Many people refer to their home as their “best investment.” Others argue that a home isn’t an investment at all because it may not go up in price or because you may never sell it.

In my opinion, anything that has a calculable (usually positive) rate of return is an investment. And it’s worth noting that buying a home can yield a positive rate of return even if the home never increases in value. (Conversely, it can have a negative rate of return even if the home does increase in value.)

Rate of Return Involves More than Home Value

The rate of return on a home purchase involves more than just the home’s market value. If you only consider the change in home value, you’re leaving out:

1. Part of the price of the investment — maintenance costs and property taxes,
2. The biggest part of the payoff — the fact that it replaces your rent, and
3. The fact that the investment was probably leveraged (i.e., paid for using a loan).

I think it’s easier to first look at the purchase as if you were buying the home with cash. That way, it’s easy to calculate the expected return on the purchase:

Expected Real Return = D + G – C, where

D = imputed rental dividend (calculated as the size of the annual rent bill that you’d eliminate by owning instead of renting, divided by the purchase price of the home),
G = inflation-adjusted growth in home value, and
C = costs (insurance, property taxes, and maintenance), expressed as a percentage of the purchase price.

For example, if you’re currently paying $1,000 in rent per month, and you buy a home for $180,000, your imputed rental dividend would be 6.67% ($12,000 ÷ $180,000). From that, add the inflation-adjusted rate at which you expect the home to appreciate, and subtract any non-mortgage costs of owning the home.

Then you can determine how your return would be affected by using borrowed money for the purchase. (In short: It only makes sense to borrow if you expect a return greater than the interest rate you’d have to pay on the loan.)

Rate of Return When Prepaying a Mortgage

A recent Get Rich Slowly post asked whether it’s better to prepay a mortgage or invest elsewhere. In the comments, several people asked questions to this effect:

“Isn’t it risky to put a bunch of money into prepaying your mortgage? After all, we’ve seen in the last few years that home prices don’t always go up.”

It’s true that home prices don’t always go up. But if you own a home, you’re already exposed to that risk — whether you decide to prepay your mortgage or not. The rate of return you get when you prepay your mortgage is simply equal to the interest rate on the mortgage. It’s got nothing to do with changes in the market value of the home.

Why I’m Not Buying a House (and Likely Never Will)

For many people, owning a home provides an emotional benefit, so they’re happy to buy a home even with an expected return that’s somewhat less than the return they could get with other investments.

I find myself in the opposite boat. From where I’m standing, owning a home looks to be:

1. A huge pain in the butt,
2. Illiquid, and
3. Extremely undiversified.

…whereas putting money into an ETF portfolio is the opposite. It’s easy. It’s liquid. And it’s diversified. As a result, I’m only going to be interested in buying a home if it appears that the expected return is significantly greater than that of other investments.

Of course, given that there are so many people willing to accept a lower return (i.e., pay more for the home), that may never happen.

In the aggregate, the value of active management is zero by definition–if somebody is outperforming the market, it’s only because somebody else is underperforming.

But there are times when you have no choice but to make an attempt at answering the question, “What will this fund’s active management be worth?”

For example, what if your retirement plan at work gives you access to two international stock funds: One is a not-particularly-cheap index fund. The other is an actively managed fund that costs just 0.05% more per year than the index fund.

• Is it worth paying that little bit extra for active management?
• What criteria should you use for making the decision?
• And what if the costs were exactly the same? (Or what if the actively managed fund actually cost less?)

People ask me about this scenario (or similar ones) from time to time, and I don’t have a very good answer.

My first response is to go with the fund that’s likely to have the lowest portfolio transaction costs (portfolio turnover being the best indicator of such costs, as far as I’m aware). But if there’s no meaningful difference there either, I’m at a bit of a loss in terms of what to suggest.

The most obvious things to look at–past performance and tenure of the fund’s manager–have both been shown to be nearly worthless as predictors of long-term future performance. (At least, that’s what every credible study I’ve read has indicated. If you’re aware of one indicating otherwise, please share.)

I’d love to hear your thoughts: When given the choice between an actively managed fund and an index fund with similar costs, how do you choose between them?

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:

Illiquidity

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.)

“Uncoolness”

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.

I’ve seen a lot of different ways to calculate the rate of return on a home purchase, but my favorite so far is the one William Bernstein provides in The Investor’s Manifesto.

First, he separates the decision to purchase a home from the decision to finance that purchase with borrowing. We calculate the rate of return from the investment itself, then we can determine how borrowing affects that rate of return.

Calculating Expected Return for a Home Purchase

Bernstein provides the following equation, which (not so coincidentally) looks very much like the Gordon Equation he uses to predict stock market returns:

Expected Return = D + G – C, where

D = imputed rental dividend,
G = inflation-adjusted growth in home value, and
C = costs (insurance, property taxes, and maintenance)

What the heck is “imputed rental dividend?”

The imputed rental dividend is the payoff from buying the home that comes from not having to pay rent. Remember, for the moment we’re assuming that you pay the whole price up front, so there’s no mortgage payment.

So, for example, if a home had a $180,000 price and it replaced a $1,000 monthly rent bill, its imputed rental dividend would be 6.67% annually. ($12,000 ÷ $180,000.)

The Rest of the Calculation

Bernstein assumes property taxes, insurance, and maintenance total approximately 3% of the home’s value each year. Obviously this will vary depending upon circumstances such as location and the age of the home.

Historically, inflation-adjusted home prices have increased at a rate of approximately 1% annually. Of course, it’s not exactly steady on a year-to-year basis, and this figure can also vary dramatically depending upon location.

All together, that gives us the following:

Expected Rate of Return = 6.67% + 1% — 3% = 4.67%

Note: The imputed rental dividend is tax free, as is, for the most part, the capital gain resulting from the sale of a home. As a result, this 4.67% expected annual return is essentially an after-tax return.

Borrowing for a Home Purchase

Of course, most people don’t purchase their homes entirely with cash. They borrow money. Borrowing money to invest is known as leveraged investing.

As with other leveraged investing scenarios, the fact that you’re borrowing money magnifies your returns (whether good or bad).

• If the return you earn is greater than the interest rate you’re paying, the return on your leveraged investment will be better than it would have been if you’d purchased the investment entirely with cash.
• If the return you earn is less than the interest rate you’re paying, the return on your leveraged investment will be worse than it would have been if you’d purchased the investment entirely with cash.

End result: In our example above, the home purchase only makes sense if our prospective home buyer can take out a mortgage with an after-tax, after-inflation interest rate of below 4.67%.

Lessons to Be Learned

In my opinion, there are two primary lessons here:

First, if you’re planning on buying a house, go ahead and take a crack at figuring out what your rate of return will be. (And don’t listen to the realtor’s estimates.) If a home is selling for 20 or 25 times its annual rental value, it’s going to be quite difficult to earn a worthwhile rate of return.

Second, this whole calculation is extremely sensitive to the assumptions we make. For example, if our home buyer ends up taking out a mortgage with an after-tax, after-inflation interest rate of 3.5%, she should be in good shape. Borrow money at 3.5%, invest it at 4.67%. Super!

But what if we guessed wrong, and her annual costs of home ownership end up being 4% of the home price instead of 3%? And what if the inflation-adjusted increase in home value ends up being only 0.5% annually instead of 1%? Now she’s borrowing money at 3.5% and investing it at 3.17%. Whoops!

Over the last ten years or so, there’s been a great deal of discussion about what constitutes a “safe withdrawal rate” during retirement. The most common rule of thumb (resulting from the famous “Trinity Study“) is to start with a withdrawal rate equal to 4% of your portfolio value on the day you retire, and adjust your withdrawals upward each year for inflation.

Using the 4% rule, the amount you need to have saved in order to retire is 25 times your annual investment-funded spending needs (that is, spending needs not already met by social security income or part-time job income).

Adjusting for Costs

The catch is that the Trinity Study doesn’t account for investment costs at all. It assumes that investors receive the entire return earned by the market. Not exactly the reality for most investors!

According to Deloitte, 401(k) administrative fees average roughly 0.72% per year.

According to the Investment Company Institute, fund expense ratios and sales loads together constitute an average annual cost of 0.99% for stock funds and 0.75% for bond funds.

According to data from the Investment Technology Group cited in Bogle’s new Common Sense on Mutual Funds, portfolio turnover costs average approximately 1.6% annually for equity funds. (I’d guess that it’s lower for bond funds, but I can’t find any good data either way.)

When you add all that up, it’s not hard to imagine an investor paying roughly 2% per year in investment costs. If you’re paying 2% per year, that 4% withdrawal rate won’t be “safe” in any way. You’ll need to look at something closer to a 2% withdrawal rate.

…and at a 2% withdrawal rate, you don’t need to save 25 times your annual spending needs. You need to save 50 times your investment-funded annual spending needs before you can retire retire.

Frugality Where It Counts

Since the economic downturn began a little over a year ago, frugality has been trendy to write about. I think that’s wonderful–I’m all for living a simple lifestyle and cutting costs where you can.

But there are few things you can do that will have as much of an impact on your financial future as being frugal with your investing. Two easy changes can literally halve the amount of money you’ll need saved in order to retire:

• Switch to low-cost index funds or ETFs.
• Get out of paying 401(k) admin fees as soon as possible by rolling over your 401(k) to an IRA when you leave your job.

Hypotheses cannot be proven. They can only be disproved. As Taleb reminds us, even with hundreds of thousands of white swan sightings and no black swan sightings, it was never possible to prove the statement “all swans are white.” Yet one single sighting of a black swan could (and did) immediately disprove the statement.

In finance, people often seek to disprove the efficient market hypothesis (and thereby give hope to active fund managers, active fund investors, stock pickers, market timers, and stock newsletter publishers that their efforts aren’t doomed to failure). The trick is that EMH is an incomplete hypothesis, and it cannot be disproved.

Testing EMH

We can say “markets are efficient” and “an efficient market would look like X.” But if we test, and find that markets don’t look like X, we don’t know whether:

• Markets are not efficient, or
• Our description of what an efficient market looks like is inaccurate/incomplete.

This is what’s known as the joint hypothesis problem. When we attempt to test EMH, we’re automatically testing two hypotheses:

1. “Market’s are efficient” <— the efficient markets hypothesis, and
2. “Efficient markets look like X.” <—the secondary hypothesis.

If the joint hypotheses are proven false, it’s impossible to know which one was proven false.

For example, we might describe an efficient market as one in which asset classes have expected returns proportional to their risk (as measured by volatility of returns). And if we found two asset classes with equal volatility where one reliably outperformed the other, we might be tempted to say that markets are not efficient.

But that’s not necessarily the case. Perhaps the market is smarter than our description of it, and there are other factors at work. For example, there may be forms of risk other than volatility (illiquidity for instance) that would cause an efficient market to allow one asset class to have higher expected returns than the other.

The Takeaway for Investors

So what’s the point of all this? The point is that you should be extremely leery anytime you see somebody claiming that:

1. “Markets are not efficient, and I have proof!” or
2. “I can help you increase your return without increasing risk.” (which, by the way, is just the I’m-about-to-sell-you-something version of claim #1).

Of course, for precisely the same reason EMH can’t be proven false, it can’t be proven true either. EMH’s value lies, in my opinion, not in our ability to prove or disprove it but rather in its usefulness as a lens through which we can examine market phenomena and perhaps come to a better understanding of why the market does what it does.