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.

Comments

  1. PatrickAugust 20, 2008 at 11:12 AM

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

    ReplyDelete
  2. Michael JamesAugust 20, 2008 at 1:41 PM

    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.

    ReplyDelete
  3. PatrickAugust 21, 2008 at 12:22 AM

    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.

    ReplyDelete
  4. Michael JamesAugust 21, 2008 at 9:21 AM

    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.

    ReplyDelete
  5. PatrickAugust 24, 2008 at 11:26 AM

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

    ReplyDelete
  6. Michael JamesAugust 24, 2008 at 12:40 PM

    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.

    ReplyDelete

Post a Comment

Popular posts from this blog

Short Takes: InvestorLine’s HISAs, 24-Hour Trading, and more

I recently moved some cash into BMO InvestorLine’s high-interest savings accounts (HISAs) that are structured as mutual funds.  Their designations are BMT104, BMT109, and BMT114, and they purportedly pay 4.35% annual interest (which they can change whenever they like).  However, the way they report the monthly interest payments is so baffling that I wasn’t able to sort it out in my first 15 minutes of trying.  A further complication is the following text in the HISA description: “The Bank may pay, monthly or quarterly, compensation to your Dealer at an annual rate of up to 0.25% of the daily closing balance in the BMO HISA.”  I couldn’t find any evidence of such a charge, but I haven’t been invested for a full quarter, and I can’t yet say that such a charge isn’t buried somehow in the confusing reporting.  I have more digging to do before I can recommend these HISAs. Here are some short takes and some weekend reading: Preet Banerjee explains the dangers of Robi...
Read more

My Asset Allocation

I’ve resisted discussing my asset allocation for some time, but now is finally the time to describe it and the reasons behind it. I’m not holding it out as a model portfolio; I believe it’s suitable for me and not necessarily anyone else. With that warning, enjoy the discussion and feel free to ask questions or take some pot-shots. The main reason why I haven’t discussed my asset allocation in detail before now is that I don’t want readers to treat it like a model portfolio and follow it blindly. Everyone’s situation is different. The need for variation in asset allocation from one investor to the next usually isn’t huge, but there is no one-size-fits-all portfolio. A secondary reason for keeping my asset allocation to myself is that I can’t be sure I’ll never change it. For example, I recently made the minor change of switching from an ETF of small-cap stocks to an ETF of small-cap value stocks . I don’t have any plans to change my current allocation, but I may think differe...
Read more

Updated Currency Exchange Method at BMO InvestorLine

There is now a more recent update of the method I use for exchanging currency at BMO OnvestorLine . I recently changed the procedure I use to convert large sums between Canadian and U.S. dollars at BMO InvestorLine. The method I use saves a lot of money compared to using the InvestorLine foreign exchange system. The latest change I made eliminated an annoying interest charge that I had to ask to be reversed. Most people don’t realize how expensive it can be to exchange currency. The extra charge banks and brokerages add gets hidden in the exchange rate. To see this extra charge, start by taking a sum in Canadian dollars, say C$10,000, and finding out how many U.S. dollars you can get. Then see what this U.S. amount would get going back to Canadian dollars. Many people might guess they’d get their original C$10,000 back, but they’d be wrong. In a recent test I did at BMO InvestorLine, I’d get back C$9754, for a loss of C$246 in two currency exchanges. That’s $123 per excha...
Read more

Archive

Show more