Question

The past five monthly returns for K and Company are 4.65 percent, 4.82 percent, -.55 percent, -.05 percent, and 9.40 percent. What is the average monthly return?

Calculate the price of a zero-coupon bond that matures in 14 years if the market interest rate is 5.30 percent. Assume semiannual compounding..

Compute the expected return given these three economic states, their likelihoods, and the potential returns:

Economic State	Probability	Return
Fast Growth	.2	31.7%
Slow Growth	.4	6.85%
Recession	.4	-2.85%

Answer 1

1) Average monthly return = sum of returns / No. of months

or, Average monthly return = (4.65% + 4.82% - 0.55% - 0.05% + 9.40%)/ 5 = 3.654%

2) Price of a zero coupon bond is the present value of the maturity amount receivable (as it pays no interest). Since we have semi - annual compounding, we require semi - annual interest rate and time period. Assuming $1000 maturity amount, we have -

Semi - annual market interest rate (r) = 5.30% / 2 = 2.65%

Semi - annual periods (n) = 14 * 2 = 28

Price of zero coupon bond = Maturity amount / (1 + r)ⁿ = $1000 / (1 + 0.0265)²⁸ = $480.78321374 or $480.78

3) Expected return = sum of (Probability x return) = 0.2 x 31.7% + 0.4 x 6.85% + 0.4 x -2.85% = 7.94%