# Fixed income securities Essay examples

1455 Words Oct 25th, 2013 6 Pages
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
For this question, assume r1 (−0.5, 0.5) = 6%.
Answer: For this ﬂoating rate bond, the reset date is once a year. The bond has time to maturity 1.5 years, so the bond is right in the middle of two reset dates.
To price such a ﬂoating rate bond, we need to ﬁgure out what the bond is worth on the next reset date (T = 0.5). Its value should be the sum of the coupon payment which is determined by the interest rate set half year ago r1 (−0.5, 0.5) = 6%, and the par value of the ﬂoating rate bond right after the coupon is paid:
100 × r1 (−0.5, 0.5) + 100 = 100 × 0.06 + 100 = \$106 which is a known number, so by applying the discounting we get the price of the ﬂoating rate bond today:
106 × Z (0, 0.5) = 106 × 0.968 569 91 = \$102. 668 41

(h) 1.5-year ﬂoating rate bond with 40 basis point spread with annual payments. For this question, assume r1 (−0.5, 0.5) = 6%.
Answer: Break down the security into simpler ones. A ﬂoating rate bond with non-zero spread is a portfolio of a ﬂoating rate bond with zero spread (priced in question f) and a constant payments based on the ﬁxed spread. The constant payments form an annuity which is just a portfolio of zero coupon bonds:
Year
0.5
1.5
Cash Flow from the ﬁxed spread: 0.004 × 100 = \$0.4 0.004 × 100 = \$0.4
Hence they should be priced at
0.4 × Z (0, 0.5) + 0.4 × Z (0, 1.5)
= 0.4 × 0.968 569 91 + 0.4 × 0.904 037 4
= 0.749 042 92
Therefore, the total value of the