The Investment Scientist

Volatility: a drag on return

Posted on: May 16, 2008

In my last article, I explained why volatility does not measure risk. It’s an assertion by none other than Warren Buffet himself. I hope the historical data I used convincingly illustrated the point.

If volatility doesn’t measure risk, then what can we learn from it?

Let’s look at this simple example. Let’s say you invest $100 in asset A, whose volatility is 10%. In year one, the asset returns 10%. In year two, it returns -10%. What is the terminal value in year two? If you’re like most of us mortals, you’d call it a wash. You’d guess $100. Not so, the terminal value is $100*(1+10%)*(1-10%)=$99.

Now let’s assume you invest $100 in asset B, whose volatility is 20%. In year one, the asset returns 20%. In year two, the asset returns -20%. What is the terminal value in year two? This time you should get it right, it is $100*(1+20%)*(1-20*)=$96. So, everything else being equal, we can say higher volatility means lower investment return.

Mathematically speaking, volatility is a drag on return.

Steve Shreve, the math professor in my quantitative finance class, would give you this formula:

Reduction in return = ½ volatility2

For instance, if the annual volatility is 20%, then the drag on annual return is ½*(20%)2=2%. This drag on return is not risk, since it is deterministic – there is nothing uncertain about it.

How to reduce volatility drag on return?

This simple answer is diversification. However, diversification requires special care. Blind diversification could do more harm than good. This is a topic best left for another article.

The author is president of MZ Capital, a RIA serving DC/MD/VA. Get his monthly newsletter in your mailbox.

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Michael Zhuang is principal of MZ Capital, a fee-only independent advisory firm based in Washington, DC.

Twitter: @mzhuang

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