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Discuss why is the relationship between expected return and standard deviation for portfolios of risky and...

Discuss why is the relationship between expected return and standard deviation for portfolios of risky and risk-free assets linear

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Answer #1

By definition, the standard deviation of risk free assets is zero and due to this there is a linear relationship between the expected return and standard deviation of portfolio of risky and risk free assets - we can look at this by simply going through the respective formulas.

Let us take a portfolio of 2 assets A (risky) and F (risk free) with weights WA and WF and standard deviation SDA and SDF.

Now ER (P) = WA * RA + WB * RB

SD (P) =

Since SDF is zero by definition, the SD (P) simply reduces to :

SD(P) =

Thus we can see that the SD becomes simply the function of proportion of portfolio invested in the risk asset/s. Since the way to increase the portfolio expected return is to invest higher proportion in risky asset (risk free asset being constant), thus as the expected return increases the SD also increases through increase in the weight of risky asset in similar proportion.

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