7. Suppose that you buy a 5-year zero-coupon bond today with a face value of $100 and that the yield curve is currently flat at 5% pa nominal. Suppose that immediately after purchasing the bonds, the yield curve becomes flat at 6% pa nominal. Assuming semi-annual compounding and that the bond is sold after 3 years, what is the annualized holding period yield on this bond?
8. Suppose that you buy a 5-year bond today with 8% p.a. coupons and that the yield curve is currently flat at 5% pa nominal. Suppose that immediately after purchasing the bonds, the yield curve becomes flat at 6% pa nominal. Assuming a face value of $100 and semi-annual compounding and that the bond is sold after 3 years, what is the annualized holding period yield on this bond?
9. Homer Simpson is considering two investment options. Option 1 involves investing in a zero coupon bond for two years. Option 2 involves investing in a zero coupon bond for five years and then selling that bond in two-year’s time. Assume for this question that three and five year bonds are illiquid at all times. Which of the following are correct?
i. According to the market segmentation hypothesis, Option 2 would be preferred to Option 1.
ii. According to the liquidity premium hypothesis, Option 2 is riskier than Option 1 because the selling price at t=2 could be very high because three year bonds are illiquid.
iii. According to the pure expectations hypothesis, the expected return from the two strategies, based on information today, is identical.
iv. According to the preferred habitat theory, Option 1 is preferred to Option 2 but Option 2 may be preferred if Homer Simpson believes that the three-year spot rate in two-year’s time is more than f2,5 .
v. According to the preferred habitat theory, Option 2 is preferred to Option 1 if Homer Simpson believes that the three-year spot rate is equal to f2,5 .
A. (iii) only
B. (iv) only
C. (ii) & (iii)
D. (i) & (iii) & (iv)
E. (iii) & (iv) & (v)
11. Suppose the yield curve is as shown below. Assuming semi-annual compounding, what is f1,4 ?
1 year spot rate: 3%
2 year spot rate: 5%
3 year spot rate: 7%
4 year spot rate: 9%
Since, multiple questions have been posted, I have answered the first one (Question 7).
To calculate the annualized holding period yield, we need to determine the price today and price after 3 years with the use of following formula for zero-coupon bonds:
Bond Price = Face Value/(1+Yield/Compounding Frequency)^(Period*Compounding Frequency)
Using the information provided in the question in the above formula, we get,
Bond Price (Today) = 100/(1+5%/2)^(5*2) = $78.12
Bond Price (At Year 3) = 100/(1+6%/2)^(2*2) = $88.85
Now, we can calculate the annualized holding period yield with the use of following formula:
Annualized Holding Period Yield = (Bond Price at Year 3/Bond Price (Today))^(1/Period) - 1 = (88.85/78.12)^(1/3) - 1 = 4.38% which is closest to 4.34%.
Answer is 4.34% (which is Option E)
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