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Crappiness Asset Pricing Model (CrAPM)

In the 1960s, a few leaders in economic/financial thought developed the Capital Asset Pricing Model (CAPM, pronounced “cap-em”) as a means of pricing securities. The CAPM states that expected returns for an investment should be directly related to the asset’s non-diversifiable risk.

Years later, Eugene Fama and Kenneth French developed their “Three-Factor Model,” which states that expected returns are influenced not only by an asset’s non-diversifiable risk, but also by its market capitalization (small companies should have higher returns than large companies) and by where it falls on the value/growth spectrum (value stocks should have higher returns than growth stocks).

Unfortunately, some of those concepts (“non-diversifiable risk” for example) aren’t exactly crystal clear for many investors. That’s why I’ve been working on my own model for determining asset prices.

I call it the Crappiness Asset Pricing Model (CrAPM, pronounced “crap-em”). It states:

An asset’s expected return should be directly related to the number and degree of undesirable characteristics (i.e., crappiness) it bears.

The idea is simple: All else being equal, the more undesirable characteristics an asset has, the lower the demand and the lower the price. And all else being equal, the less you pay for an investment, the greater its future returns.

For example, the following characteristics should each increase expected returns:


It’s nice to be able to get to your money when you need it. (Or to put it differently, illiquidity is a bit crappy.) So illiquid assets should generally have higher expected returns than liquid assets.

By way of example, consider a checking account as opposed to an online savings account. They’re both FDIC insured, yet checking accounts are more liquid. CrAPM says: Higher expected returns for the savings account.

Volatility of Returns

It’s rather inconvenient not to have any idea what an investment will be worth tomorrow, a month from now, or a year from now. Therefore, volatile asset classes (e.g. stocks) should have higher returns than stable asset classes (e.g. short-term government bonds).

(Note: This is essentially the “non-diversifiable risk” included in the original CAPM.)


It’s neat to be able to brag that you own shares of a trendy company. If an investment comes with bragging rights, it probably also comes with lower expected returns.

For example, which is cooler: Owning shares of Google or owning shares of General Electric? CrAPM says: Higher expected returns for the uncool companies.

(Note: This is roughly akin to the “value” factor included in the Three-Factor Model.)

Dubious Ethical Nature

One of the most common reasons people give me for not investing in index funds is that they’re not comfortable owning shares of unethical companies–tobacco companies, for instance. If unsavory business models reduce demand for stocks in a given industry, they should also increase its expected returns.

On the other end of the spectrum, consider companies in green industries.  They’re both ethical and cool. CrAPM says: Not-so-hot expected returns.

Two Final Notes

  1. Your actual returns may differ from expected returns.
  2. Sorry about the mild vulgarity. I just liked the idea of spoofing the acronym. 🙂

How Do You Define Risk?

The finance community and financial services industry most commonly define “risk” as variability of annual returns.

I’ve never much liked that definition.

For example, in my retirement portfolio, I don’t care in the slightest what happens on a year-to-year basis. I’m much more concerned with what my annualized return will look like over the next 30 years. So why on earth would I measure risk as the variability of annual returns?

When I first read Jeremy Siegel’s Stocks for the Long Run, I enjoyed it tremendously. Rather than looking at variability of annual returns, he looked at variability of inflation-adjusted returns over various periods, thereby allowing an investor to glean some information as to how predictable stock and bond returns tend to be over the applicable time horizon. Perfect!

[Side note: What he found was that over periods of 30 years or more, bond returns are actually less predictable than stock returns. The conclusion, therefore, is that for anybody more concerned with 30-year periods than 1-year periods, stocks are safer than bonds.

Many people have pointed out that Siegel’s analysis only looks at the U.S. and only over a period of explosive economic growth. That’s true. So it’s possible that his conclusions are invalid. But at least he was measuring the right thing.]

Risk is personal.

While Siegel’s definition of risk is perfect for me, it might not be the best measure of risk for you.

For example, I might say that, for an investor with a 30-year time horizon, an investment is safe if it’s likely to earn a predictable return over that 30-year period.

But what if the investor in question is the type who’s likely to be scared by a decline in value at any point over those 30 years, even if the return over the entire period is fairly predictable? Well, then perhaps my “safe” investment isn’t safe for that investor after all.

What scares you?

I think most investors would do well to spend some time thinking about what it is that really scares or upsets them when they think about money.

Does it bother you every time you see your portfolio value go down? Then perhaps you should measure “risk” as probability of loss. (And for the period in question, use the frequency with which you check your portfolio.)

Are you scared of outliving your money? Then perhaps you should consider “risk” to be the variability of returns over periods equal in length to your current life expectancy.

Does it frustrate you to no end when everybody else seems to be making money, but your portfolio is lagging? Then perhaps some version of tracking error would be a good measure of “risk” for you.

Until you know precisely what it is that you’re trying to avoid, there’s no way to know what’s safe and what’s risky. (And you can’t rely on other people’s statements on the matter, because their definition could be different from your own.)

Risks Involved in Buying Bonds

There’s a poker saying that if you can’t spot the sucker at the table, you must be the sucker. The investing corollary:

If you can’t spot the risk in an investment, you don’t understand the investment.

Bonds are generally assumed to be a low-risk investment. And in many (though not all) cases, that’s true. But they’re never risk-free.

For example, there are three ways you can lose money by investing in bonds. (For the moment, we’ll ignore risks such as reinvestment risk that, while they can cause your return to be lower than expected, do not cause a loss of capital.)

Default Risk (a.k.a. Credit Risk)

The first and most obvious risk involved in a bond transaction is default risk: the risk that the borrower will go belly-up and be unable to make the promised payments.

  • Junk bonds have high default risk.
  • Corporate bonds have moderate default risk.
  • Municipal bonds (usually) have low default risk.
  • Treasury bonds are assumed to be free of default risk.

In every case except for Treasury bonds, buying a bond fund or ETF rather than individual bonds can help you reduce default risk via diversification.

Inflation Risk

Unexpected inflation is a significant risk when your interest payments are held constant.

For example, had you bought a 10-year Treasury bond at the end of 1971, you would have received a nominal return of 5.9% over the life of the bond. Unfortunately for you, inflation over your 10-year holding period was an annualized 8.7%. Ouch.

The longer the term of the bond, the greater the threat of inflation risk. So one of the best ways to minimize inflation risk is to own short-term bonds.

A second way to protect yourself from inflation risk is to buy Treasury Inflation-Protected Securities (TIPS). These bonds promise a specific after-inflation return rather than a specific nominal return.

Interest Rate Risk

When interest rates go up, bond prices go down (and vice versa).

For example, imagine that you buy a 10-year Treasury bond paying 3% interest. Now, imagine that one year later, the interest rate on new Treasury bonds has gone up to 4%. If you wanted to sell your 3% bond, who would buy it? Nobody.

…unless they were able to buy it at a discount–specifically, a discount large enough for them to earn an effective 4% rate.

Two notes about interest rate risk:

  1. The longer the maturity of the bond, the more its market price will fluctuate as a function of current interest rates. End result: If you have a short time frame, a 30-year bond (even a US Treasury bond) is not a safe investment.
  2. While TIPS are not subject to inflation risk, they are subject to interest rate risk. This means that you can lose money by purchasing TIPS if you have to sell them prior to maturity and market interest rates are higher than they were at the time of your purchase.

Paul Samuelson, and What We Owe Him

“A respect for evidence compels me to incline toward the hypothesis that most portfolio decision makers should go out of business.” – Paul Samuelson

Paul Samuelson, 1970 winner of the Nobel Memorial Prize in Economic Sciences, died today.

Samuelson had a tremendous influence in the field of economics. (And judging from Amazon sales ranks, his book Economics might be the single most-used economics textbook in print.)

The reason I’m writing about him here, however, is that he played a direct role in the creation of the first index fund.

In John Bogle’s Common Sense on Mutual Funds, he credits Samuelson’s article “Challenge to Judgement” as serving as an inspiration for his creation of the Vanguard Index Trust (the first retail index fund, now known as the Vanguard 500 Index Fund).

Bogle writes:

“[Samuelson] pleaded ‘that, at the least, some large foundation set up an in-house portfolio that tracks the S&P 500 Index–if only for the purpose of setting up a naive model against which their in-house gunslingers can measure their prowess.’…Samuelson had laid down an implicit challenge for somebody, somewhere to launch an index fund.”

It it weren’t for Samuelson, Bogle, and other thought leaders of that era, we might still be stuck constructing diversified portfolios stock-by-stock or paying the unwarranted fees (and shouldering the uncompensated risk) that come with active management.

Tax Planning in Retirement

Question: If you have the choice of investing $750 at an 8% rate of return for 10 years, or investing $1000 at an 8% rate of return for 10 years, then paying a 25% tax on the ending value, which should you prefer?

Answer: Neither. The ending value in each case is exactly the same.

In other words, if you have the choice between taking a 25% tax-bite out of an investment at the beginning of a period or at the end of a period, there’s no difference (because of the commutative property of multiplication).

However, anytime you have the choice to pay a tax of a certain percent now or a tax of a different percent later, then we have an opportunity for tax planning. That is, by planning carefully, you can reduce your total tax bill and leave more money in your wallet/bank account/IRA/mattress.

Retirement Tax Planning Opportunities

If you’re like most people, when you retire, your taxable income will decrease, as will your tax bracket.

And when you reach age 70½, you must start taking required minimum distributions (RMDs) from your traditional IRA. When that happens, your tax bracket is likely to increase.

End result: There’s likely to be a period between the date at which you retire and the date at which you turn 70½ during which your tax bracket is both lower than it’s been in recent years and lower than it will be in the future. And that means…

Tax Planning Opportunities!

Spend Down Taxable (and Tax-Deferred) Accounts

Each year during retirement, you’re likely to have to sell some of your investments to pay your bills. By properly choosing which assets to liquidate first (or more specifically, which accounts to liquidate first), you can lower your overall tax bill.

In years in which you’re in a lower tax bracket than you expect for later years, it makes sense to spend from your 401(k), traditional IRA, and taxable accounts first. This way, you can save your tax-free money (Roth IRA money) for years in which you expect to be in a higher tax bracket.

Roth Conversion

When you convert an amount from a traditional IRA to a Roth IRA, the amount of the conversion counts as taxable income, and when you later take it out of the Roth, the money comes out tax-free (assuming you satisfy a few rules).

If you’re in a lower tax bracket when you execute the Roth conversion than you expect to be in later (once your RMDs kick in, for example), this can be a great way to cut down your overall tax bill.

Pay Off Your Mortgage

Lastly, if you haven’t done it yet, it probably makes more sense than ever to pay off your mortgage. Being in a lower tax bracket makes the tax deduction from mortgage interest less valuable, thereby making your after-tax interest rate higher.

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Review: The Intelligent Asset Allocator

I recently finished reading Bill Bernstein’s The Intelligent Asset Allocator.

In the introduction to Bernstein’s most recent book (The Investor’s Manifesto), he describes The Intelligent Asset Allocator as a failed attempt at writing a plain-English guide to prudent investing:

I was gratified with the response to it, both among academics and general readers. Sadly, I was less than pleased by what my friends and family told me, which usually went something like this:  ‘Jeez, Bill, it seems you know what you’re talking about, but I fell sound asleep by the second chapter.’

So I went in with the assumption that this book was going to be packed full of calculus functions and statistical jargon.

Not at all. It was really quite readable.

The Gordon Equation

As in Four Pillars and The Investor’s Manifesto, one of Bernstein’s major points is that it’s important to pay attention to valuation levels before buying an investment. For example, he argues that we can achieve a reasonable estimate of future stock market returns by using the Gordon Equation, which states that:

Expected Return = Dividend Yield + Dividend Growth Rate

It’s worthwhile to note that one of his messages in The Intelligent Asset Allocator (written in the late 90s) was that stocks were highly priced and had very low expected returns going forward, whereas in The Investor’s Manifesto (written in early 2009) the message is the opposite: stocks have taken a beating, and have pretty good expected returns going forward.

Important reminder: The Gordon Equation, while rather accurate over extended periods (20 years or more), has essentially no predictive ability for short periods–what the stock market will do next year, for instance.

Efficient Frontier

A second major lesson of The Intelligent Asset Allocator is the concept of  the “efficient frontier.” The idea is that, for any given period, there are a number of efficient portfolios, each of which provides the highest return for a given level of volatility, or the lowest volatility for a given level of return.

Of course, there’s no way to know ahead of time precisely where the efficient frontier will lie for a given period. But if we look at enough periods, we can get a sense of the types of portfolios that tend to be pretty close, thereby allowing us to draw some conclusions about intelligent portfolio design. For example:

  • A portfolio comprised 10% of stocks and 90% of bonds often has higher return and lower volatility than a 100% bond portfolio.
  • Over most extended periods, allocating a portion of your portfolio to international stocks will simultaneously increase return while decreasing volatility.

Would I Recommend This Book?

Absolutely–if you’re someone who finds mathematical explanations to be “meaningful and practical” rather than “abstruse and boring.”

That said, before reading The Intelligent Asset Allocator, I’d recommend reading Bernstein’s newer The Investor’s Manifesto. The message is similar, the writing is arguably better, and the data is more up-to-date (and, therefore, more relevant-feeling).

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