F97Q2.1
Consider the following STRIP table:
| Bid | Ask | Asked Yield | |
| Oct 98 | 7.00 | ||
| Oct 99 | 86:30 | 86:31 | 7.10 |
Assume 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 98 STRIP. This STRIP will pay $100 in one year. The current 1 year semi-annually compounded (m=2) interest rate is 7%. Thus, the value of the STRIP today is:
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 98 is worth $93.35 today and $100 in Oct 99 is
worth $86:31 ($86.97) today. The bond pays $100 in Oct 98 (10% of
$1000) and $100 again in Oct 99. It also pays back its principal
in Oct 99 ($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 99 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%.