Question

The five-year risk-free rate of interest is 3.8%. A five-year, zero-coupon, $1,000 face value bond has a market price today of $800.

a. What is the yield to maturity on the corporate bond? (Careful: I am looking for the annualized rate and this is a five year period.)

b. What is the yield spread between this corporate bond and the risk free bond?

c. Can we estimate the beta risk of this corporate bond using the CAPM equation? (Same answer as above.)

Answer 1

Risk-free rate - 3.8%

No.of years - 5

Face value - $1,000

Market price - $800

In case of zero-coupon bond, the YTM is calculated using the following formula,

YTM = (Face value/ Market price) ^ (1/years to maturity) - 1

= (1000/800) ^ (1/5) - 1

= 1.25 ^ (1/5) - 1

= 1.04564 - 1

= 0.04564

= 4.56%

b. Yield Spread = YTM of corporate bond - risk-free rate

= 4.56% - 3.80%

= 0.76%

c. CAPM equation:

Expected return = Risk-free rate + beta * (market return - risk-free rate)

Assumption: Expected return = Market return

4.56% = 3.80% + beta * 0.76%

beta * 0.76% = 4.56% - 3.80%

beta * 0.76% = 0.76%

beta = 1

If the beta = 1, then the risk of the stock is equal to the risk of the stock market. For exmaple, if the stock market moves up by 5%, then the stock will move up by 5%.