http://www.snapback25.com/index.php/diam ond-supply-co-snapback-hats.html

In a boom-and-bust cycle, there is a tendency to over-expand capacity and (following the bust) end up having to write down plants and inventory. This was deadly for the fiber/telecom industry in 2001.

In a bust-and-boom cycle, there is a strong temptation to pull back on innovation and cut costs, limiting future revenue growth when the rebound comes. (May also run into financing problems.)

Either way, you are likely to end up paying large management bonuses in the “boom” half of the cycle, even if the overall movement is comparatively small.

The price swing can simultaneously reflect value destruction and lead to additional value destruction. The latter is the best argument against market volatility — it reduces the efficiency of the economy.

Long term outperformance certainly needs regular short term underperformance. Targetting returns that are unachievable on an adequate risk base is a recipe for disaster though. In the words of Benjamin Graham “turning investors into speculators with a speculator’s result.”

The Hawaii Employees’ Retirement System probably is moving into a bracket here that its investors and overseers cannot shoulder. The worst possible decision of course would be to de-risk following a plunge in risk asset value and realising the losses. Reversing course mid way on the down leg consistently is the worst option of all.

I do agree with his concluding lines, “if you overshoot on the way up and you overshoot on the way down, you end up underperforming overall.”

Mathematically, you can imagine a set of inputs for which overshooting on the way up more than makes up for overshooting on the way down. (You shouldn’t simply assume that the deltas sum to zero.)

But more practically, overshooting a large drop in the market is likely to involve massive value destruction, beyond simple market volatility. You can’t ride out the storm if the company you own sinks under the waves.

Moreover, Wall Street has a known bias towards optimism, a known tendency to downplay risks. The calculation that supposedly proves that a riskier company offers a higher expected return may simply be overestimating the upside and underestimating the downside. This is especially true in times of economic turmoil, when optimistic projections are regularly blown to smithereens.

I do agree with the conclusions. I simply hesitate to accept a mathematical “proof” that is strongly dependent on its assumptions.

We agree that the geometric mean of a non-negative sequence is lower than the arithmetic mean of the same sequence. This does have valid applications in finance, particularly in the “gambler’s ruin” paradox. (Any game in which you have a potential return of -100% will eventually leave you broke, no matter what the expected value of the outcomes suggests.)

But Felix seemed to be applying this in a very different manner. He was beginning from the assumption that we are in a flat market. In a flat market, where the long-term return is 0%, the percentage gains will be larger than the percentage losses (for exactly the reason you describe). His mistake, and yours, was in assuming that the arithmetic mean of the returns in a flat market should be zero. Garbage in, garbage out, even if your mathematics is sound.

Maybe financial theory should adjust its choice of metrics? Perhaps if they did so, we would see fewer hedge funds falling prey to gambler’s ruin?

(1 + (m+d)) (1 + (m-d)) – 1

( 1 + ((m+d)+(m-d)) + (m+d)(m-d) ) – 1

1 + 2m + (m^2 – d^2)

Whereas with just returning m in both periods, you’d get (1+2m+m^2). Again, the difference is the -d^2, and you necessarily underperform, and this outcome is totally general.

There’s actually a term for this in financial theory — volatility drag.

Just think about two periods, where the average return across the two is mu, but in period 1 we outperform by delta, and in period 2 we underperform by delta:

(mu + delta) (mu – delta) = mu^2 – delta^2

Given that delta^2 must be positive, we know that this return is worse than if we’d had no volatility.

This argument can be extended by induction to any number of periods.

QED.

But that plays out over years (e.g. 1997-2008 for the “M” or 2000-2010 for the “W”). There aren’t enough contributions/withdrawals over shorter periods to make a difference.