Wednesday, July 8, 2015

Questions America Wants Answered: Is Semi-Variance A Better Measure of Risk?

Yes.
(the exception that proves the rule of Betteridge's law of headlines)

The post immediately below,"Charlie Munger on “Loading Up,” Tracking Error, and Value Investing", had a line that reminded me we hadn't posted on semi-variance recently:
In investment management today, everybody wants not only to win, but to have a yearly outcome path that never diverges very much from a standard path except on the upside....
I think I first mentioned semi-variance on the blog in 2008 (in reference to how much I'd forgotten).
If you've also forgotten, here's the Fama/French Forum at Dimensional Fund Advisers:

Q&A: Semi-Variance: A Better Risk Measure?
Is semi-variance a more useful measure of downside risk than standard deviation? My clients aren't worried about market surges, they're worried about market crashes.
 

EFF/KRF: In his classic 1959 book that defined modern portfolio theory, Markowitz considers the semi-variance as a potential measure of risk. Interest in the semi-variance fell by the wayside among academics because, at least for short holding periods (e.g., monthly), distributions of returns are rather symmetric. For symmetric distributions, the true variance and semi-variance are interchangeable, but because all the data are used to estimate the variance but only negative returns are used to estimate the semi-variance, estimates of variance are more accurate than estimates of semi-variance. For longer holding periods (e.g., a year or more), distributions of returns are right skewed, and no single measure of dispersion (e.g., the variance or the semi-variance) summarizes the overall risk of the distribution.

Let's now examine whether you really believe what you say about your client's tastes. In our (academic) terms, your statements imply that your clients are risk neutral on the upside but risk averse on the downside. If this is the case, the semi-variance, which ignores upside risk, is probably a better single measure of risk than the variance, but the conclusion is subject to the caveats above about the skewness of return distributions for longer return horizons....MORE
If interested see also:
June 2014
"The Equation that Will Change Finance"
June 2014
Climateer Quote of the Day: Volatility Edition (VIX)
... Leading us to:
1) Understanding why Izzy's Capping the Gold Price was so interesting.
2) Sam Cooke singing Johnny Mercer, naturellement: 
You've got to accentuate the positive
eliminate the negative
Latch on to the affirmative
But don't mess with mister inbetween
You've got to spread joy up to the maximum
Bring gloom down to the minimum...
June 2013
Barron's on Gold and Real Interest Rates

And a handy little (14 page PDF) chapter from Markowitz' Portfolio Selection: Efficient Diversification of Investments via the Cowles Commission.