What the impact on risk and return would be (the correlation here is .09).

Your Company has a portfolio made up of 2 assets, One from the USA and the other from Swaziland. Their information is as follows:

USA Swaziland

Return 12.2% 18.4%

Deviation 10.5% 23.8%

Weight 50% 50%

The company has asked me to estimate risk and return involved in the existing portfolio (the correlation is .15). They then asked me to estimate if Swaziland holdings were sold and replaced with assets from Pushistan, What the impact on risk and return would be (the correlation here is .09). Then choose the best based on lowest risk levels.

Pushistan

Return 16.7%

Deviation 14.9%

Weight 50%

Solution Preview

Hello!
Let's first find the risk of the first portfolio. The risk is defined as the standard deviation of the portfolio. In order to find the std dev, we must first fin the variance.

Let's call Ra to the return of asset A, Rb to the return of asset B, 'a' to the fraction of the portfolio that corresponds to asset A (for example, 0.3 if it is 30%) and 'b' to the fraction of the portfolio that corresponds to asset B. The formula for the variance of this two-asset portfolio is the following:

Var(portfolio) = (a^2)*Var(Ra) + (b^2)*Var(Rb) + 2*a*b*Corr(Ra, Rb)*StdDev(Ra)*StdDev(Rb)
[the ^ symbol means "to the power of"]

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