## Monday, September 7, 2009

### Risk Aversion and Morningstar

This is a Labour Day edition of the usual Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy.

Your reaction to a game show scenario can reveal important information about your attitudes as an investor. It can even tell you what mix of investments are appropriate for your portfolio.

Let’s get right to it. You are playing Deal or No Deal and you are down to two amounts: one penny and a million dollars! What is the minimum offer you would accept from the banker?

For those not familiar with this game show, here is the situation. You are about to toss a coin. If it comes up tails, you get nothing (and lose nothing). If it comes up heads, you get a million dollars. Just before you toss, someone offers you a sum of money to give up your chance to toss for the million dollars. What is the minimum such offer you would accept?

It turns out that your answer depends on how rich you are. Bill Gates would likely accept an offer of half a million dollars, but not much less. However, someone in a desperately poor country might accept an offer of \$5000.

To make a proper apples-to-apples comparison, we need to take into account your wealth. So, let’s look at how much money is in your portfolio. I’m not talking about your house, cars, and emergency stash of cash. Just consider the value of your investments that you are trying to grow for the long term.

Instead of tossing for a million dollars, imagine that you are tossing for 10 times your current portfolio size. I’ll continue this discussion as though your portfolio size is \$100,000, but you will have to multiply or divide all the numbers I use by some appropriate factor.

If you are an investor who seeks to maximize the long-term compounded return on your portfolio, then the lowest offer you accept to give up your chance at the million dollars is \$230,000. In the language of portfolio optimization (for example, see the paper Portfolio Optimization by John Norstad (2002-09-11)), you have a “coefficient of relative risk aversion” of A=1.

If the thought of coming away with nothing after the coin flip scares you enough that you would accept an even lower offer, then your value of this risk-aversion number A is higher. At A=2, the lowest offer you would accept is \$83,000.

At A=3, the lowest offer you would accept is \$41,000. It might seem ridiculous that someone who has \$100,000 in his portfolio would accept only \$41,000 and pass up a 50/50 chance at a million dollars, and I agree. So why am I talking about this silly A=3 case?

Morningstar uses A=3 in their risk-adjusted return calculation to rate mutual funds. Morningstar provides detailed information about both US and Canadian mutual funds. When you hear that some fund has a 4- or 5-star rating, this is based on Morningstar’s formula for comparing mutual funds.

From the notes with Morningstar’s formula, “γ=2 [which corresponds to A=3] results in fund rankings that are consistent with the risk tolerances of typical retail investors.” I can’t speak for other investors, but this definitely doesn’t apply to me.

This formula gives strong preference to funds with low predictable returns. Funds with higher returns but more volatility are punished severely.

Everyone has different thoughts about how much risk is acceptable. Personally, I’m in the A=1 camp trying to maximize the long-term compounded return on my investments. This makes Morningstar’s ratings completely irrelevant to me.