Question

The beta of a corporate bond is 0.4. Currently, the risk free rate of interest is 1% and the expected rate of return on the market portfolio is 8%. The bond is anticipates to pay coupons of $80 at the end of the year and it has been anticipated that its price at the end of the year will be $1,020. The current price of thebond is $1,070.

i. Calculate the required expected rate of return and the actual rate of return on the bond

ii. At the current price of $1070, is the bond underpriced or overpriced?

iii Show your naswer by plotting a security market line.

Answer 1

Part (i)

Expected rate of return = R_e = Risk free rate + Beta x (Expected return on market - risk free rate) = 1% + 0.4 x (8% - 1%) = 3.80%

Actual rate of return = (P₁ + C - P₀) / P₀ where P₁ = price of the bond at the end of year 1 = $ 1,020; C = annual coupon = $ 80 and P₀ = price of the bond currently = $ 1,070

Hence, actual return = (1,020 + 80 - 1,070) / 1,070 = 30 / 1,070 = 2.80%

Part (ii)

Expected Price of the bond today = PV of coupon + PV of expected price at the end of year 1 = (80 + 1,020) / (1 + R_e) = 1,100 / (1 + 3.80%) =  1,059.73 < 1,070 = actual price of the bond today. Hence, at the current price of $1070, the bond is overpriced.

Part (iii)

Please see the graph below. Actual return of the security = 2.8%. The bond gets plotted below the security market line and hence it's over priced.