Question

An investor is considering two portfolios (Portfolio 1 and 2). Both possible portfolios consist of a 50% weight on Asset A: this asset has an expected return of 12% and a standard deviation of 18%. The other half of Portfolio 1 consists of Asset B: it has an expected return of 8% and a standard deviation of 10%. The other half of Portfolio 2 consists of Asset C: it has an expected return of 8% and a standard deviation of 14%. Can we say that the standard deviation of Portfolio 1 is smaller than the standard deviation of Portfolio 2?

Answer 1

Given that :

Portfolio 1 = Asset A (return:12%) SD 18% + Asset B (return: 8%) SD 10%

Portfolio 2= Asset A (return:12%) SD 18% + Asset C (return: 8%) SD 14%

It is evident that the other half of both the portfolios is giving similar return with different SD value.

Lets assess the value of the other half of both the portfolios considering that SD of Asset A is constant for both portfolios

Lets say the 8% return amounts to USD 100.

Case 1: Asset B gives a return of = 110 (SD =+10%)

and Asset C Gives a return of = 86 (SD= -14%)

Here total SD of Portfolio 1 > total SD of Portfolio 2

Case 1: Asset B gives a return of = 90 (SD =-10%)

and Asset C Gives a return of = 114 (SD= +14%)

Here total SD of Portfolio 2 > total SD of Portfolio 1

Conclusion : Hence we cannot say which portfolio is having higher SD and which is having smaller.