Friday, October 15, 2010

Volatility is not Risk

This is something economists seem to have a very hard time with, and I've been meaning to write about for a while.
Imagine an asset, "Safey the Asset", that pays out $10 a year forever. First payment is immediate.
The value of this stream is 10 + 10/d + 10/(d^2)...
After each payment, the value of the stream drops (the 10 up front goes away) by a factor of d, and then increases at a constant rate back up to initial value before dropping again at the next dividend. Volatility of the stream is low; incorporate the dividend and reinvest it at d, and the volatility is 0.
Now imagine a company, "Nukey the Power Plant", that with 99% probability pays out $10 and lets you roll again next year. First "dice roll" is immediate.
There is a 1% probability that it will pay out nothing and its assets will explode, never yielding any more cash.
For discount rate d, the value of this stream can be determined probabilistically:
There's a 1% chance this is worth 0
There's a 99%*1% chance this is worth 9.9
There's a 99%*99%*1% chance this is worth 9.9 + 9.9/d 
There's a 99%*99%*99%*1% chance this is worth 9.9 + 9.9/d + 9.9/(d^2)
The exact value of the stream depends on d, but you'll notice that the value of this stream can stay pretty close to constant. In exactly one year, if the assets didn't explode, the value of the stream will be determined by:
There's a 1% chance the rest of the stream is worth 0
There's a 99%*1% chance this is worth 9.9
There's a 99%*99%*1% chance this is worth 9.9 + 9.9/d 
There's a 99%*99%*99%*1% chance this is worth 9.9 + 9.9/d + 9.9/(d^2)
The price will be the exact same in one year as it is today. Like Safey, it will fluctuate in the interim only due to time value of money effects, which is determined by the size of d, and is pretty small - for a d of 10%, the value of the stream drops 10% when the money is paid out, and then climbs at a constant rate back up to initial value until the next dividend is paid. Again, observed volatility of the stream is low; incorporate the dividend and reinvest it at d, and the observed volatility is 0.
Of course, there's that pesky 1%  - if you get very unlucky, your entire asset is destroyed.
You'll notice here that observed volatility and risk have nothing to do with one another. You could go for 100 years constantly just seeing 10% price fluctuation ignoring the dividend as you win every time - on an observed volatility basis, Nukey and Safey are identical.
Perhaps the "intrinsic volatility" of Nukey is higher, because it incorporates unseen events, but intrinsic volatility is a) completely unobserved and b) completely uncorrelated with observed volatility.
This link between observed volatility and intrinsic volatility is an assumption of most finance papers, but I'd posit that it's very, very wrong.
In case you think I'm making up random examples, this "Nukey the Power Plant" asset fits the profile of a lot of different types of assets - oil rigs and power plants (ignoring energy price fluctuation - the point is the stream continuing or not), tech companies (you have unmatchable products with no competition and incredible margins... until someone comes up with something better and you lose your profit stream), event-related insurance (super cat, property, reinsurance, etc), banks (hello last 3 years), pharma (FDA pulling approvals), even fashion (you're the hip look til you're not), etc... there's almost no types of company this type of risk is NOT relevant for. I'd say the "it could go to 0" component of the risk is a much more important risk than the "look at the price of the asset oscillating" risk.
More theoretically, volatility requires semi-strong-form efficient markets hypothesis to be useful on open-ended assets.
I define open-ended assets as assets without a fixed point at which you sell or exercise the asset. So an American option is a closed end asset, because you have a specific amount of time to derive value from the option but can do so anytime in the interim. I think it's pretty easy to see why volatility matters. A bond is similar.
However, equities can be held until whenever it is that their price is good - if you can observe an underlying value that others are not seeing, this value is increasing, and that price moves stochastically with a drift towards the intrinsic value, you can buy an equity and hold it for as long as it takes to get to the intrinsic value. If the price drops, or undergoes a lot of volatility in a region that is nowhere near intrinsic value, that doesn't imply more risk, because value keeps increasing and price will eventually move towards underlying value. The longer it takes, the higher value is and the more price appreciation you'll see. The path doesn't affect the endpoints.
Thus, observed volatility is only relevant to risk if there IS no disconnect between price and value. In this case, prices need to constantly reflect all public information, at least, meaning you require the semi-strong form EMH.
I'd caution you against subscribing too strongly to semi-strong EMH. These are the same people who think that Renaissance Capital and Warren Buffett and George Soros "just got lucky" - I'd recommend "The Superinvestors of Graham and Doddsville":  I can imagine a response of either "Buffett's cherry picking" or "they just chose a method which happened to randomly work for that time period but there's no proof it will continue...." You're welcome to your opinion, but the theoretical grounds for the method were there before the method worked, were justifiable by economic theory excluding EMH, and were not rationalized ex-post. As I say to dedicated members of political parties all the time, watch out for your own confirmation biases when it comes to EMH.

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