Arnold Kling  

Rent Vs. Buy Calculation

Healthy Debate... Fun Time: An Exercise in Trans...

James Hamilton writes,

Let's look at a particular property in such a community whose rental income nets the owner $4,000 per year after expenses. If the property price is determined by the condition that the owner must earn a 3% real return, the property would have a fair market value of $200,000. One arrives at this fundamentals-based price through the following calculation. If the current price were $200,000, next year the owner could sell it for $202,000 (in real dollars). The rental income of $4,000 plus the capital gain of $2,000 provide the requisite 3% return on capital of $200,000. Next year's $202,000 price is likewise warranted by next year's $4,040 rental income and prospect of 1% capital gain on $202,000, and so on. There's no bubble because both the price-to-rent ratio and the rent-to-income ratio remain constant over time.

Now suppose instead that population and income gains are expected to produce economic growth for the community of 3% each year rather than 2%. In this case, if the stock of available housing is still only growing at 1%, the rental rate would now grow at 2% each year. The analogous calculation to the one above implies that the same piece of property earning the same $4,000 rental would now be worth $400,000 rather than $200,000. The owner is now rationally expecting to earn $4,080 in rent next year and to be able to sell the property for $408,000. The $8,000 capital gain plus the $4,000 current rental income again justify the property value in terms of giving the owner a 3% real return.

Hamilton's point is that you might see a large jump in house prices over a short period if there is a change in the expected growth rate of population and income in an area.

What we should observe, assuming that this expected growth rate takes place, is an increase in the growth rate of rents. If instead rents are sluggish, that would be a strong indicator of a housing bubble. I have to admit that I have not been tracking rents that closely. If someone has a good index of rents in some of the alleged bubble areas, please leave a comment.

UPDATE: A reader points to the Harvard study of the state of the housing market. The chapter on rental housing describes a market that is recovering from a slump, but with few markets showing increases in rents. I take that as not very supportive of the notion that house prices are rising because of fundamentals.

I would add that what Hamilton says about housing markets is also true for stocks. That is, the equilibrium price is highly sensitive to changes in the expected rate of growth of profits. That leads to a question about whether it is rational for the expected growth rate of profits to change suddenly. There is a "variance bounds" literature which argues that realized long-term average profits change very slowly. Some authors argue that large variations in expected returns, and large movements in stock prices, are inconsistent with the relative stability of realized returns.

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COMMENTS (1 to date)
spencer writes:

I do not have specific market data, but what is happening on a national level is that we are seeing an upward shift in the share of the population purchasing and as a consequence a downward shift in rental demand. Consequently,
rental rates are growing much slower then home prices.

One of the interesting places this is showing up is in the CPI. Some 23% of the CPI is home owner equivalent rent -- what home owners would expect their home to rent for. But this is what the CPI reflects rather then home prices. Consequently, the reported inflation rate is being held down by the sharp jump in home ownership.

On the specific issue, as a general rule rents are determined more as a function of cash flow. Rents are set to cover cash flow and the owners take their profits in the form of long term capital gains.

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