Most commentators advise investors to shift money from equities to fixed income as they age, and this makes sense. We may disagree on the exact asset allocation percentages and exactly how soon before (or after) retirement to start lightening up on equities, but it seems clear enough that the average 40-year old should have more in equities than the average 80-year old. However, there is a body of academic work that argues that investors should maintain a constant asset allocation regardless of their age. This work is based on what is known as constant relative- risk aversion (CRRA). I’ll show the problems with CRRA in an example below. One consequence of the CRRA assumption is that the optimal asset allocation percentages remain constant regardless of the length of the investor’s investment horizon. Paul A. Samuelson advocates this view in his keynote address to “The Future of Life-Cycle Saving and Investing” conference. I first heard of this conference and the correspondin...

Most commentators agree that we should include some bonds in our long-term investments. My quest for a reasonable analysis to support this conclusion continues. Previously, I have discussed the ideas of Gordon Pape and Morningstar on this subject. I’m starting to feel like I’m in some sort of boxing match. So, let’s do it right: “In this corner ... Roger C. Gibson, esteemed author of ‘Asset Allocation: Balancing Financial Risk’ now in its fourth edition. He’s a well-respected expert whose ideas have been endorsed by Sir John M. Templeton and Don Philips, Managing Director, Morningstar.” “And in this corner ... some guy who figured out how to use Blogger.” Oh well. I lose on the credibility meter. My only chance is that people actually think about the arguments. Gibson does an impressive amount of analysis and explains many important concepts clearly. When it finally comes time to figure out an optimal asset allocation, he tosses in an interesting assumption about our tolera...

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 si...

Here is a bonus post today in case you’re not following the book review. 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 despera...

You may have heard of risk-adjusted returns in connection with mutual funds. The basic idea is that a risky investment may not be better than a predictable investment even if the risky investment has a higher expected return. There is some validity to this, although it is too often used to justify the poor returns of mutual funds compared to the overall stock market. Normally, any discussion of risk-adjusted returns includes some intimidating math. I’ll explain the problems with risk-adjusted returns without needing the math, and I’ll give pointers to where the math can be found for those who are interested. According to the theory, before comparing investments, you should do a risk-adjusted return calculation that will reduce the returns according to how risky they are. The riskier they are, the more the returns are lowered before any comparison. By “risk” here, we mean volatility, which is a measure of how much the returns vary over time. An investment that grows steadily has low...