On Investment Modeling, Part 1

Investing is a battle between the past, present, and future.

The past tempts all to look and see what has happened, and extrapolate, or assume mean-reversion.  It tempts academics to use simplistic math, and calculate alphas, betas, standard deviations, R-squareds, and more.  They consider the past to be prologue.  They estimate assumptions for asset allocation off of averages of past returns, sometimes even making the error of arithmetic averages, rather than geometric averages.

But the past is the past.  It happened, and it usually has little bearing on the future, aside from momentum effects when few are following momentum.  Those who calculate models off of historical data describe the past in a stylized way.  The past is a historical accident; generalizing from it in precise terms is difficult.  In some ways I think that analogies from the more distant past have more validity, partly because they are less known by the average market participants.

Those who use the past for asset allocation are doomed for failure.  The past is the past.  Bonds returned well in the past, but the best estimate of a bond’s return over its maturity is the YTM now.

The present intrudes on the past that way. With stocks, the same thing happens measuring current P/Es, P/Bs, P/Ss, versus long term average returns.  It is far better to be a buyer when a stock is out of favor, but not dying.

In the present we can estimate implied volatilities from options, and even implied correlations in certain cases.  Real-time as those are, they give the knife-edge of the estimate of how things react presently.

But as for the future?

We have precious little in the way of clues.

Yes, value and momentum may give us some guidance when they are underfollowed, but they are poor and weak guides to the future.

The truth is that we just don’t know.  Our models are often regime-dependent, because data has been collected over a limited period of time.  I smiled at the Denver conference that I recently attended, as models were trotted out that were based on 20 years of data or fewer.

Now, I don’t blame the researchers, including myself, much.  We all look for the biggest, longest set of clean data we can find.  We realize there are things that we aren’t testing.  We should know that there are hidden variables that haven’t varied much during a regime, that might our results quite different when the regime shifts, but for the most part those are Rumsfeldian “unknown unknowns.”

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Excursus: I once did a seemingly hopeless project to try to estimate withdrawal sensitivity to interest rate movements on deferred annuities.  I completed it in 1998, with 16 years of data, on hundreds of thousands of policies.  Big known problem: interest rates had fallen over the whole period.  But the need for the project was evident, because interest rates had nowhere to go but up, right?  With a little clever modeling, though, I teased out the statistically significant result that a one percent rise in the difference between competing and our deferred annuity yields would lead to additional withdrawal of 2%/yr.

At first, I thought 2% was too small, but then I realized it was an option not efficiently exercised.  So I left padding  in my analysis, assuming that if the market ran away and we couldn’t keep up, that withdrawal levels would be far higher than a ratio of 2.  I built my asset-liability model, which had the capacity of running multiple scenarios developed from my multivariate mean-reverting lognormal interest rate model, built from my homegrown quasi-monte carlo multivariate random number generator.

I did not set the model to optimize investment policy.  Instead, I set it to do well on two criteria that I weighted: minimize losses in the lowest 5% of the tail, and best average result.  When I got the results, they looked wrong; but the more I looked at them, I realized they were right.  I did two versions, one that allowed for the use of interest rate options, and one that didn’t.  Knowing  that my investment department had no quants, I realized the options would be a tough sell — indeed, they chose the option without them.  But then they asked me, “Dave, these are deferred annuities; crediting rates vary annually.  You’re telling us to invest three years longer than we are currently in duration terms — that’s huge.  And why 20% in 30 year bonds?”

My answer was a simple one.  We were all concerned about rates rising and withdrawals that would occur from that.  We missed the other issue, because interest rates can only go up from here, right?  Floor guarantees.  If rates continued to fall, we would have no ability to lower rates further on an increasing amount of the policies; those policies also would have low lapse rates.  When I explained how close we were to the floor we were they caught on, and realized that we had a rare “free lunch.”  Limit risk and improve returns all at once.

Actually, it meant we had mismanaged the business previously, because it was the first withdrawal study in the history of that line of business, but at that point it increased the profits of the company significantly.  What’s more — rates didn’t rise as we all knew they would.  The change in investment policy saved the insurer that merged/acquired the company a lot of headaches.

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So, with whatever our results seem to be, we have to take caution and not overdo what our results seem to prove.  Risk control should be the order of the day.  Buffett said that all he wanted in life was an unfair advantage, but with our limited knowledge of how markets work, we have to realize that we probably have less advantage than we think.

I have more to say here, but I have to hit the publish button — too long already; more coming in part 2.

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