# Asset Allocator Comparison

I compare the results of 11 popular asset allocators freely available on the web.

The scenario. A 66 year old U.S. male born in 1950. They have just retired and receive \$15,000 a year in Social Security income. They have no other income. Their investment portfolio totals \$200,000. They are unlikely to achieve it, but their desired income level is \$40,000. This is all intended to be relatively realistic of the situation faced by many retirees. Now the part that is slightly less realistic. They have constant relative risk aversion of consumption with a coefficient of relative risk aversion which they know to be 3. They are financially highly sophisticated, and provided it is in keeping with their moderate risk aversion (sensitivity to change in consumption), have a high risk tolerance (psychological sensitivity to investment portfolio loss).

I have framed things as above because the problem is then, apart from adding in the expected asset class returns, fully specified. This means the problem has a precise mathematical solution. Moreover, the precise mathematical solution can be computed using a mathematical technique known as stochastic dynamic programming.

Stochastic dynamic programming isn't for the faint of heart. It is somewhat technical and compute intensive. The answer I computed to this problem using stochastic dynamic programming is the retiree should adopt a 100% stocks, 0% fixed income portfolio. This might seem surprising, but what is happening is the Social Security income provides a stable cushion, much like bonds, that reduces the effect of a decline in stocks on consumption levels. My calculations using stochastic dynamic programming are in keeping with those of J.P. Morgan Funds in their paper Breaking the 4% Rule, although they don't show results for portfolio sizes as "small" as \$200,000, and they use a higher coefficient of relative risk aversion.

Recommended asset allocations can vary significantly owing to uncertainty in the equity premium given the limited historical data and high volatility. But the above scenario has been chosen so that the answer computed using stochastic dynamic programming will be 100% stocks for a broad range of possible equity premiums.

The table below shows the recommended asset allocations computed using different asset allocation calculators. Wherever possible inputs to the asset allocation calculators were in keeping with the above scenario, a moderately aggressive risk tolerance, and answers to other questions kept to their default values.

Who Type Stocks
Bank of Montreal risk tolerance 35%
Bankrate mixed questionnaire 46%
CNN Money risk tolerance 50%
Janus risk tolerance 51%
Nationwide risk tolerance 60%
Vanguard risk tolerance 60%
Yahoo finance risk tolerance 65%
Money-zine mixed questionnaire 80%
Wells Fargo mixed questionnaire 80%
TIAA-CREF risk tolerance 85%
AACalc (this website) mathematical (Merton's method) 100%

So there you have it. Recommended allocations to stocks ranged from 35 to 100%. Caveat emptor.

Most calculators are basically risk attitude questionnaires. Attitude towards investment risk plays an important role in the asset allocation decision, but it is not the only factor. As important, or more important, are consumption requirements, and the resources available to satisfy that consumption. This is part of investment companies thinking in terms of investment, and missing the big picture, which is investments are there to satisfy consumption. Investment companies should seek to play a role in informing and shaping attitudes towards investment risk based on consumption needs and resources, rather than purely seeing risk tolerance as something that is pre-ordained and needing to be divined. Only one website (this one) asks about Social Security income which is the primary source of income for most retirees, and as such one of the primary determinants of how much risk should be taken with the investment portfolio.

We have seen how the risk tolerance approach alone can underweight equity requirements. The reverse is also possible. The risk tolerance approach by itself will put risk tolerant investors with small amounts of guaranteed income into aggressive investment portfolios when something less aggressive might be in keeping with their consumption risk aversion.

An ideal solution would be to blend the risk tolerance and mathematical approaches. To recommend, here is the optimal mathematical strategy, but here is the strategy you should employ given your apparent risk tolerance.

Footnote: Merton's method is different from stochastic dynamic programming, although the two approaches are in agreement for the above scenario.