Analysis of Fixed Income Investments

In: Business and Management

Submitted By desmondf
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Question 1 Are interest rate changes predictable?

Interest rates are not entirely predictable but can be inferred from present interest rate prices. For example, when current interest rates are exceptionally low, future interest rates can be expected to rise and vice versa.

Question 2 Consider a two year coupon bond which pays an annual coupon of 5% with a principal value of $100. Using the zero coupon bonds B(0, 1) and B(0, 2):
1. What is the strategy to replicate the coupon bond?
2. What is the strategy to hedge the coupon bond?

PV of 2 year coupon bond = 5 B(0,1) + 105 B(0,2)

1. To replicate the bond, I should buy 5 units of B(0, 1) bonds and 105 units of B(0, 2) bonds.

2. To hedge the bond, I should do the opposite and sell 5 units B(0, 1) bonds and 105 units B(0, 2) bonds.

Question 3 Consider three zero coupon bonds; B(0, 1)=0.95, B(0, 2)=0.90, and B(0, 3)=0.85:
1. What is the zero rate term structure?
B(0,T) = e-rT/365 r(0,T) = -ln( B(0,T))365/T

r(0,1) = -ln 0.95 = 0.0513 r(0,2) = -(ln 0.90)/2 = 0.0527 r(0,3) = -(ln 0.85)/3 = 0.0542

2. What is the forward rate term structure at one year intervals? In other words, f(0, 1, 2) and f(0, 2, 3).

f(0,1,2) = B(0,1) / B(0,2) – 1 = 0.95/0.9 – 1 = 0.05556 f(0,2,3) = B(0,2) / B(0,3) – 1 = 0.90/0.85 – 1 = 0.05882

3. Name two other possible term structures that can be inferred.
The other term structures are discount rate and simple interest rate structures.

Question 4 The current date is January 9, 2003. The price of a Treasury bond with a 12% coupon that matures on October 12, 2009 is quoted as 102-07. What is the cash price? For the accrued interest, it has been 89 days since the last coupon (Jan 9, 2003 - Oct 12, 2002) with the entire interval between coupon payments being 182 days (April 12, 2003 - Oct 12, 2002).

Quoted Price = 102 + 7/32 = 102.21875
Accrued interest = 12% x…...

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