# Good PR for the Housing Market

Dr. Eric Gaze

Director of the QR Program

Bowdoin College

**Numb:** Las Vegas has a PR ratio of 11.

**Number:** Las Vegas' median home price as of June 2010 is 11 times their average yearly rent price.

**Numbest:** Las Vegas' median home price as of June 2010 is 11 times their average yearly rent price, down from a 31.8 Price-to Rent (PR) ratio in 2005 at the peak of the housing bubble. The current low PR ratio of 11 makes Las Vegas one of the 10 best cities in America to consider buying over renting.

The idea of the Price-to-Rent ratio (PR ratio) should remind you of the PE ratios used in stock valuations. In a November 2007 Fortune article, Real Estate: Buy, Sell or Hold, by Shawn Tully, the Yale economist Robert Shiller confirms this and tells us we can expect home and rent prices to essentially be proportional: "Rents exercise a kind of inevitable gravitational pull on prices. The ratio of prices to rents 'behaves much like price/earnings ratios for stocks,' says Yale economist Robert Shiller. 'Like P/Es, price-to-rent ratios are mean-reverting.' In other words, while prices soar from time to time, sending the ratio to exceptional heights, sooner or later the relationship is bound to return to its historical average." In essence, these two quantities can be imagined to be connected by a rubber band, so that when the gap between home and rent prices stretches beyond the historical PR ratio, market forces will pull them back into proper proportion. And home prices did indeed soar at the start of the last decade, fueled by ever lower interest rates and teaser home loans offered by banks to sub-prime borrowers.

In cities across the country the price-to-rent ratios soared as well, with the national PR ratio rising from 15 to 24 over the five year period 2000-20005, after having stayed consistently in the 14-15 range throughout the 1990's.

2) Source: http://www.nytimes.com/2010/04/21/business/economy/21leonhardt.html

3) Source: http://money.cnn.com/magazines/fortune/price_rent_ratios/

4) Source: http://www.nytimes.com/2010/04/21/business/economy/21leonhardt.html

5) Source: http://www.trulia.com/blog/rudy_bachraty/2010/06/new_trulia_real_estate_index_rent_vs_buy

Just as sky high price-to-earnings ratios put a huge "Buyer Beware" warning on stocks, these PR ratios should have tipped off the banking industry that the housing market was indeed in a bubble scenario about to burst. Unlike the stock market however, the housing market had never collapsed, and the 2001 tech implosion on Wall St. had risk averse investors lining up for nicely packaged mortgage backed securities. Bankers on Wall St. were making too much money to try and figure out just what a "collateralized debt obligation" was and what sort of risk was involved.

The numbers didn't lie and the housing market did burst, sending the US economy into its worst recession since the Great one. To be fair the overblown home market was just the tip of an overspending iceberg, with most nations leading the way in terms of borrowing and spending more than they earned. The good news is that homes have become affordable again, as PR ratios have now slipped below their historical averages. The 2007 Fortune article mentioned above was prescient in their prediction for housing prices to fall. In particular Miami headed their list of cities whose PR ratios had the farthest to fall to get back to historical norms. Trulia.com just released on June 3, 2010 the PR ratios of the 50 largest cities in the US and Miami now has third lowest PR ratio at 7.8 with a median home price of $189,556 and average monthly rent of $2,019.

An interesting side note here for the readers looking for a quantitative skills challenge. The Fortune table above computes the percentage drop needed for the 2007 PR ratio to return to its historical level. They then say that on average the PR ratios need to fall 28%. Putting aside how this average was computed, they also report that rent prices are expected to rise by 12% thus home prices only have to drop by 16%. My Q-sense starts tingling anytime someone starts playing with percentages like this, adding percentage change is a common mistake. If something grows by 20% and then 20% again the total growth rate is 44% not 40%. So by how much do housing prices have to fall assuming rent goes up 12% and the current PR ratios need to fall 28%? I'd love to hear from you!

Current PR ratios tell us it is a buying opportunity for those interested in home ownership, and provides a great topic for a Quantitative Reasoning class project. I have had my QR classes do a Buy vs. Renting project for the last 5 years, and have always found it to be enlightening. My students are given the scenario of a couple trying to decide whether to buy now or rent for 10 years and then buy a home. The buying scenario has them create an amortization schedule for the home loan, using savings for a down payment. Taxes are computed with deductions for mortgage interest and property taxes given. The renting scenario has the initial savings being invested in a mutual fund, with yearly savings being computed: no home maintenance or property tax but more income tax, and that savings also invested. There are many assumptions that have to be made in this project, including the inflation rate, mortgage rate, and rate of return on investment. It is very eye-opening to students, most of whom have no idea how a loan works or what a mutual fund is.

I was happy to find a nice article in the NY Times by David Leonhardt, In Sour Home Market, Buying Often Beats Renting, which has an interactive buy vs. rent calculator. The calculator includes all of the assumptions in my project and a few more. One major drawback is that it is a black box, meaning you just set the different rates and the calculator has all the formulas already programmed, so it simply spits out its recommendation. The Excel project I use in class forces the students to come up with their own formulas to compute all the relevant outputs. Still the interactive calculator is fun to play with and has a nice graphical output. One intriguing discovery was how important the rate of return on your investment is in making this decision. The calculator is initially set to 4% for investment return while my project has students getting a 12% return, which was the historical average of the stock market back in 2005. Also the online calculator computes the amount spent each year, so it lists return on investment as "lost opportunity cost", while in my project I simply have the renters computing the growth of their investment. I was pleased that my conclusion for the project was verified by the online calculator, although I realized that I had seriously underestimated the rent (from Trulia.com) for Boston :O)

I'll close this column with a quote from GEMiller in his 20somethingfinance post, Buy or Rent: The One Number You Need to Look At. He is talking about how trying to time the housing market is just as tricky as timing the stock market, there are always going to be people saying the market is heading in different directions: "Using the price-rent ratio is brilliant in that it takes the guessing out of the equation. Just look at the cold hard numbers and let them make the decision for you."

**Sapere Aude!**