Algorithmic Trading Strategies Are Short the Volatility of Volatility in the Short Run, but Long the Volatility of Volatility in the Long Run

I think this from the thoughtful and intelligent Emanuel Derman is wrong:

Emanuel Derman's Blog: Algorithmic Trading Strategies: It always seemed to me, and recent occurences seem to confirm it, that most algorithmic trading strategies are long volatility but short volatility of volatility...

It seems to me that this is probably wrong in a subtle fashion. When volatility declines, the value of the current positions held by a smart algorithmic trading strategy are likely to rise--it is going to report gangbusting profits in its current accounting period. But the decline in volatility means that it has little opportunity to exploit mispricings now and in the future. So when volatility declines funds pursuing smart algorithmic trading strategies are worth less of a premium going forward. So a fall in volatility should lead them to (a) report large profits, but (b) cut their fees because they can offer less value-added in the future, and (c) reduce their scope of operations.

By contrast, a rise in volatility sees funds pursuing smart algorithmic trading strategies get absolutely hammered. But they have great opportunities going forward.

Hence we right now have the interesting spectacle of people saying today: (a) we lost half our clients' money, but (b) our strategies are sound and (c) are opportunities going forward are unbelievable, so (d) you should invest and (e) we should raise our fees because we can offer more value added, and (f) we are expanding our operations.

The problem of course, is that when you have just lost half your clients' money it takes either an incredibly sophisticated or an incredibly unsophisticated investor to take that as a sign of your fundamental excellence. See, once again, Shleifer and Vishny. See also John Meriwether, trying to make these points to his investors in the LTCM context in 1998: http://delong.typepad.com/sdj/2005/06/an_historical_d.html.

Comments

[jerry]

The problem of course, is that when you have just lost half your clients' money it takes either an incredibly sophisticated or an incredibly unsophisticated investor to take that as a sign of your fundamental excellence

Sounds an awful lot like surge and last throes theory to me..... There are fewer deaths? The surge is working! There are more deaths? Of course there are, we're in the surge!!!

[mike]

In other words, buy low sell high.

Or, buy hedge funds now that they've tanked...

[mike]

In other words, buy low sell high.

Or, buy hedge funds now that they've tanked...

[mike]

In other words, buy low sell high.

Or, buy hedge funds now that they've tanked...

[John]

The problem is that the volatility of future volatility is not typically taken into account in these algorithms. Instead, pricing is based on the estimate of current volatility (= the current estimate of volatility) and the pricing doesn't involve integrating out the volatility component w.r.t. its probability distribution over the future.

Perhaps they are less sophisticated, in this respect, than you believe...

[Maurice Lanselle]

Nitpick: "the value of the current positions held by a smart algorithmic trading strategy are likely to rise" => the value _is_ likely to rise.

But seriously, should algorithmic trading strategies be arbitraging the value of the Brooklyn bridge? Illiquid CDOs may be a little more liquid than that landmark, but they weren't designed to be liquid, were they? They were designed to satisfy the maturity-matching demands of life insurance, pensions, etc.

[y]

Is there any reason to believe that hedge funds actually are algorithmically smart, as opposed to algorithmically complex? We've seen recently that many of them did not understand their own volatility, which I would say means their models are bunk. Why shouldn't we think that they're just another rediscovery of the principle that in a rising market the one with the most leverage wins?

[meno]

This was Glyn Holton's point after the Amaranth debacle. Can't find the link just now...

VaR measures typically measure volatility based on an equally-weighted sample of the last n measures (2 years is typical).

You can easily (easily if you're smart - and Wall Street has the dosh to buy lots of smart) change that to weight the more recent vol samples higher and exponentially decay that back in time.

Which is better? Well, that depends what you want. In a market where volatility has declined recently the second approach has risks.

The point is that you need smart market risk people telling you which numbers are important right now, and systems that support multiple approaches.

But there's often an organisational issue: if you think the risk managers are the cops keeping the traders in line, then it's very hard for them to get subtle and say "last week we said to use this measure, but this week we think we should consider using this other measure". If you think the market risk guys are assisting the traders, that's different: but rewards for traders are famously short-term.

[meno]

As for Brad's upbeat assessment of investing in funds that just took a bath: not so fast.

The problem is that many funds pursue statistical arbitrage and other such measures that simply rely on sophisticated correlations: ie on the future being like the past. But when market shake-ups occur some things that had correlated nicely in the past stop correlating.

Certainly some funds that did very badly will now rebound very well. And some funds will close. And some funds that should now do well if they keep trading will close anyway because everyone bails - and you could lose money investing in them even if you know that their strategy is now a winner. Can you say "crisis of confidence"?

[low-tech cyclist]

A mathematical function measures position over time.

Its first derivative measures its change over time.

The second derivative measures the change in the rate of change. This is where volatility is measured: volatility is rapid change in the rate of change.

The volatility of volatility would be measured by the third derivative of the original function.

Trying to make the third derivative of a function mean something always makes my head hurt.

[Francis]

lessee:

velocity, then
acceleration, then
change in acceleration (what my high school physics teacher called jerks), then
change in jerks.

yah, my head hurts too.

but just thinking about the drive home, I can see that delta-jerks is going to bounce around a lot in a very short period of time. And having money invested in a thing which makes rapid changes in short periods is a great way to make/lose large $ quickly.

[wood turtle]

"Hence we right now have the interesting spectacle of people saying today: (a) we lost half our clients' money, but (b) our strategies are sound and (c) are opportunities going forward are unbelievable, so (d) you should invest and (e) we should raise our fees because we can offer more value added, and (f) we are expanding our operations."

This is barf-a-rama to the max.

Well, at least the investors can say that their money was lost by the best and the brightest that Wall St. has to offer, and that will have to be the consolation.

[Dennis]

Brad:

Your observations may be correct, but your description of them definitely isn't. What you say is that declines in this month's vol are money-makers (and increases money-losers), while the reverse is true for vol in some longer time period. This isn't a position in the vol of vol, it's a spread on future vol (as one might have on natural gas). To be long or short vol of vol is to benefit/lose when volatility is more volatile -- when the market switches between a state of large swings and one of total calm. This, I think, Derman is probably right about; the state of the world where a quant fund is losing lots of money every other month is unlikely to be a good one for the fund, even if it does make some of the money back.

But it's in environments when volatility changes that they clean up in the long-run: the low-vol periods create the rule-of-thumb behavior they profit from. But in environments when vol changes they get totally trashed in the short run...]

[David Lloyd-Jones]

Very touching to read Meriweather, but he fails to admit just one small thing. His model, the core engine of LTCM, was wrong.

When Russia tanked, the model pointed to the need for investment in ver-ree long Treasuries, but on this planet thirty years is the longest there is (was at that time).

A model which produces demands for a product which doesn't exist is quite plainly a false model.