Tuesday, August 19, 2008

Risk versus Long-Term Return

There is a tendency for higher investing returns to come with higher risks. The difference in expected return between safe and risky investments is called the risk premium. It’s obvious that once you choose a risk level, you should go for the highest returns possible. The challenge is to choose an appropriate risk level.

One barrier to understanding risk is the way it is usually expressed. Saying that the S&P 500 has a 20% standard deviation means little to most people. In his book, The Intelligent Portfolio, Christopher L. Jones offers a good solution to this problem. Jones first assigns a risk level of 1.0 to the market portfolio, which is an average portfolio consisting of all asset classes in the proportions that exist in the marketplace. All other portfolios then have their risk level expressed relative to the market portfolio’s risk.

So, an all cash portfolio has a risk level of about 0.2, and a single large-cap stock has a risk level of about 3.0. This seems like a much more intuitive way to express risk than talking about standard deviations.

Armed with this metric, Jones works out several optimal portfolios at different risk levels. By “optimal” I mean that the portfolios have the highest possible expected return (based on a number of assumptions) without exceeding the chosen risk level.

Each of the optimal portfolios has a mix of cash, bonds, large-cap stocks, international stocks, and small- and mid-cap stocks. Jones analyzes three of these portfolios in detail:

Risk level 0.4: Safe portfolio (90% cash and bonds, 10% stocks)
Risk level 1.0: Market portfolio
Risk level 1.4: All stock portfolio

For each of these portfolios, Jones uses Monte Carlo analysis to compute the range of possible real returns. By “real returns” I mean the returns after subtracting out inflation. Here are the 30-year median returns:

Safe portfolio: 119%
Market portfolio: 326%
All stock portfolio: 444%

For money that I don’t expect to need for 30 years, the all stock portfolio looks like a significant improvement over the market portfolio. It certainly makes sense to look at the range of possible outcomes for each portfolio, but for me the added return outweighs the added risk.


  1. 444% over 30 years is only 5.1% annualized. Is that right? I thought stocks averaged more like 8%.

  2. Patrick: Good question. It's actually 5.8% per year (the 30th root of 5.44 rather than 4.44).

    There is roughly a 2% gap between the expected one-year return and the expected yearly compound return. This is the difference between arithmetic and geometric means.

    This gets us up to an expected one-year return of about 7.8%, which is not too far from what we would expect based on historical returns.

  3. Oh, ok, so it's a 444% gain rather than ending up with 444% of your original investment. As a computer science guy, I sometimes have a hard time telling when these financial types choose to subtract that 1. :-)

    Well, that's disappointing. I've always had a rule of thumb that stocks double every decade, but apparently that's too optimistic.

    Sheesh... who would use arithmetic means for these things? I guess the same people that push dollar-cost averaging, or say things like "reinvested dividends are responsible for 70% of the market's returns over the last century". Or the folks that thought up the Dow Jones Industrial Average, for that matter.

  4. Patrick: "Returns" should always be given after subtracting the 1, but I agree that many people get this wrong and it can be difficult to tell which is which.

    Keep in mind that the returns from The Intelligent Portfolio book are real returns. So, Jones thinks that stocks won't double after subtracting inflation in the coming decade, but that they will more than double in absolute terms. This is just a prediction based on a pile of unstated assumptions built into the Financial Engines software that Jones uses.

    Mixing up arithmetic and geometric means is very common. My guess is that most of the time it is the result of ignorance, but sometimes it is done deliberately to produce desired statistics.

  5. I've read that you can get higher risk with higher reward from a small-cap index fund. Is that true?

  6. Patrick: It's definitely true that small-cap index funds have higher risk. Most experts agree that they have a higher expected return as well. So, this is one way to increase risk and reward somewhat over a large-cap index fund. But, when you look at the expected compound returns, the difference between large-cap and small-cap stocks is small enough that many investors wouldn't want to add the extra risk.