Tuesday, March 4, 2014

Stock/Bond Asset Allocation (Part 4) - Schrödinger's cat's pension

When considering portfolios with different holding periods, as I have in recent posts, I find a paradox.  I wonder if anyone has a solution to this paradox.

Consider this graph.  This compares the outcomes of 3 portfolios over time - a stock portfolio, a long-duration bond portfolio, and a 50/50 mixed portfolio.

This seems like pretty straightforward standard analysis to me.  The longer your investment horizon, the more exposure you can withstand to temporary fluctuations, and the more risk you would want to position yourself with.

Here, we can see that, historically, the worst 20 year period for the stock portfolio was better than the worst periods for both the bond and the mixed portfolios.  So, given this binary choice, I recommend holding 100% stocks for those holding periods.  If a friend asked for my free advice, I would say, "Look, over that time frame, stocks have never done worse than these other options.  Put all your money in a low-cost stock index, and don't look at it for twenty years.  It's going to have big up years, and big down years.  You are getting paid for your lack of concern about those fluctuations."

In fact, when I invest in volatile small cap stocks, this phenomenon happens in a much shorter time frame.  A family member may invest in the small cap, and if it goes down 40%, I might get a phone call, and I say, "When you bought this, you were saying, implicitly, that the price was incorrect.  So, now the price is more incorrect.  Or, maybe the price is correct, and by the time we realize we were wrong, it will be too late to escape our losses.  So, you committed to losing all of your money the day you bought those shares.  Don't look at the price.  Just figure that money's gone.  If, by chance, a year from now, that stock is up 500% and it hits our target, we'll figure that, as best as we can tell, the price has corrected itself.  Then, we can look, and we will sell.  Until then, DON"T LOOK."

It's amazing how much our portfolios change, just as a product of us looking at them.

But, this isn't just a battle with our cognitive and emotional challenges.  As with the holding period portfolios above, our looking actually changes the portfolio.  Let's say that, having bought into my analysis above, you put all your retirement savings into a diversified set of stock funds, to be recalibrated in 20 years, when you will start to plan for eventual cash withdrawals.  This analysis depends on holding through potential volatility.

So, what happens if in 15 years, you decide to look at your portfolio to see how it's doing?  As soon as you open the file, that 20 year portfolio becomes a 5 year portfolio.  Now, you're thinking, this is too risky, I need to prepare to recalibrate this in 5 years, and if stocks take a dive, I'm going to be in big trouble.

It seems like we should plan for that transition ahead of time, but the problem is, every extra step along the life of that portfolio that we add, changes the context of the portfolio.  If we say, look, in 15 years, the portfolio is going to need to start being more safe to prepare for a recalibration, then we might say, ok, let's do all stocks for 15 years, and then see what changes we need to make to make sure we are ok in 20 years when we recalibrate.  But, now we can make the same observation about that 15 year portfolio that we did about the 20 year portfolio, and very quickly, this becomes turtles all the way down.

It doesn't take a lot of effort to start at the end point, and work our way backward, and decide that we need to be in all cash.  I don't see a hard and fast way to avoid this paradox.  Do we just create heuristics that treat portfolios as slightly shorter in duration than they really are?  Is that why we don't generally concern ourselves with the suboptimality that comes from assuming normal distributions in our stock/bond analysis?  Because the end result of that error is simply to construct portfolios with a bias toward a shorter holding period, and this solves the paradox through conservative portfolio construction policies?

If my analysis concerning the stock/bond allocation problem is correct, American households could be sorely mis-allocating their long-term investments, because this bias would not lower both risk and returns, as one might expect.  An inappropriate match between asset classes and investment horizons may be increasing risk with no benefit at all for longer-horizon portfolios.

On the other hand, my solution, which is to not look, hardly seems prudent as a systematic rule.

Follow up post.

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