Fixed income securities Essay

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Fixed Income Securities
Chapter 2 Basics of Fixed Income Securities
Problem Set
(light version of the exercises in the text)
Q3.
You are given the following data on different rates with the same maturity (1.5 years), but quoted on a different basis and different compounding frequencies:
• Continuously compounded rate: 2.00% annualized rate
• Continuously compounded return on maturity: 3.00%
• Annually compounded rate: 2.10% annualized rate
• Semi-annually compounded rate: 2.01% annualized rate
You want to find an arbitrage opportunity among these rates. Is there any one that seems to be mispriced?
Answer: This exercise tests your knowledge of dealing with interest rates with different compounding frequency.
Given the interest …show more content…
668 41 + 0.749 042 92
= $103. 417 45

Q6. Consider the data in the following table:
Maturity T
0.50
1.00
1.5
2

Yield r2 (0, T )
6.49%
6.71%
6.84%
6.88%
3

Consider two bonds, both with 2 years to maturity, semiannual payments, but with different coupon rates. Let the two coupon rates be 15% and 3%.
(a) Compute the prices and the yields to maturity of these coupon bonds.
Answer: The term structure of interest rate is the same as in Q4. We can just copy the discount factor table here:
Maturity T Yield r2 (0, T ) Discount Factor Z (0, T ) = 1/ (1 + r2 (0, T ) /2)2×(T −0)
0.50
6.49%
1/ (1 + 0.0649/2)2×0.5 = 0.968 569 91
1.00
6.71%
1/ (1 + 0.0671/2)2×1 = 0.936 131 84
1.5
6.84%
1/ (1 + 0.0684/2)2×1.5 = 0.904 037 4
2
6.88%
1/ (1 + 0.0688/2)2×2 = 0.873 465 90
The 15% 2-year coupon bond with semiannual payments has been priced in Q4, so we can just copy the results here:
Pc (0, 2) = 7.5 × Z (0, 0.5) + 7.5 × Z (0, 1) + 7.5 × Z (0, 1.5) + 107.5 × Z (0, 2)
= 7.5 × 0.968 569 91 + 7.5 × 0.936 131 84 + 7.5 × 0.904 037 4 + 107.5 × 0.873 465 90
= $114. 963 13
The yield to maturity (YTM) on this bond is defined through the equation:
Pc (0, 2) = 114.96313 =

7.5
7.5
107.5
7.5
2×0.5 +
2×1 +
2×1.5 +
(1 + y/2)
(1 + y/2)
(1 + y/2)
(1 + y/2)2×2

Solution is: y = 6. 865 540 8%. (You won’t have Excel to help you find the root in the exam.
However, I expect you to be able to write down the defining equation for YTM.)
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