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Tale Of Two Volatilities
Written by Brad Zigler   
Wednesday, 19 March 2008 15:28

Then comes the pregnant pause. It's here I'm supposed to issue the advice that either soothes or incites. Folks are crestfallen when all I can offer is a weak "Uh, well, they are at that." Without a blackboard or laptop projector handy, it's just not that easy to expound upon relative volatility.

A certain amount of exposition is necessary because there's more than one conceptualization of volatility. The concerns voiced by inquiring partygoers typically bespeak a fear of downside volatility. It's a safe bet that if Mr. Soon-to-be-wearing-a-lampshade bought a commodity derivative, he'd be deliriously happy if prices subsequently shot higher.

But commonly used measures of volatility weight downside and upside volatility equally as if both are bad. Take the standard deviation of daily returns, for example. Over the past year, it was 18.7% for the S&P 500. The S&P/GSCI Total Return, the benchmark underlying the iShares commodity ETF (NYSE Arca: GSG), cranked out a modestly higher reading of 20.2% over the same period. From this, commodities can indeed be said to have been, albeit weakly, more volatile than stocks.

Here's were the blackboard comes in handy.

Downside volatility for the commodity index has actually been lower than that of the stock benchmark. If you only count down days - days in which daily returns were negative - the standard deviation for stocks is 11.8%. Commodities come in at 10.9%. Commodities come off as less volatile measured this way.

It's the proximity of these readings, though, that should give investors pause. It won't take much to push volatility around. For either market. That means that risk-adjusted metrics like the well-known Sharpe ratio and the downside variance-based Sortino ratio could easily flip over if the return spread starts to narrow. And that could precipitate a flow of funds.

Try explaining that to a guy wearing a lampshade as a hat. 

 

12-Month Performance: S&P 500 vs. S&P/GSCI Total Return

 

 

 

SPX

SP/GSCI

TR

Return

-5.1%

56.1%

Standard Deviation

18.7%

20.2%

Sharpe Ratio

-0.47

2.59

Downside Variance

11.8%

10.9%

Sortino Ratio

-0.75

4.79

 

 
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Comments (2)

 Thursday, 20 March 2008 16:40 EST - Posted by Kyle

 
Wonderful piece, and very timely too with the present downturn across the board. It would be an interesting comparison as well to look at just very recent history and compare the two, and I'm certain equities would not fare much better with triple digit swings in the Dow more the rule than the exception these days. Long time reader, first time comment on HAI. All together a great piece. Thanks.

 Friday, 21 March 2008 11:00 EST - Posted by Brad Zigler

 
Kyle -

Thanks for the kudos. Your wish is our command.

Recent returns actually state the 'Tale of Two Volatilities' case more strongly.

Year to date, the S&P 500 is down 8.3% With a standard deviation of 24.6%, the blue chip index earns a Sharpe ratio of -0.34. Downside variance is 16.62%, yielding a -0.72 Sortino ratio.

The S&P/GSCI TR has contemporaneously risen 16.6%, exhibiting a standard deviation of 26.3%. That produced a 0.63 Sharpe ratio. The index's 1.05 Sortino ratio arises from a downside variance of 13.7%.



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