Sunday, February 26, 2012

Time Diversification

This past week I was appointed as the Curriculum Director for the Retirement Management Analyst (SM) Designation Program operated by the Retirement Income Industry Association. I'm quite excited about this opportunity, as it will allow me to help build their curriculum by incorporating the latest research results on retirement planning and retirement income distribution strategies, much as I have been doing here at my blog. 

As I have been starting to discuss here recently, there really is more to retirement planning than just deciding on a safe withdrawal rate. We can talk about Monte Carlo simulation with its thousands of trial runs and find a strategy that minimizes the probability of failure. But retirees only get one shot at retirement. If failure is something they view as catastrophic, then the objective becomes to eliminate the chances for failure, not just minimize them.

In considering how to best accomplish this, there are all sorts of tradeoffs that one must consider. Retirees want to maintain control of their assets, but also they want to obtain guaranteed income sources that often require relinquishing control. Retirees want to spend as much as possible to enjoy their retirement, but they also fear running out of wealth later in life. 

The research I want to work on, and the research which I want to work hard to more fully incorporate into the curriculum, relates to how one can best balance all of these competing tradeoffs to find the most personally satisfying retirement income path that will work no matter what happens with financial markets during retirement.

The fundamental goal of retirement planning is to “first build a floor, then expose to upside.” If you want to read more about what this means, it is the approach Moshe Milevsky has in mind when he recommends that you “pensionize your nest egg” and it is the way that Zvi Bodie suggests you can “risk less and prosper” in retirement. 

Also, over the weekend I read some articles on "Modern Retirement Theory" by Jason K. Branning and M. Ray Grubbs. What they are doing also very much ties in with the ideas in the RMA Curriculum. A brief overview of "Modern Retirement Theory" can be found in this special report supplement from the December 2010 Journal of Financial Planning.

 That was a rather long lead-in to today's topic, time diversification, which is something that may have already been discussed to death at other places. But I just wished to run some simulations of my own about it, and I think it could be useful to share.

Consider someone who puts $1 into a portfolio of stocks and lets that dollar sit and grow for 30 years. I will look at 100,000 Monte Carlo simulations for what happens to this dollar over the ensuing 30 years. I'm doing things in real terms, assuming at the average annual real stock return is 7%, but that the standard deviation of annual returns is 20%. This means that the compounded real return for stocks is 5%.

The classic argument about time diversification is that the longer you invest, the more likely your average returns will match the compounded 5% average.  The classic picture shown in support of time diversification looks like this:

We can see that in the median case, we get the 5% compounded real return we expect. As time passes, the distribution of average returns also gets narrower to focus in more on the 5% return. I've shown a 90% confidence interval, meaning that 90% of the time we would get an average return falling within the red bands. 5% of the time the average return would be even higher than the top dotted red line, and 5% of the time it would be even less than the bottom dotted red line.

But that is not the whole story. People don't really care about these average returns. What they should care about is the money!  How large will this dollar grow over the ensuing 30 years?  That is what I show in the next picture. The distribution of wealth accumulations gets wider as time passes, not narrower. And not only that, but the distribution is not symmetric (it is a lognormal distribution). There are chances for extreme wealth, but don't let that obscure anything happening on the downside.

Let's look more at the downside.  First, some good news. As more time passes, the probability of experiencing bad outcomes will decrease. Here I show the probability of having less than $1 (in inflation-adjusted terms) as time passes. That implies experiencing negative compounded growth over the whole time period. This probability does decline over time, but still there is about a 7% chance that your accumulated wealth will be less than $1 even after 30 years of experiencing 7% average real returns.

And finally, risk is not just the probability of bad outcomes.  It is probability times magnitude.  The final picture shows bad news, which is that as time passes, the wealth accumulation in the worst-case scenario falls even further. Even after 30 years of 7% expected growth, there are cases where the person only has about a nickel (5 cents) left. Remember, this is about accumulation and there are no portfolio withdrawals. Those losses are due to stock market losses.

People only get one simulation path for their own life. Despite the extreme potential upside seen in the second picture, people may reasonably wish to protect on the downside. Though I've just shown a simple example about wealth accumulation rather than retirement distribution, this is the basic idea behind "first build a floor, then expose to upside."

This example is also overly simplying in two ways, one that is good news and one that is bad news.  First the bad news: I assume that the stock returns are normally distributed in this example, but a common complaint we hear about this is that there are fat tails. That means the chances of getting really bad stock returns are higher than the normal distribution implies.  That would make things look even worse on the downside.

But the good news, I think there is some long-term mean reversion that can help protect on the downside. This Monte Carlo simulation assumes that each year has returns independent from the past. There is no notion of market valuations, which may get unrealistically low in some cases. But more generally, there is no notion such bad luck simulations would be met with such widespread social and economic problems (as everyone experiences this bad luck at the same time) that the issue of enjoying retirement may fall by the wayside no matter what. Just for some edification about Monte Carlo simulation, here are the returns experienced by the person who had the lowest wealth accumulation after 30 years out of 100,000 tries. Notice in particular the almost continuous series of negative returns experienced between years 11 and 20.  Could things ever get that bad in the real world?  I don't know, I can't predict the future.

          Year       Stock Return
          1.00         -7.90
          2.00        -33.73
          3.00         16.68
          4.00          4.12
          5.00        -21.76
          6.00        -32.96
          7.00         18.28
          8.00         34.97
          9.00         51.02
         10.00          4.68
         11.00        -11.90
         12.00        -12.97
         13.00        -23.53
         14.00        -10.76
         15.00          0.20
         16.00        -17.89
         17.00        -42.85
         18.00        -15.81
         19.00         -4.48
         20.00        -27.38
         21.00         33.42
         22.00        -30.39
         23.00        -26.04
         24.00         -8.59
         25.00         -6.15
         26.00        -16.06
         27.00         -6.19
         28.00          6.63
         29.00        -16.84
         30.00          5.56


  1. This 94% loss result corresponds to no 30 year period ever experienced, at least in the USA, Canada, Sweden, Australia, Switzerland, South Africa and a number of other countries. Should we take it as a serious possibility? Why do Monte Carlo simulators only use 1-year returns? Why not 2-, 3-, 5- or 10-year returns from which to build the sampling distribution? The problem with the Bodie approach is that a person would have to save about half their income through a 35 year working life to fund a 35 year retirement. Taxes reduce net returns, to almost zero. The Credit Suisse Global Investment Returns Yearbook gives a much more encouraging picture of long run stock, bond and portfolio returns.

    1. Thank you. Yes, I hear you. I'm not sure how prudent it is to even plan with such a worst-case scenario in mind, because surely such events would surely descend the world into chaos anyway. Looking at longer periods for the distribution sounds like an interesting approach, but I suppose we have even less data to deal with that.