### CFA Practice Question

The risk-free rate prevailing in Nirvania is about 6.5%. Nirvania's market risk premium has been estimated at 8.9%. If the market's excess return per unit of risk is 0.77, the risk-to-reward ratio of an efficient portfolio, P, which consists of 35% invested in the risk-less asset equals ______.
A. 1.33
B. 0.44
C. 0.61
Explanation: This questions requires you to know the definitions of "risk," "excess returns," "risk premium," "risk-to-reward ratio" and "efficient portfolio," all in the presence of a risk-less asset.

Unless otherwise specified, "risk" should be taken to mean "standard deviation" of returns. "Excess returns" refers to expected returns in excess of the risk-free rate and is synonymous with "risk premium." Thus, the market's standard deviation is calculated as 8.9/0.77 = 11.56%. The expected return on the market equals 8.9% + 6.5% = 15.4%

It is also important to remember that in the presence of a risk-less asset, an efficient portfolio is a combination of investments in the market portfolio and the risk-less asset. Hence, the expected return of P is 0.35 * 6.5% + 0.65 * 15.4% = 12.285%. The standard deviation of P equals 0.65 * 11.56% = 7.51% (Note that the risk-less asset has a standard deviation of 0%. Hence, the standard deviation of a portfolio consisting of a risk-free and a risk-less asset is directly proportional to the fraction invested in the risky asset). Thus, the risk-to-reward ratio of P equals 7.51/12.285 = 0.61.

User Comment
mm04 Excellent question!
sarath Amazing question...
dimanyc yeah, i just wish it was possible to figure out and calc all that in time given :)
Kuki Basically what they have given in the question is this:
risk-free rate 'Rf' = 6.5%
market risk premium 'Beta(Rm-Rf)' = 8.9%
Excess return per unit of risk 'Rm-Rf' = 0.77
Therefore Beta or STD Dev = 8.9/0.77 = 11.56

Expected return-using CAPM = E(R) = Rf+Beta(Rm-Rf) = 6.5% + 8.9% = 15.4%

using the portfolio weights given we get
E(Rp) = .35*Rf + .65*E(R) = .35*6.5% + .65*15.4* = 12.285

and STD DEV(p) = .35(0) + .65(11.56) = 7.514

Risk to Reward Ratio = 7.514/12.285 = 0.61 Ans

krisc Great !!!!!
wtwaf risk= standard deviation.. great job kuki
pstebelp I thought CAPM was = Risk free + Beta(Market risk premium). But Kuki implies that "Beta(Rm-Rf)" is the market risk premium. Isn't "Rm-Rf" the market risk premium?
aragarwal market risk premium is rm -rf....

here i think the beta for market is taken as 1 ....while calculating expected return from market...