Consider two assets A and B for which return distributions can be summarized as
ID: 2717259 • Letter: C
Question
Consider two assets A and B for which return distributions can be summarized as follows
1?What is the risk of the minimum risk portfolio composed of these two Stocks? (Hint: Use the calculus to minimize sp2). Is the risk of the minimum risk portfolio below that of every constituent asset? What is the expected ROR on the minimum risk portfolio?
2?Consider two other assets A’ and B’, which are identical (in statistical summary), respectively, to A and B above except that rAB = 1. Write down the answers to the same question as in 1?.
EIR, ] = 3% EIR,1-7% 0 Og = 2%Explanation / Answer
1) risk = std dev=( w2A*2(RA) + w2B*2(RB) )^0.5
Minimum risk is when allocation to B is 0
there fore risk = (1^2*1 + 2^2*0)^0.5 = 1%
ROR = WA*RA +WB*RB = 1*3 + 0*7 = 3%
2) std dev=( w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*(RA)*(RB))^0.5
Cor(RA, RB) =1
therefore std dev= WA*A +WB*B
Again risk can be minimized by having 0 exposure to B
= 1*1 + 0*2 = 1%
ROR = WA*RA +WB*RB = 1*3 + 0*7 = 3%