Finance Problem Sets

¶ … 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.