Volatility: A Serious Drag on Return

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:

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. If you’d like to receive it, please subscribe to my monthly newsletter – The Investment Scientist.

Comments

[dlaw:]

First, your articles contradict each other. Mr. Buffett's point is exactly counter to yours. He is saying that there are times when high volatility has to be ignored. It is therefore NOT a drag on returns, in his "value" view.

Mr. Buffett's belief that he can predict the future is actually based fundamentally on a prediction about VOLATILITY. He gets it from one of his core businesses - insurance. In that business - which is a TEMPLE built to volatility and statistics - the assumption is that high volatility will "come in" or "return to the mean" as some say.

Mr. Buffett's approach relies on the belief that there are two markets between which he can arbitrage. One is in stocks which is relatively volatile and one is in free cash flow which is relatively non-volatile. It's no accident that he is an innovator in the reinsurance market - again a play between more and less volatile markets.

Like any good insurance man, he plays the percentages by betting the two will converge.

Finally, your thesis assumes that people confuse volatility and risk. But the reason people look at volatility in the first place is because Black-Scholes taught people to develop a valuation strategy that is agnostic as to fundamental risk. Using a beta assumption is the practice of ignoring risk in the near term. But anyone who uses beta also uses a "beta risk" assumption - and that is that beta (however one measures it and whatever one compares) will narrow or widen with time.

Finally, you forget liquidity constraints. High beta *is* high risk because of liquidity constraints. Most market theory ignores liquidity constraint, with the predictable result we see in credit markets today.

2008 May 17 02:50 PM

[bill d:]

Very informative from both of you.
I wish I was smart enough to be able to make a comment on this which means I must be smarter than I thought.

2008 May 17 07:48 PM