Thursday, March 6, 2008

Equity Allocation vs. Age

Most commentators advise people to reduce the percentage of stocks in their portfolios as they age. Some popular rules of thumb are to make the stock percentage 100 minus your age or 120 minus your age.

Larry Swedroe in his excellent book “Rational Investing in Irrational Times” offers his own advice. Swedroe expresses his advice in terms of how long until you need the money (time horizon) rather than age. (Canadian Capitalist also posted on this subject last month.)

Here is Swedroe’s table of time horizon vs. percentage in stocks:

0-3 years: 0%
4 years: 10%
5 years: 20%
6 years: 30%
7 years: 40%
8 years: 50%
9 years: 60%
10 years: 70%
11-14 years: 80%
15-19 years: 90%
20 years or longer: 100%

How do we test this advice?

Unlike almost everything else in his book, Swedroe offers this table with no analysis of where the numbers came from. I decided to try to come up with my own answer to this question.

It is surprisingly difficult to come up criteria for optimizing a portfolio for some end time. The best I have come up with so far is to optimize a portfolio for a particular target dollar amount. This is similar, but admittedly not exactly the same thing.

So, given a particular dollar amount you are trying to save up, what portfolio mix should you use to minimize the expected time before reaching this goal? Of course, the goal amount should grow with inflation so that you will end up with some fixed amount of purchasing power regardless of how long it takes.

I assumed you start with an initial investment without adding any more money along the way. I also assumed that you were limited to stocks, bonds, and risk-free short-term government debt with returns and volatility as compiled by John Norstad in this paper.

The results

Before letting my computer run for a couple of days to get the answer, I guessed that when you were far from your goal, the portfolio would be heavy with stocks and would start shifting money to bonds and risk-free investments as the goal came nearer.

When the results came in, my guess was more or less correct, but not in the way I expected. The optimal portfolio mix is 100% stocks until you get to 93% of the goal portfolio value. From 93% to 99.8% of the goal, stocks are smoothly shifted into risk-free investments. From 99.8% of the goal onwards, the portfolio is entirely risk-free investments.

At a few points the optimal portfolio had 5% bonds, but for the most part, bonds were completely absent.

Expressed in terms of time, the portfolio mix is 100% stocks until 18 months from the goal. Then stocks are sold steadily until the goal is two months away, and after that everything is in risk-free investments.

What does this mean?

Obviously the answer I came up with is radically different from Swedroe’s table. My table would look something like this:

0-2 months: 0%
6 months: 25%
10 months: 50%
14 months: 75%
18 months or longer: 100%

I don’t recommend using this table. I don’t think you should have any money you will need within 3 years in stocks. A retired person should have at least 3 years worth of living expenses in fixed income investments. This gives you time for planning and adjusting to big upward or downward swings in the stock market.

However, I think it is likely that Swedroe’s table is too conservative. I would like to have seen how he came up with it.

12 comments:

  1. Hi Michael,
    great post as usual.

    When doing your number crunching, what kind of equity portfolio did you use? Do you use one basic equity index like the S&P500 or a globally diversified one?

    Thanks

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  2. Jay:

    The numbers I used came from Norstad's paper which is based on the S&P 500 from 1926 to 1994. I'd be happy to re-run the simulation with other numbers, but I haven't dug around enough to find parameters for global equities over a long enough period.

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  3. Be careful using expected values when devising a strategy for something you'll only do once. The entire notion of "expected value" is based on the law of large numbers; if you're talking about your retirement plans, you only get one shot, and so you can't use expected values to combine risk and reward into a single metric.

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  4. Patrick:

    I agree with your comment, but I'm not exactly sure how it applies to my post. All my computations took full account of the variability of returns.

    Since I computed a strategy that minimized the expected time to reaching a target amount of money, perhaps that is what you are referring to. It would be interesting to key on say the 99th percentile of time to reaching the target and devise a strategy that minimizes this time. I'm not immediately sure of how to do this, but I'll give it some thought.

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  5. Hi Michael,

    Well, I'm not sure what I'm suggesting either. Maybe start with your minimum-expected-time as a baseline, then use a confidence-interval kind of calculation that says "this strategy gets you within X% of the minimum expected time Y% of the time" and then fix X (or Y) and maximize Y (or minimize X). That math would be way beyond me but I imagine it's possible in principle.

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  6. Patrick:

    I've got an idea to make it possible to compute an answer in a reasonable amount of time. Look for something next week on this. I'll get my PC crunching on it this weekend.

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  7. One way to look at Patrick's question would be to test your theoretical asset allocation for people retiring every quarter from 1926 to 1994. How many retirees of the roughly 270 would be up or down x% from the time they started shifting away from equities, to the time they retire? I'd hate to be the guy with the target retirement date of Sept '01. Would that guy be better off using the the more traditional & gradual rotation away from equities?

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  8. AAI:

    Testing on historical data is an interesting idea. Maybe I'll try to put this together sometime soon.

    As for the guy who retired in September 2001, as long as he had 3-5 years worth of money he needed to live on in fixed income, he could have weathered the storm reasonably well. It's always possible to find a period where some strategy works well. Even the all penny stock portfolio works if you choose the right penny stock at the right time.

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  9. I guess now, just a few short months later, we're pitying the guy who retired in October 2008...

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  10. Patrick: ... unless he cashed out all his stocks in July! I'm not a fan of selling all stocks at the start of retirement, but it certainly makes sense to have at least 3 years of living expenses in fixed income. At least then you can plan to make 3 years worth of cash stretch to cover 4 years and avoid selling any stocks for at least a year.

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  11. I just learned of your blog and was checking it out and found this post.
    Here is how I came up with the table.

    First, you should not have money in the market if you know that you will need your money with certainty within a three year period. Just to risky as the last few years have demonstrated.

    Second, at horizons of 10 years stocks had outperformed bonds about 70% of the time. So that seemed like a reasonable guideline as the MOST risk one should take.

    Third, at 20 years stocks have beaten bonds almost all the time. So you could take UP TO 100 percent risk. But one should only do so if you also had the ability and need to take it.

    For years 4-10 I simply added 10% a year. Then beyond 10 years added another 10 percent in two more brackets.

    I hope that is helpful

    BTW-feel free to email anytime at lswedroe@bamstl.com. Always happy to answer questions from readers.

    And note that I have a new blog that I hope you will find of interest at http://moneywatch.bnet.com/investing/blog/wise-investing/?tag=content;col2

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  12. Larry: Thanks for the information about how you came up with the table. I've been following and enjoying your blog for a while now.

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