## How volatility hits pension plans

Nanea Kalani of Honolulu Civil Beat has obtained non-public performance numbers for the Hawaii Employees’ Retirement System, and they’re not pretty at all: in the three months to September 30, the fund managed to lose $1.4 billion, or 11.2% of its value.

What we’re seeing here is the brutal effect of volatility on portfolio performance. Let’s say you start with $1,000. If your portfolio falls by 5% and then rises by 5% — or, for that matter, if it rises by 5% and then falls by 5% — you end up with $997.50 — just a quarter of a percentage point away from where you started. But if it falls and rises (or rises and falls) by 20%, then you end up with just $960, down 4% on your initial investment.

There’s two different lessons to be drawn from the way that Hawaii is investing its money. Firstly, going for active rather than passive investment doesn’t work very well. The policy benchmark — what the fund would have returned if it was passively invested rather than actively managed — has consistently outperformed actual performance. And

Secondly, Hawaii hasn’t chosen its managers very well: it’s also consistently underperforming the median public pension fund. If you’re relatively small (about $10 billion, in this case), it’s hard to outperform. As the Pension Consulting Alliance note puts it, “Relative underperformance can largely be attributed to the Plan’s equity (domestic and international) managers’ combined performance trailing their respective benchmarks”.

But there’s a deeper problem here, I think — and that’s related to the fact that the fund is being asked to return an “assumed actuarial rate” of return of 8% per year — in an environment of high volatility and extremely low interest rates. The right thing to do is to say “sorry, I can’t do that” — but that’s a great way to get fired. So instead, fund managers move further and further out the risk curve, in an attempt to hit their target returns. With predictable consequences.

Sometimes, the strategy works. In fact, the strategy is *always* going to work some of the time. The note proudly says that “the Plan outperformed the policy benchmark and the Median Plan in three of the last five 12-month periods”. But this is the problem with volatility: if you overshoot on the way up *and* you overshoot on the way down, you end up underperforming overall.

I’m not particularly picking on Hawaii, here, I’m just using it as an example. Most public pension plans have very similar problems. They take on more risk than they should, just because they’re being asked to hit unrealistic return targets. And the losers, of course, are all of us.

Felix, your second paragraph is smoke and mirrors. While mathematically accurate, there is fundamentally no reason for a 20% drop to be matched against a 20% rise. You could argue symmetry, but as you point out it is NOT a symmetric outcome. The symmetric match for a 20% drop is a 25% rise.

You have yet to give a cogent argument why volatility is bad. The first time I remember you bringing it up was in May 2010, when you argued that volatility increases risk, and thus only an idiot would be investing in stocks at that point. Subsequently the S&P rallied 20% over the next 12 months. Now you are pulling numbers out of a hat and pretending that they prove something?

I do agree with your broader point. When the market is overpriced, and forward returns are low, the rational behavior is to REDUCE risk in the portfolio. The rationale for increasing risk should be *high* expected forward returns, not the reverse.

And finally, I agree that an “assumed actuarial rate” of 8% per year is ridiculous in the present environment, especially for a “balanced” portfolio. We could argue whether or not stocks will return 8% per year over the next decade (I’m skeptical, though they might come close), but I am REALLY CERTAIN that ten-year bonds yielding 3% will not return an 8% total return.

And I’m also certain that stocks won’t return the 12%+ that would be necessary to balance out those abysmal bond returns.

“If you’re relatively small (about $10 billion, in this case), it’s hard to outperform.”

My three-month return (7/1 through 9/30) on my retirement accounts was -4.5%. It is very easy to outperform during periods of volatility, especially if you are small.

Thanks TFF for articulating the ridiculousness of the ‘volatility hurts performance’ argument that just won’t die. Now if we used continuously compounded returns instead, this wouldn’t be an issue.

Which is why the Fed should offer state pension funds a 5% TIPS bond – reducing Federal borrowing volatility and reducing expected social costs of the collapse of all these mismanaged state pension funds.

That should be Feds with an “s”.

Felix, this post really makes no sense. Mean-reverting noise gets you back to the mean.

What TFF and Stevensaysyes said. The problem is with a dumb metric, not with volatility.

The point about yield-chasing is good, and the agency problems that help lead to it, but it’s mixed together with a sort of anti-arithmetical innumeracy.

Volatility actually *can* be a concern for pension plans, but for another reason… If you are making steady contributions (dollar-cost averaging?) into an “M” shaped market, you end up buying at valuations higher than the terminal point. If you are making steady withdrawals from a “W” shaped market, you are eroding your share balance more rapidly than you would in a steady market.

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.

Picking the same up and down around zero is arbitrary, but you guys are wrong on the math here. A perfectly non-volatile performance — consistently hitting the average return for a series of time steps — will produce a higher final return than any other series of returns that could produce the same average.

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.

Oh, whoops, sorry, in a hurry, forgot to do the “1+r” part of the calculation above. It of course doesn’t alter the conclusion

(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.

Auros, my mathematical background is probably stronger than yours. I also understand the danger of reasoning from assumptions that have no basis in reality. Do you?

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?

Perhaps I’m misreading Felix’ assumptions?

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.

There are very few people and institutions with true holding power today. Even long term investments are presented in quarterly or monthly reports and benchmarked.

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.

The problem with a 20% rise-and-fall as compared to a 5% rise-and-fall has nothing to do with volatility. It has to do with the fact that in the first scenario, there is greater destruction in value. Percentages are a useful tool for our limited brains to comprehend comparative values, but don’t forget that a percent gain or loss represents an absolute increase or decrease in value. In your scenario, “volatility” is just a way of describing what happened–volatility didn’t actually “cause” the decline in value.

@DAL, from a fundamentals perspective a small rise-and-fall may have no impact at all on the underlying value of the company, yet a larger rise-and-fall can distort operations and truly destroy value.

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.

Gambling with public pensions is like flirting with dynamite! I’d bet anything California will end up with almost a trillion dollar pension deficit before long-just california! Capitaal preservation is the nak=me of the game now-can you hold on to your principle! double digit ROIs is dreaming/gambling now folks-call it greed!

If you’re gambling for high returns, your group should cover the loss, NOT THE TAX PAYER! NO BRAINER!

fire those investment managers! and make sure you give them a good bonus! WHY HAVENT WE LEARNED A THING YET?!

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