Quizmaster, Doug Hutchinson, has come up with a great quiz that illustrates how adding an asset with higher volatility can actually lower overall volatility of a portfolio. Let’s see what the math has to say.
Good luck!
Consider this scenario:
Your friend Mary has a portfolio consisting of one asset, Asset A. She is considering adding a second asset to the portfolio and her new portfolio would be weighted as 50% Asset A and 50% of the new asset.
She would like the new two asset portfolio to have the lowest risk (as measured by standard deviation) possible, given the other options that she is considering adding to her portfolio: Asset B and Asset C.
Risk measures of the three assets are listed below.
Note: Standard deviation is a volatility measure that quantifies how much a series of numbers (such as returns of an asset) varies around its average. The more an asset's returns fluctuate from time period to time period, the greater its standard deviation.
Note: Covariance is a statistical measure of the strength of correlation between two variables. If covariance between two assets is positive then the assets move in the same direction. If assets have a negative covariance, then they move in opposite directions. If the covariance is zero, then the assets have no relationship.
Standard Deviation:
Asset A: 0.50
Asset B: 0.60
Asset C: 0.65
Covariance:
Asset A and Asset B: 0.40
Asset A and Asset C: 0.05
Should Mary’s new portfolio be 50% Asset A and 50% Asset B or 50% Asset A and 50% Asset C?
Solution:
The standard deviation of a two asset portfolio is a function of 1) the weightings of the assets, 2) the standard deviation of each of the assets, and 3) the covariance between the assets.
The exact equation for the standard deviation of a portfolio of 2 assets is:
Portfolio standard deviation1,2 = [weight12 x standard deviation12 + weight22 x standard deviation22 + 2(weight1)(weight2)(Covariance1,2)]1/2
Running through the equations for both options, we'll see that the standard deviation of a portfolio that is 50% Asset A and 50% Asset B is 0.5937 and the standard deviation of a portfolio that is 50% Asset A and 50% Asset C is 0.4395.
Mary should choose the portfolio that is 50% Asset A and 50% Asset C since that portfolio would have the lower standard deviation.
Note that Mary is able to lower the overall volatility of her portfolio (as measured by standard deviation) despite adding an asset (Asset C) that has a higher standard deviation than the original asset, Asset A. This is because of the low covariance between Asset A and Asset C.
This quiz is intended for informational and illustrative purposes only. This material is not intended to be relied on as a forecast, research or investment advice, and is not a recommendation, offer or solicitation to buy or sell any securities or to adopt any investment strategy. The information presented is general information that does not take into account your individual circumstances, financial situation or needs, nor does it present a personalized recommendation to you. The information and opinions contained in this material are derived from sources deemed reliable, are not all-inclusive and are not guaranteed as to accuracy.
