | 0 | $831.87 |
4 | 0 | $786.14 |
Determine the YTM of each bond as an EAR and plot the yield curve. Then answer the questions below.
a. What is the YTM of the 6-month zero-coupon bond, as an EAR?
Report your answer as a percent, not a decimal, with at least 4 significant digits.
For example, if the answer is 0.024354, then enter an answer of 2.4354.
b. What is the YTM of the 2-year zero-coupon bond, as an EAR? Report your answer as a percent, not a decimal, with at least 4 significant digits.
c. What is the YTM of the 3.5-year bond, as an EAR? Report your answer as a percent, not a decimal, with at least 4 significant digits.
d. Determine the No-Arbitrage price of a 2 year, 2.5%, semi-annual coupon bond with a face value of $1000. Keep your precision high.
e. Determine the No-Arbitrage price of a 3 year, 8.0%, semi-annual coupon bond, with a face value of $1000. Keep the precision of your computations high.
f. What is the YTM when measured as an EAR? Report your answer as a percent, not a decimal, with at least 4 significant digits.
g. What is the YTM when measured as an APR? Report your answer as a percent, not a decimal, with at least 4 significant digits.
h. What is the YTM when measured as an Effective 6-month rate? Report your answer as a percent, not a decimal, with at least 4 significant digits.
i. What is the YTM when measured as an effective per-decade rate? Report your answer as a percent, not a decimal, with at least 4 significant digits.
j. Now assume that the 2-year, 2.5% coupon bond in Part D is not trading at the No Arbitrage Price computed earlier in Part D. Instead, in reality its currently trading at an actual price of $951.05.
Is there an arbitrage opportunity here? Yes or no?
If there is an opportunity to earn an arbitrage profit, then compute the available Arb. profit per bond.
If there is no Arb. profit available, then enter 0.0000
**I need help with the following**
For the 2-year, 2.5% coupon bond in Part J, fill out the table below regarding what five specific trades you would implement immediately in order to extract an arbitrage profit. Assume that all bonds have a face value of $1000.
In the table, please report the smallest possible number of bonds you can trade in order to take advantage of the Arb opportunity (if there is one).
HINT: The minimum number of coupon bonds to trade is 80 because $1000 face value divided by the $ coupon amount per period ($12.50) gives 80. That is, for times 0.5, 1.0, and 1.5, the semi-annual coupon payments of $12.50 must be scaled up by a factor of 80 in order to give the face value of the corresponding zero-coupon bonds (=$1000).
Maturity of Bond (years) | Coupon Rate of bond (APR) | Are you Buying or Selling? | Actual price Of the Bond | Quantity Bought or Sold | Overall Cash Flow From buying or selling. (with Neg. sign for outflows) |
0.5 | 0% | Selling | 991.12 | 1 | +991.12 |
1.0 | 0% | Selling | Part N | 1 | Part Q |
1.5 | 0% | Selling | 963.64 | Part O | Part R |
2.0 | Part K | Part L | 942.60 | Part P | Part S |
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2.0 | 2.5% | Part M | 951.05 | 80 | Part T |
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| Overall Arb. Profit = | Part U |
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For example, the first row in the table describes one of the five trades. More specifically, it shows that one of the trades involves selling one, 6-month, zero coupon bond for $991.12. Your task is to fill in the missing data for the four other trades, and to compute the overall Arbitrage Profit (Part U).
Note: Part U is the sum of the five valued directly above it. It gives the overall CF associated with the trades described.
k. What is the coupon rate on the 2-year bond (in the 4th row)?
Enter your answer as a decimal, not as a percent.
l. For the 2-year zero-coupon bond, are you buying or selling?
m. For the 2-year 2.5% coupon bond, are you buying or selling?
n. What is the actual price of the 1-year zero-coupon bond?
o. What is the quantity of the 1.5-year zero-coupon bonds that youll trade?
p. What is the quantity of the 2-year zero-coupon bonds that you will trade? Be careful here. The answer is neither 1 nor 80.
q. What is the overall cash flow associated with trading the one-year zero-coupon bonds? If you are buying (selling), then make sure you enter a negative (positive) value.
Helpful Insight for Parts Q to U: The overall arbitrage profit (i.e. Part U), (within a small amount of rounding error in the 5th Significant digit) is equal to the mispricing per coupon bond ($40.00 from Part J) times the number of coupon bonds traded (=80), which gives $3200.00. Use this to check your answers in the last column.
r. What is the overall cash flow associated with trading the 1.5-year zero-coupon bonds? If you are buying (selling), then make sure you enter a negative (positive) value.
s. What is the overall cash flow associated with trading the two-year zero-coupon bonds? If you are buying (selling), then make sure you enter a negative (positive) value.
t. What is the overall cash flow associated with trading the two-year, 2.5% coupon-bonds? If you are buying (selling), then make sure you enter a negative (positive) value.
u. What is the overall cash flow associated with ALL of the bond trading? That is, what is the overall arbitrage profit? If the profit is positive (negative), then enter a positive (negative) value.
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