12.1

Consider the following STRIP table:
 

Assume that it is Oct 2017 and that the yields are correct (based on 365 day years) and that they are quoted as semi-annually compounded APR’s.
 
 

At what price could you purchase a 1-year STRIP? (1 pt)
 
 

This question is asking for the Asked Price for the Oct 18 STRIP. This STRIP will pay $100 in one year. The current 1 year semi-annually compounded interest rate is 7%. Thus, the value of the STRIP today is:

\( \Large PV= \frac{100}{\left( 1 + \frac{.07}{2} \right)^{2}} \) = 93.35

What would the price be for a 2-year 10% coupon bond with a par value of $1000 and annual coupons? (2 pts)
 
 

$100 in Oct 18 is worth $93.35 today and $100 in Oct 19 is worth $86.97 today. The bond pays $100 in Oct 18 (10% of $1000) and $100 again in Oct 19. It also pays back its principal in Oct 19 ($1000). Thus, the PV of the bond’s cash flows is:
 
 

$100 (.9335) + $1100 (.8697) = $1050.02. You could arrive at the same answer if you discount the cashflows using the ask yields, provided you treat them as semi-annually compounded rates (m=2) even though your cashflows are annual.

If interest rates go up, what will happen to the price of the 2 year bond? WHY?(1 pt)
 
The price of the 2 year bond will go down. Future cash flows will be worth less today. The bond pays a fixed stream of payments which become less attractive when cash flows implied by current rates get higher.
 
 Of the 3 securities (the two STRIPS and the bond), which should have the highest yield-to-maturity? WHY? (1 pt)
 
This is a difficult question, but answerable if you remember that YTM’s are an average of spot rates and that the YTM=spot rate for any security with only one cash flow (such as a STRIP). The YTM’s on the 2 STRIPS are 7% and 7.1%. The YTM on the bond will be an average of these 2 rates. Thus the highest YTM will be 7.1%, belonging to the Oct 19 STRIP. Even though the bond pays 10% coupons, its YTM will be between 7 and 7.1%. The price of the bond adjusts so that the return on your investment still equals only between 7 and 7.1% per year. In fact, its YTM is an effective rate of 7.22%, which corresponds to a semi-annually compounded YTM of 7.099%.

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