Sunday, March 18, 2007

Don't Doubt the Power of Compunding

by Tom Bozzo

Roger Lowenstein plays the real estate bull in a NYT magazine real estate supplement, seemingly to accompany all the ads for luxury condos and apartments surrounding the article. Lowenstein makes a valid point that, unlike a dot-com stock, a house will keep the rain off of one's head. But at the heart of the article, there's a subtle but important bit of innumeracy:

The dirty little secret of home ownership is that it lets you play with other people’s money. Say you want to purchase the median home (in California the cost would be about $565,000, but let’s take the United States median, which would run you $220,000). Typically, you would take perhaps $50,000 from savings as a down payment, borrow the balance and pay the monthly mortgage from your income.

But wait! Just before you close, a friendly real estate bear points out that you could rent the same house, or a similar one. Your monthly payment would go to the landlord, not the bank. And you could invest the $50,000 in stocks, which, with dividends, might appreciate at close to 10 percent a year, rather than the 5 percent or so you could expect from your house.

That would be a very dumb move. Suppose the stock market did rise 10 percent; after a year you would be up $5,000. Whereas the gain on your home would be 5 percent over the entire purchase price — or $11,000. Over 10 years the gap becomes huge — not to mention over 20 or 30 years.

Eh, what? There's always a time horizon over which higher-return assets dominate lower-return ones, however large the head start you give the latter. In the case of the simple example Lowenstein provides, the equity gap initially increases (peaking around year 17, by some relatively simple math), but over the longer haul closes and, in fact, at 32 years you'd be as well off not buying. Beyond that, the 10% stock market takes off and trounces the slow-appreciating house. That's a long time, but less than a typical span between graduating from college and retiring, say.

For an additional complication, Lowenstein's example seems to assume that the homeowner isn't paying more implicit rent on a house (basically, interest, property tax, and maintenance, after income tax breaks) than on an equivalent rental. That's often tough to test, since the rental market is far from complete — in many markets, it's distinctly thin in rentals equivalent to the owner-occupied single-family housing stock. (*) But in some of the bubblier markets, the "rational" rent you'd need to charge yourself might considerably exceed what you'd pay on an actual rental. That would favor not buying.

Furthermore, a lesson of the stock market bust (not to mention the real estate bust of the early nineties) is that buying at the market peak can subject you to lower-than-typical returns for a long time. Someone who had stuck a chunk of money into a fund tracking the major stock market indexes in early 2000 wouldn't be ahead — especially after inflation — seven years on.


(*) This is one sense in which fancy mortgage arrangements that amount to rentals by another name (i.e., with little or no amortization) may, as the Marginal Revolutionaries might say, drive the world towards Markets in Everything.

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Not sure why you focus on the time horizon. I would think the more obvious problem is the lack of mortgage interest. For any reasonable mortgage interest rate, there is NO time horizon over which the house in his example beats the stock market, and yet he still calls putting the money in the stock market a "dumb idea". Maybe it is financial advisors using Lowenstein math that have helped drive the real estate bubble.
The lack of mortgage interest only looks like a problem in Lowenstein's example. As I said in the post (maybe a bit cryptically), he's assuming that the 'equivalent rent' implicit in the mortgage and the market rent for an actual rental unit are the same. Since there's the same 'rental' payment in both scenarios, that consideration washes out and the point is that the faster growth of the stock market ensures that the gap eventually will close, contrary to Lowenstein's implication that the gap only gets bigger over time.

While I note that cases where house price gains causes the implicit rents on owned houses have outstripped market rents undercut Lowenstein's example further, there is a countervailing issue that market rents are subject to inflation whereas you can (in theory) make fixed payments on the mortgage in current dollars.

A bigger potential issue is with the claim regarding the average rate of appreciation for housing. Shiller's house price series show effectively zero real increases over very long periods of time -- basically, apart from the recent 'hockey stick' feature that looks like the bubble. There's a lot of remodeling expenditure thrown at houses that tends to be misidentified in many (or most) house price series as appreciation.
Ah, you're right, that does appear to be his assumption. I live in California so the thought that the cost of paying a mortgage might be comparable in cost to renting an equivalent place simply hadn't occurred to me. It certainly is a fiction around here. Your argument is obviously correct.
It is a mistake is to assume stocks are the higher return investment. This is true most places, but not in many metropolitan areas. Leverage in these areas boost returns to better than stocks, but it does take large amounts of leverage. Another mistake is to compare it to stocks when bonds are the closest equivalent. (Shiller asserts flat real prices than illustrates prices in Cleveland have appreciated 2% a year.)

Cost wise, rents may be cheaper than owning, but rents increase with inflation while owning falls with inflation making owning the better long term proposition, though long term can be very long indeed at current levels. It may take as little as 15 years to come out ahead when valuations are reasonable, but more than 30 years when they are not. In mid america renting is cheaper, though, not necessarily better.
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