You are a portfolio investor and, for simplicity, are investing in only two asse

Question

You are a portfolio investor and, for simplicity, are investing in only two assets. You must invest in one asset(called Asset A) and then choose one additional asset from a choice of 3 assets. The asset you must invest in has a variance of 0.09. Now, you must choose 1 asset from the following 3.

i) asset B has a variance of 0.04 and a correlation of 0.90 with Asset A.

ii) Asset C has a variance of 0.04 and a correlation of 0.45 with Asset A.

iii) Asset D has a standard deviation of 0.25 and a correlation of 0.35 with Asset A.

Assume equal weights in Asset A and the 2nd asset you choose. You are to choose the asset that provides you the lowest portfolio risk. Which asset do you choose?

Explanation / Answer

Need to find variance of all three alternatives

Variance = W12*Var1 + W22Var2+ 2*W1*W2*SD1*SD2*Corelation

SD = SQRT(variance)

i)

Variance = 0.52*0.09 + 0.52*0.04 + 2*0.5*0.5*SQRT(0.09)*SQRT(0.04)*0.9 = 5.95%

ii)

Variance = 0.52*0.09 + 0.52*0.04 + 2*0.5*0.5*SQRT(0.09)*SQRT(0.04)*0.45 = 4.60%

iii)

Variance = 0.52*0.09 + 0.52*0.252 + 2*0.5*0.5*SQRT(0.09)*0.25*0.35 = 5.13%

Choose Asset C as portfolio A&C has the lowest variance

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.