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What is the relationship of the portfolio standard deviation to the weighted average of the standard deviations of the component assets?

Short Answer

Expert verified

It is equal to each other

Step by step solution

01

Definition of Optimal Portfolio

The set of optimal portfolio is the one that offers the highest expected return for a defined risk or the lowest risk for a given expected return.

02

Explanation on diagrams

When all assets are positively correlated, the standard deviation of portfolio is equal to the weighted average of the component-asset standard deviations.

According to its formula, the portfolio variance is the weighted sum of the elements in the covariance matrix, with the products of the portfolio proportions as weights. This is represented as:

σ2P = (wB σB)2 + (wS σS)2 + 2(wB σB) (wS σSBS

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