## Monday, February 11, 2008

### How Conservative Are Investors?

Everything I read about asset allocation says that investors are very conservative and must put a significant fraction of their money into fixed income investments like bonds even though stocks have historically given much higher returns.

All of these commentators may be right about their assessment of investor psychology. Of course, this says nothing about what would be best for investors; it is just a reflection of how investors think.

Morningstar has formalized this view of investors in a formula for assessing investments. This formula calculates what they call the Morningstar Risk-Adjusted Return (MRAR). I spoke about this somewhat in a previous post. Morningstar describes it in more detail in a 4-page write-up that is no longer available online, but that's okay because all the math in their expanation tends to obscure what is going on.

Let’s look at a simple example. Suppose that each year a particular investment returns either 50% or -20% with equal probability.

A simple view of this investment is that its average return is (50% + (-20%))/2 = 15%. Morningstar’s MRAR calculation can handle different degrees of conservatism, and this simple kind of average corresponds to MRAR(-1).

Another way to look at this investment is that after two years you will probably get 50% once and -20% once. So, \$1 would grow by 50 cents to \$1.50, and then lose 20% of \$1.50 (30 cents), leaving \$1.20. The two-year return is 20%. This corresponds to an annual compound rate of 9.5%. After many years, the odds are about 50/50 whether your long-term annual return would be above or below 9.5%. This kind of average corresponds to MRAR(0).

You can think of the drop from 15% to 9.5% as a penalty for volatility. And this high penalty is appropriate. This is a very volatile investment.

But Morningstar thinks that the volatility penalty should be much higher than this to match the “risk tolerances of typical retail investors”. I’m not sure, but I think “retail investors” is a reference to dolts like you and me. Presumably, professional money managers have different risk tolerances.

Morningstar says that the typical investor is so conservative that we should use MRAR(2), which gives a risk-adjusted return of minus 0.2%! If Morningstar and other commentators are right, investors would rather stick their money in a zero-interest bank account than try this investment.

Maybe most investors really are this conservative, but I’m not. I make sure that I have adequate cash reserves, and have safe investments for any money I will need in the next three years. After that everything is invested for the long term, and my risk tolerance is consistent with MRAR(0).

1. Michael,
I totally agree with you on Pape's model portfolios; that is just too much fixed/variable income to my taste. But it is a great read otherwise.

I read your blog often, among other blogs. Your posts cover many investment areas I am interested in, and I value the mathematical content in some of them. Like you, I love Math. Thanks a lot for sharing.

For a Canadian investor who is interested in diversification, would you write on recommended ETFs? For the equity portion, would you please include percentage allocations among the different asset classes that you would choose? Do you include US small value, international small cap, REIT etc...?

I have an RRSP accout and an investment/cash account, and I am trying not to buy the same ETF in both accounts (to avoid fees). Perhaps you can suggest a model RRSP portfolio and a model tax-efficient non-registered portfolio. I know there are plenty of great model portfolios out there, but I am sure that the portfolio of a Math enthusiast would be more efficient :).

Thanks again for sharing and thanking you in advance for reading my comment/request.

J.

2. J.,

Thanks for the kind words. Whether you love math or not, it is necessary to mix math with common sense to arrive at correct conclusions when it comes to investing and many other aspects of life.

I'm afraid that I don't have your answer for a recommended mix of ETFs. The main barrier is coming up with believable characterizations of the ETFs. For each ETF, I would need to know the expected return, variance, and covariance with all other ETFs. I am still reading opinions on this from several writers.

One rule of thumb I use is to avoid ETFs with higher MERs. It makes no sense to try to boost returns by 0.1% by getting the perfect mix of assets, and then mix in an ETF with a 0.5% MER.

As I begin to draw firmer conclusions, I'll post them on this blog.

Michael