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In: Finance

Compare two cases all portfolio weights are non-negative with the min SD allow portfolio weights to...

Compare two cases

all portfolio weights are non-negative with the min SD

allow portfolio weights to be negative with the min SD

Solutions

Expert Solution

In the first case, if the portfolio weights are non-negative with the minimum SD, the SD will be lower. This is because the SD of the assets (with minimum SD) will have a higer proportion in the portfolio thereby, lowering the overall volatility (or SD ).

However, if the assets with minimum SD are allowed to have neagtive weights, meaning the weight of risky assets will be higher, that would increase the overall volatility (or SD) of the portfolio.

Example: A is a less risky asset (min SD) and weights are positive, the SD of the portfolio = 11 %

Assets Return SD Weight Expected Return SD of the portfolio
A 10 5 0.4 16 11
B 20 15 0.6

If A's weight becomes negative, SD of portfolio = 17%

Assets Return SD Weight Expected Return SD of the portfolio
A 10 5 -0.2 22 17
B 20 15 1.2

Note: SD of the portfolio is calculated as =

jeff jeffy answered 2 years ago
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