looking for a step by step solution as to tackle this problem!! I. Suppose there

Question

looking for a step by step solution as to tackle this problem!!

I. Suppose there is a risk-free asset whose return is 4% and that the market portfolio has an expected return of 11%. The standard deviation of the market portfolio is given 20% (a) Find the security market line. (b) Suppose there is an asset whose covariance with the market is given by 450% Find its equilibrium price according to CAPM (c) Consider an asset with A = 1.5 and expected return of 14%. Can an investor use this asset to make a risk-free profit through arbitrage? Explain your answer.

Explanation / Answer

Rm=11%

Rf=4%

Equation of SML or Security Market Line: required return=Rf+beta*(Rm-Rf)

Hence, required return=4%+beta*(11-4)

=>required return=0.04+0.07*beta

Standard Deviation of market=20%

So, Variance of market=20%*20%=0.04

Given Covariance of Stock with Market=450%%=0.045

Beta=Covariance of Stock with Market/Variance of Market=0.045/0.04=1.125

So, as per above equation of SML, returns should be 0.04+1.125*0.07=0.11875=11.875%

For beta=1.5, returns should be 0.04+0.07*1.5=0.145=14.5%

But we are getting 14% that means asset is overvalued

Hence Ri<Rf(1-beta)+beta*Rm

We sell the lower side i.e., left side and buy the greater side i.e., right hand side

Hence sell the asset worth $1

For 1$ buy (1-beta)=(1-1.5)=-0.5 risk free. As it is negative, it means we are borrowing. Hence, borrow 0.5$ risk free

And buy 1.5$ of market.

So, total proceeds from sale of asset=1$

borrow=0.5$

purchase of market=1.5$

Net cash outflow=0

Now, the asset would become 1.14..Hence, you have to spend $1.14 to cover your short in asset..Short covering =$1.14

you would have to return 0.5*1.04=$0.52..hence, cash outflow for borrowing=$0.52

your market would become 1.5*1.11=$1.665..Hence, cash inflow from market=$1.665

So, total cash inflow=$1.665-$1.14-$0.52=0.005

Thus return of 0.005/1=0.5%, this is the difference between required return and expected return on asset

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