Question

A Treasury bond with 6 months to maturity, with face value of $100, and a coupon rate of 5% trades for 99:25 and a Treasury bond with 1 year to maturity with a face value of $100 and a coupon rate of 5% trades for 98:27. Determine the 6-month and 1-year risk-free rates of return

please do without excel or a financial calculator and show formulas used

THE QUESTION IS PRICED LIKE T BILLS BUT ITS SUPPOSED TO BE A T BOND*****

Answer 1

The Treasury Bonds are assumed to make semi-annual coupon payments.

Bond 1: Coupon Rate = 5 % per annum

Face Value = $ 100 and Remaining Maturity = 6 months or 0.5 years

Current Price = $ 99.25 and Semi-Annual Coupon = 0.5 x 0.05 x 100 = $ 2.5

Let the yield for this bond be R1 per half-year

Therefore, 99.25 = 102.5 / (1+R)^(1)

R1 = [(102.5/99.25) - 1] = 0.032746 or 3.2746 %

Annualized Rate = 3.2746 x 2 = 6,5492 %

Bond 2:

Face Value = $100, Remaining maturity = 1 year , Current Price = $ 98.27 and Semi-Annual Coupon = 0.05 x 0.05 x 100 = $ 2.5

Let the yield for this bond be R2

Therefore, 98.27 = 2.5 / (1.032746) + 102.5 / (1+r2)^(2)

98.27 = 2.4207 + 102.5 / (1+R)^(2)

95.8493 = 102.5 / (1+R2)^(2)

R2 = [{102.5/95.8493}^(1/2) - 1] = 0.034112 or 3.4112 %

Annualized Rate = 3.4112 x 2 = 6.8224 %

As Treasury Bonds are backed by the full faith and taxing power of the Federal Government, they are considered to be risk-free for all practical purposes. Hence, the yields of these bonds corresponding to particular maturities can be considered to be the risk-free rates for those maturities,

Therefore, 6-months Risk-Free Rate = R1 = 6.5492 % and 1-year Risk-Free Rate = R2 = 6.8224 %