Question

Assume that the expected rate of return on the market portfolio is 15% and the risk-free rate is 5%. The standard deviation of the market is 20% and assume that the market portfolio is efficient.

a) What is the equation for the Capital Market Line?

b) if an expected return of 40% is desired, what is the standard deviation of this position?
If you have a 1000$ to invest, how should you allocate it to achieve the above position?

c) If you invest 300$ in the risk-free asset and 700$ in the market portfolio, how much money can you expect to have at the end of the year?

Answer 1

Data Given:

Expected Return on Market Portfolio = 15%

Risk Free rate(Rf) = 5%

Standard Deviation of Market = 20%

CML is the tangent line drawn from the risk free point to the feasible region for risky assets. This line shows the relation between rP and σP for efficient portfolios (risky assets plus the risk free asset)

The tangency point M represents the market portfolio, so named since all rational investors (minimum variance criterion) should hold their risky assets in the same proportions as their weights in the market portfolio.

Equation of the CML: r = rf +( rM − rf)/ σM σ,

where r and σ are the mean and standard deviation of the rate of return of an efficient portfolio. Slope of the CML = rM − rf σM = price of risk of an efficient portfolio. This indicates how much the expected rate of return must increase if the standard deviation increases by one unit

from the above

  rf(Risk free retutn) = 5%

rM(Return of market) = 15%

σM(market Stadard Deviation) =20%

σ(Standrd Deviation of return assumed to be at 40 %) =40%.

CML = 5%+(15%-5%)/20%*40%

= 5%+(10%/20%)*40%

=25%