Financial Mathematics Text

Tuesday, December 18, 2012

Is Housing an Investment?

The conventional wisdom says that it is. I'd like to suggest it's a little more complicated than that. Rather than suggesting that housing is an investment, I will argue that housing can be an investment and spell out under what conditions it is.

To some extent I will be relying on the Graham & Dodd definition of an investment. According to Graham & Dodd (from Security Analysis):
An investment operation is one which, upon thorough analysis, promises safety of principal and a satisfactory return. Operations not meeting these requirements are speculative.
 Regarding speculation, two types of speculation are classified (Graham & Dodd):
  1. Intelligent Speculation - The taking of a risk that appears justified after careful weighing of the pros and cons.
  2. Unintelligent Speculation - Risk taking without adequate study of the situation.
Most home buyers would classify as not giving "adequate study of the situation".

So when is a house an investment? 

A necessary, but not sufficient, condition for housing being an investment is that the house must be rented out for income. As the definition above suggests, we need to give considerations to both "safety of principal and a satisfactory return."

So what does that amount to? While I don't think I can give an exhaustive account on how to select real estate for investment (frankly, I don't have the expertise), there is one thing that I think can be given consideration. In fact, our friends Graham and Dodd have already spelled it out with regard to mortgage bonds:
...under normal conditions obtaining in the field of dwellings [houses], offices, and stores, the property values and the rental values go hand in hand.
This idea was picked up by the economist Robert Shiller and spelled out in his book, Irrational Exuberance. One way to look at this explicitly is known as the Price to Rent ratio (based on data obtained from here).

Figure 1:

It becomes painfully obvious where the housing bubble occurred.

The Global Property Guide has rental yield (e.g. the inverse of price to rent) on a number of cities throughout the world.

Now suppose that you are going to buy a house for the purpose of renting it out. What kind of return will you get for that?

Well, we need to incorporate another factor: expenses. Owning a house comes with various expenses. Some examples include property taxes, lawn care expenses and repair expenses (plumbing, electrical, etc). So when you rent out a house, your income isn't just going to be rent. You have to pay these expenses. This lends to the idea of what is called Capitalization Rate or simply Cap Rate.

Cap Rate = (Annual Rental Income - Annual expenses) / House Price

The cap rate can then be used as a comparison with other investment vehicles such as bonds. There are some similarities and differences and those factors need to be taken into account. Here are some examples:
  • Rent, while contractually guaranteed while a lease is present, is not guaranteed without a tenant. Rental income can fall off for a couple of months in between tenants. Furthermore, the credit worthiness of the renter has to be taken into account. This suggests that these should be more like junk bonds in terms of spreads.
  • Since housing is a decent inflation hedge, rental income (assuming long-term lease agreements are not made) can go up with inflation. This suggests that the "Cap Rate" spread should be compared with inflation protected bonds such as TIPS. On the deflation side, however, rental prices can decline thereby reducing returns on investment in the future whereas bonds do well (in real terms) in a deflationary environments (assuming no defaults.)
  • Another feature that many bonds have which real estate investment does not is "callable". If interest rates, for example, go down, the bond appreciates in value but callable bonds can be paid off early by the issuing organization. This places a limit on selling with price appreciation. 
There are, of course, plenty more differences to be taken into account when comparing cap rates and bond yields but that's at least a start.

We all have a short position in housing.

That's an interesting claim that was made at The Zikomo Letter.

So when you purchase your home, you're not making an investment but rather you're purchasing a hedge against your short position. (To keep it simple, a hedge in finance is some asset that negates or reduces risk.)

If you rent a home, you typically sign short term leases (say 1 year) thereby locking in your rent price for only that short period of time. If rent goes up in the future, you'll have to come up with the cash to make your future rent payments. When you purchase a home, you lock in a price right now.

The article also makes a good point regarding the increase in home value. Many people have been using the equity in their homes as a kind of piggy bank, borrowing against that equity for some cash now. But if house prices are going up (in a sensible manner) then rent prices are also going up. It's not a wise move all around.

Concluding Thoughts
  1. Purchasing a home should be thought as an expense (or hedge against a short housing position). Home prices should be compared with rent to get an idea of which alternative is a better way to meet that expense.\
  2. Houses are a good investment when that home is rented out to a tenant. Estimating the cap rate and comparing that to alternative investments (and borrowing costs) will give some idea on whether or not it's a good investment.
  3. Home equity is not a piggy bank. Leave it alone unless it's an absolute emergency.


  1. While buying a house isn't likely to be an investment unless you rent it out, I think you've also suggested that there is an area where buying is cheaper than renting. I'm referring mostly to the idea of protection from increased monthly rates. Do you know of any resources that help tease the exact details regarding the factors that affect whether renting or buying is the lesser expense? Also, can you speak on rent to own?

  2. Buying can definitely be a better value to renting. The fact that you can lock in your home expense and protect yourself from inflation is a good example. It's just a matter of weighing all of the costs and benefits of each and figuring out which one is right for you.

    In terms of costs, some are going to be easier to estimate than others. You should be able to find good info on things like tax rates. You'll want to factor in PMI rates if you put less than 20% down.

    Maintenance costs are a little trickier which will depend on whether you're buying a brand new house with new appliances or and old one that has some wear and tear. You should figure at least 1% of home value for that.

    As for rent to own, it will probably depend upon the contract but from the sounds of it most act as if you are doing two things:

    1) Renting a house
    2) Buying a Call Option on price of that particular house.

    That option gives you the right (but typically not the obligation) to buy the house at a specified price. To get this right, you have to pay a premium. And if you decide for whatever reason not to buy that house, all of that money will be gone. (If you do buy, some of gets applied to the down payment.)

    So basically you'd be making a substantial side bet on the price of that of that particular house. And it's not just betting like $10; it's going to be a several thousand dollar side bet.

    The other thing is: is the price of the embedded call option a good one? That's not going to be easy to estimate. Even though I'm not a huge fan of it, you could consider trying to value it using the Black Scholes Formula. It will at least give you some idea of whether the embedded call option is an appropriate price.

    Based on data from Robert Shiller, home prices have annual volatility of about 4.3% (1890-present) though they don't appear to be terribly close to a normal distribution (one of the assumptions required to use Black Scholes.)


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