213.1

1.Consider the following STRIP table:
 

1. At what price could you buy a Feb 19 STRIP? (4 pts.)

   FV=100, r=0.62/2, n=2:

   \( \large PV = \frac{100}{ \left ( 1 + \frac{.062}{2} \right)^{2}} = 94.077 \)

   b. What would be the price of a 9%, $1000 par bond with semi-annual coupons, maturing in Aug 19? (the next coupon payment is due in Aug 18)? (6 pts.)

The cash flows look like this:

From the STRIP table and part a, we know the following PV's for $100:

So the price of the bond is: $45(.9663)+$45(.94077)+$1045(.9114)=$1038.23

c. Is this bond selling at a premium or a discount and why is it doing so? (4 pts.)

Premium. It is selling at a premium because its coupon rate is higher than current market rates (around 6% according to the STRIP table). That is, if you bought a $1000 bond today, you could expect to get around $60 a year in interest whereas this one offers $90 a year. It is relatively more attractive and sells for a higher price. Another way of looking at it is that it would sell for par at 9% and since the rates are lower, it must sell for more (i.e. the interest rate enters into the denominator).

d. Of the bond and the four STRIPS, which should have the most volatile price? EXPLAIN. (4 pts)

The Feb 20 STRIP will have the most volatile price. Longer term securities have more volatile prices because the effect of a change in the interest rate is magnified more for every year the bond has to maturity (think of how you would feel if interest rates moved for or against you and you had a very long term security).

e. Rank the bond and the 4 STRIPS from lowest to highest Yield-to-Maturity. EXPLAIN (5 pts.)

Aug 18, Feb 19, Bond, Aug 19, Feb 20. For STRIPS, the spot rate is the YTM because they have only one payment. For the bond, the YTM is a weighted average of the spot rates. The bond's YTM must then lie between the Aug 18 and Aug 19 spot rates. Specifically, since most of the money comes at the end, the average will be pulled toward the later rate, the Aug 19.

f. Give me two reasons why the yield curve might be shaped the way it is here. (5 pts.)

  The 3 acceptable reasons are:

1. The market expects rates to rise in the future
2. People prefer shorter term securities because they have more liquidity, so higher rates must be offered on long term securities.
3. There are more people investing for the short term than the long-term, so higher rates must be offered on long term securities to entice them to invest in them.

g. If inflation is expected to be 3% this year (expressed as a semi-annually compounded rate), what are the expected real rates over the next 6 months and the next year? (4 pts.)

\( \Large \frac{\left( 1 + \frac{.061}{2} \right)}{\left( 1 + \frac{.03}{2} \right)} \) = 1.015251 for the next 6 months. (= 3.054% APR on a semi-ann. comp. basis)

\( \Large \frac{\left( 1 + \frac{.062}{2} \right)^2}{\left( 1 + \frac{.03}{2} \right)^2} \) = 1.01576 every 6 months or 3.15% APR semi-annually compounded.

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