Finance problem sets and solutions

¶ … bond pays you $1,000 at the end of this year (Year 1) and $1,500 at the end of Year 2. The current one-year spot rate is 4% and the current two-year spot rate is 4.5%. Calculate the duration of this bond.

Use DURATION function on Excel ?

Using the partial durations calculated in #4a, how much would the bond's price change if the one-year spot rate decreased by 100 basis points and the two-year spot rate dropped 50 basis points?

Percentage price change = - Duration x Yield change x 100

-2.6 * -0.01 * 100 = 2.6% increase for r1 =3%,

-0.005 * 100 = 1.3% increase for r2 = 4%

The one-year spot rate (r1) is 6%, and the forward rate for a one-year loan maturing in year 2 ( f2) is 6.4%. Similarly, f3= 7.1%, f4 = 7.3%, f5 = 8.2%. What are the spot rates r2, r3, r4, and r5?

(1+r (0,2))2 = (1+r (0,1)) x (1+f (1,2))1, (1+.06) x (1+.064) = 1.12784, (1.12784) 1/2 = 1.061998,

1.061998 -1 = 6.1998% ? 6.2% = r2

(1+r (0,3))3 = (1+r (0,2))2 x (1+f (2,3))1, (1+.061998)2 x (1+.071) = (1.12784) x (1.071) = 1.20791664, (1.20791664) 1/3 = 1.06499, 1.06499-1 = 6.499% ? 6.5% = r3

(1+r (0,4))4 = (1+r (0,3))3 x (1+f (3,4))1, (1+.06499)3 x (1+.073) = (1.20791664) x (1.073) = 1.29609455, (1.29609455) 1/4 = 1.066987, 1.066987-1 = 6.6987% ? 6.7% = r4

(1+r (0,5))5 = (1+r (0,4))4 x (1+f (4,5))1, (1+.066987)3 x (1+.082) = (1.29609455) x (1.082) = 1.4023743, (1.4023743) 1/5 = 1.069973, 1.069973-1 = 6.9973% ? 7.0% = r5

If the expectations hypothesis holds, what can you say about expected future interest rates?

According to the expectations hypothesis, the expected yield curve seems to have an upward sloping, so long-term bonds should continue to have higher yields than short-term bonds. The general expectation is that rates will continue to rise.

10. You have determined the best risk-free investment for a liability payment for on Nov. 20, 2011 is a stripped principle (np) U.S. Treasury STRIP maturing on Nov. 15, 2011. You purchase the STRIP on February 23, 2010 and settlement occurs two days after your purchase.

Maturity

Bid

Asked

Chg

2011 Nov 15

91.849

91.896

0.053

Find the YTM.

Use YIELD function in Excel: YIELD (DATE (2010,2,25),DATE (2011,11,14),0,91.896,100,2,3) = 4.98% YTM

11. What is the invoice price for a T-bill future based on a notional amount of $1 million if the index price is 93.0? Assume there are 90 days in the contract period.

Invoice price = $1,000,000 -- (DY*$1,000,000*t)/360

100-93 = 7% = DY; $1,000,000 -- ((.07*$1,000,000*90)/360) = $1,000,000 -- $17,500

= $982,500

15. A long time ago, in a Galaxy far, far away