Suppose Asset A has an expected return of 10% and a standardard deviation of 20%. Asset B has an expected return of 16% and a stanbdard deviation of 40%. If the correlation between A and B is 0.35, what are the expected return and standard deviation for a portfolio consisting of 30% asset A and 70% asset B?

## EXPERT ANSWER

here E[A]=10/100 SD[A]=20/100 E[B]=16/100 SD[B]=40/100

correlation(A,B)=0.35

or, COV(A,B)/(SD[A]*SD[B])=0.35

or, COV(A,B)=0.35*20/100*40/100=0.028=28/1000

let Z=30A/100+70B/100

so E[Z]=30/100*E[A]+70/100*E[B]=30/100*10/100+70/100*16/100=14.2/100=14.2% [answer]

V[Z]=(30/100)^{2}*V[A]+(70/100)^{2}*V[B]+2*30/100*70/100*COV(A,B)=0.3^{2}*0.2^{2}+0.7^{2}*0.4^{2}+2*0.3*0.7*0.028=0.09376

so SD[Z]=sqrt(V[Z])=0.30620=30.62% [answer]