Fun with Normal Distributions: The annual returns of an emerging markets bond fu

Question

Fun with Normal Distributions: The annual returns of an emerging markets bond fund are assumed to be normally distributed with a mean return of 10% and a standard deviation of 15%. The normally distributed annual returns of a US bond fund have a mean return of 6% and a standard deviation of 10%. The correlation of emerging bond returns with US bond returns is 0.4.

a.What is the expected return on a portfolio allocated 40% to emerging bonds and 60% of US bonds?

b.What is the standard deviation of returns on a portfolio allocated 40% to emerging bonds and 60% of US bonds?

c.What is the probability that this fund will yield returns less than 0% in a given year?

Explanation / Answer

here as return =0.4*Emerging bonds return +0.6*US bonds return

let emerging bonds are A and US bonds are B

a) expected return =E(X)=0.4*10+0.6*6 =7.6

b) std deviation =((0.4*SD(A))2+(0.6*SD(B))2+2*0.4*0.6*r*SD(A)*SD(B))1/2 =

=(0.4*15)2+(0.6*10)2+2*0.4*0.6*0.4*15*10)1/2 =10.0399

c)

probability that this fund will yield returns less than 0% in a given year

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