Question

2. The following data was collected for zero coupon Treasury bonds. Based on this information, compute the risk-free rates for the 6month – 10-year horizon, in increments of 6 months (i.e., compute risk-free rates for 6 months, 1-year, 1.5- year, etc.)

Maturity	Price	Risk-free rate
0.5	98:26
1.0	97:15
1.5	96:31
2.0	96:09
2.5	95:04
3.0	94:18
3.5	93:14
4.0	91:04
4.5	90:18
5.0	89:13
5.5	86:19
6.0	85:30
6.5	84:23
7.0	83:20
7.5	82:19
8.0	81:12
8.5	80:03
9.0	79:14
9.5	77:06
10.0	75:20

Answer 1

The risk free rate is given by yield to maturity of a zero coupon treasury bond.

Yield to Maturity = (Face Value / Current Price of Bond) ^ (1 / Years to Maturity) - 1

This formula is used to compute the risk free rates for the 6 month – 10 year horizon, in increments of 6 months.

For example, for the zero coupon bond with maturity of 0.5 years, risk free rate = (100/98.26)^(1/0.5)-1 = 0.0357 or 3.57%

Maturity	Price	Risk-free rate
Par value	100
0.5	98.26	3.57%
1.0	97.15	2.93%
1.5	96.31	2.54%
2.0	96.09	2.01%
2.5	95.04	2.06%
3.0	94.18	2.02%
3.5	93.14	2.05%
4.0	91.04	2.37%
4.5	90.18	2.32%
5.0	89.13	2.33%
5.5	86.19	2.74%
6.0	85.30	2.69%
6.5	84.23	2.68%
7.0	83.20	2.66%
7.5	82.19	2.65%
8.0	81.12	2.65%
8.5	80.03	2.66%
9.0	79.14	2.63%
9.5	77.06	2.78%
10.0	75.20	2.89%