Question

9. Using the following data given in the Table below, answer these questions: Type US Treasury Note US Treasury Note US Treasury Note US Treasury Note US Treasury Bond US Treasury Bond Coupon 7.25% 10.75% 5.75% 5.00% 8.75% 6.13% Maturity 2 year 3 year 8 year 9 year 18 year 27 year Bid 110:00 123:12 112:00 106:24 143:26 114:11 Ask 110:01 123:13 112:01 106:25 143:27 114:12 Yield (Ask) 2.07% 2.55% 3.97% 4.09% 5.02% 5.13% US Treasury Strip US Treasury Strip US Treasury Strip US Treasury Strip 0.00% 0.00% 0.00% 0.00% 2 year 3 year 8 year 9 year 96:03 92:19 71:13 67:06 96:04 92:21 71:17 67:08 2.00% 2.55% 4.24% 4.47% Express your answers to (a) and (b) as effective annual interest rates. (A) What were the 2-, 3- and 8-year spot interest rates? (B) What is the forward interest rate from 1 year to 2 year (ifi) and from 6 year to 7 year (1f6)? (3 marks) (4 marks) (C) What does the slope of the term structure imply about future interest rates? Explain briefly. (3 marks)

Answer 1

Solution to Question A

Spot interest rates are nothing but yields on zero-coupon Treasury or Treasury Strip

Hence, 2-year spot interest rate = 2.0%, 3-year spot interest rate = 2.55%, 8-year spot interest rate = 4.24%

If yields weren't already provided, you can also find out the spot interest rates by using the formula ((FV/P) ^(1/n) -1)*100

where FV is the face value of the bond, P is the current price of the bond and n is the bond's maturity in years.

Solution to Question B

Using the implied interest rates from zero-coupon bonds, we can derive forward rates, given the assumption that there is no arbitrage.

In the case of 1f1, it stands for the one-year forward rate one year from now. Basically it means that an investor who has a two-year investment horizon will get the same returns, whether he invests in a two-year bond, or whether he invests in a one-year bond and reinvests the proceeds on another one-year bond.

The formula for 1f1 is (1+S2)^2/(1+S1) - 1 where S1 is the spot rate for year 1 and S2 is the Spot rate for the second year/

Lets say that currently, a two-year bond is yielding 5%, and lets say a 1-year bond is yielding 4%. The the one-year rate one year from now will be, (1.05^2)/(1.04)-1 = 6.01%. In other words, the one-year rate after one year needs to be 6.01% for an investor to be indifferent between buying the 5% 2-year bond or reinvesting the proceeds of the 4% one-year bond after one year.

Similarly 1F6 is the one-year forward rate six years from now. The formula for calculating it is (((1+S7)^7)/((1+S6)^6)-1)*100 where S7 is the spot rate for 7 years and S6 is the spot rate for 6 years.

Solution for Question C)

The yields on the given yields on 2-, 3-, 8-, 9-, 18-, and 27-year bonds are increasing with maturity. That means it is an upward-sloping yield-curve for the Treasury yields.

When this happens, it indicates that investors expect interest rates to rise in the future. This is usually the case when investors are bullish about the economy, with inflation rising. Investors expect the Fed to hike rates in the future, to rein in inflation.

When the yield curve is flat or inverted, investors expect a slowdown in the economy and hence, factor in lower interest rates and lower inflation.

Earlier this year, the US Treasury yield curve was inverted for a few days. Currently, the curve is more or less flat.