Question

A zero-coupon bond has a beta of 0.3 and promises to pay $1000 next year with a probability of 95%. If the bond defaults, it will pay nothing. One -year Treasury securities are yielding 2%, and the equity premium is 5%. What is the promised rate of return on this bond? Round your answer to the nearest tenth of a percent. 6.9% 8.0% 8.2% 8.9%

Answer 1

A zero coupon bond with face value of $1000 and maturity of 1 year.

As per CAPM equation

$ER = R_{f} + \beta *MRP$

ER = Expected Return

R_f = Risk free Rate = 2%

MRP = Market Risk Premium = 5%

ER 0.02 + 0.3 * .05

ER = 3.5%

Now price or present value of Zero coupon bond

FV PV, = (1 + ER)"

FV = $1000

ER = 3.5%

n= 1 year

1000 PV= (1.035)1

PV966.18

but it has probability of 0.95, so required price

РУ-966, 18 * 0.95 917.87

So, the promised return for zero coupon bond

PV

here FV = 1000, PV = 917.87, n= 1 year

10001 917.87

r= 8.9%