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The Value of Low Volatility
July 11th, 2007 by 
investoid
Volatility plays an important part in the long term performance of our portfolio. At times, I find that volatility is erroneously considered as ‘downside risk’ or ‘value at risk’, which are quite different. Volatility is simply the standard deviation of returns, typically in an annualized format. In of itself, volatility is a neutral measure. It does not mean that stocks are more likely to go up or down, but rather how much they go up and down. Skewness (the third moment of deviation of returns), is what measures whether period returns tend to be more positive than negative.
On an individual stock basis, volatility can be a good thing. Value investors actually like some volatility, or else they would never be able to find a stock that was undervalued. Short term investors are looking for stocks which can appreciate quickly, and thus they are looking for volatile stocks as well. But when it comes to portfolios, volatility is a bad thing.
You don’t want your portfolio to be bouncing around for one simple reason: it hurts your long term performance. One of the co-founders in my last company put it this way (he’s a math guy):
“A squared (A^2) is more than (A+B)*(A-B)”
This is simple to check: (A+B)*(A-B) = A^2 - B^2. In every possible value for A and B, A^2 >= (A+B)*(A-B). Furthermore, (A+B1)*(A-B1) > (A+B2)*(A-B2) when B1 < B2.
So if B is your portfolio's volatility, the lower it is the higher your compounded returns are. It may seem great if you make 20% one year and 10% the next, but you would have been better off earning 15% annually.
What does this mean? Look for uncorrelated assets to fit into your portfolio to minimize volatility. I talked a bit about some assets uncorrelated to the overall market in my inflation post. Larry MacDonald also discusses what big pension funds are using to minimize volatility.
Maximizing your retirement portfolio is all about steady, stable growth. It is definitely not the assets you want to be chasing the hot stock or sector de jour with. By keeping an eye on the long term, you will ensure that your retirement portfolio reaches its potential.
Posted in Investment Strategy | 
July 12th, 2007 at 1:39 pm
Stupid math, I guess there’s no way to argue with that :-).
Very interesting post! I’d recently come to accept volatility, thinking “it all comes out in the wash”, but this has me back to my old uncompromising prejudice against it (damn you volatility!!!)
July 12th, 2007 at 1:54 pm
Wait a second. Say you had an investment that paid you once a year and you put $100 into it. After two years at 15% you’d have $132.50. If you earned 20% the first year and 10% the next, you’d have $151.80 after the second year. If you had the same situation over 10 years, and consistent 15% return would give you $351.79 and an investment that fluctuated from 10-20% year to year would give you $418.96.
Am I missing something?
(A+B)(A-B) also assumes that you’re gaining a certain amount of money, then promptly losing the same amount of money (not sure why you’re multiplying them together). The expression for the situations you described would be A*0.15^2 vs (A*1.2)*1.1 - maybe this would be expressed as something like A*B^2 vs A*(B+v)(B-v) where B is the average rate of return and v is the volatility.
July 12th, 2007 at 1:58 pm
Sorry I was confusing my variables above. For some reason I started thinking A was the principle, when obviously it was the rate and B is the volatility. I just looked at my excel again and I messed that up to (the 20% year followed by the 10% year would be $0.25 less then the 15% twice).
I’ll go away now
July 12th, 2007 at 3:23 pm
Hi Mr. Cheap,
Sorry, I should have specified more clearly what A and B are. A is your mean return and B is your deviation in return. To be clear, you really need to add 1 to the equation to make it work, with A and B being in decimal form:
(1+A)^2 >= (1+A+B)*(1+A-B)
July 13th, 2007 at 6:58 am
Investoid: My fault, I figured out what everything meant AFTER I mouthed off (perhaps I should rethink the order of that in the future ;-).
One thing I *was* thinking about last night though, is that I think you’ve clearly proved less volatile is better then more volatile, but its a pretty small effect. If the choice is between a higher average rate or a lower volatility, it doesn’t take much of a rate difference to make the higher volatility enticing (such as bond funds vs stock index funds). Would you agree with that? (e.g. a consistent 15% return is WORSE then a 11% return one year followed by an 21% return the next).
July 13th, 2007 at 8:40 am
Mr. Cheap, you’re definitely right that if the average return is higher, then volatility matters less. If it wasn’t the case, then the risk/reward adage wouldn’t make sense.
July 14th, 2007 at 11:59 am
Well, this math teacher was entertained following this discussion…