Question

The market price of a security is Kshs. 40, the security’s expected rate of return is 13%, the riskless rate of interest is 7% and the market risk premium, [E(Rm) – Rf], is 8%.
What will be the security’s current price if the its expected future payoff remain the same but the covariance of it’s rate of return with the market portfolio doubles?

Answer 1

Given,

Market price = 40

Expected rate of return = 13%

Risk less rate of return = 7%

Market risk premium = 8%

Solution :-

if the covariance with the market portfolio doubles, then risk premium would also double.

So,

New risk premium = (expected rate of return - risk less rate of return) x 2

= (13% - 7%) x 2

= 6% x 2 = 12%

New discount rate = new risk premium + risk less rate of return

= 12% + 7% = 19% or 0.19

Expected dividend = market price x expected rate of return

= 40 x 13% = 5.20

Now,

Current market price = expected dividend/new discount rate

= 5.20/0.19 = 27.37

Thus, security's current market price will be kshs. 27.37