# A Better Price-Rent Ratio

The typical formulation for an aggregate price-rent ratio in a particular area is to find the median listing price for homes posted for sale in the area and divide that number by twelve times the median rental price for similar homes listed for rent in the area (sometimes, you see closed sale price substituted for listing price and sometimes people use a mean versus median). For example, one could look at all two-bedroom homes for rent in a given market and compare the typical rental price (annualized) of this set of homes to the typical list or sale price of two-bedroom homes in the same market. The idea of this metric is to give one some sense of how annualized rents compare to purchase prices. The lower the ratio, the smaller the gap between annualized rental and purchase costs and the more attractive the decision to buy a home versus renting a similar one.

A potential problem with this approach is that it relies on two different sets of homes: those for rent and those for sale. That’s not a problem as long as these two sets of homes are similar in terms of the underlying value of the homes in each set. That’s the reason for applying some common selection criteria for identifying both sets of homes; for example, homes with the same number of bedrooms or with similar square footage of living space. But even when doing this, substantial differences might still exist between the two sets of homes. For example, they might differ substantially in terms of attributes not used as filters. Or they may be located in different sectors of the city, locational differences which could lead to different underlying home values themselves, quite independent of the rental and for-sale prices.

To demonstrate that this issue is a practical and not just academic one, Table 1 shows the price-rent ratios for top metro regions computed using this basic approach. This price-rent ratio is computed for two-bedroom rental homes and two-bedroom homes for sale in the market, so we are looking at homes that are similar on a very basic level. But, if these two sets of homes (rental and for-sale) were, in fact, similar to each other, we’d expect the underlying home values for each set of homes to be similar. Figure 1 shows the median estimated market value (Zestimate as of August 27, 2010) for both sets of homes. As you can see, in some metros, there are substantial differences between the median values of the rental and for-sale homes used to compute the price-rent ratio, particularly Los Angeles, New York, and San Diego.

The fundamental concept behind the price-rent ratio is to look at homes with similar underlying values and then utilize the differences between rental and purchase prices to infer something about the purchase price itself (e.g., is it a fair value relative to renting). If, instead, one compares two sets of homes, each with fundamentally different underlying values overall, then looking at rental and purchase prices tells you nothing about purchase price levels. In the case when the median value of the for-sale homes is greater than the median value of the rental homes, you’d naturally expect the purchase prices to be much higher than the annualized rental costs because the for-sale homes are more valuable than the rental homes.

A better approach would be to look at the same set of homes and observe the rental and purchase prices for each home. To date, the problem with doing this has been that few homes are marketed both for-rent and for-sale simultaneously, making it hard to obtain both prices for a given home. But what if we looked at rental homes and then compared the rental price to the estimated market value for each home? Then we’d have both a rental price and an estimated market price on exactly the same set of homes. With this data, one could compute a price-rent ratio for each house and then find the median price-rent ratio across all the homes. Doing so, we could be guaranteed that there were no biases introduced into the ratio due to differences in the sets of homes on which the rental and purchase prices were based; there would only be a single set of homes. In Table 2, we’ve added an additional column to the data presented in Table 1 and this column represents the price-rent ratio computed using this second approach (along with a column showing the differences between the two approaches).

As you can see, the metros with the largest differences between the two approaches are the same metros with the largest differences in underlying home values between rental and purchase properties shown in Figure 1. To better understand the strong relationship between, on the one hand, differences in overall home values between the pool of homes for rent and the pool of homes for sale and, on the other hand, differences in the price-rent ratio computed using the two approaches, Figure 2 graphically displays these two differences relative to each other (in this chart, the x-axis is the last column from Table 2 and the y-axis is the percentage difference in the blue and red lines in Figure 1). As you can see, there’s a pretty strong relationship (Pearson correlation coefficient =90%).

Notice also that the difference in the price-rent ratio computed under the two approaches is not equally positive and negative across the various markets. The price-rent ratio computed using the older method is usually lower than that computed using the new approach, driven by the fact that the median home value in the rental set of homes is typically higher than the median value in the for-sale set of homes. This means that, even after controlling for a basic attribute of the homes (number of bedrooms), the rental properties are typically more expensive than the for-sale homes. A possible reason for this fact is that rentals might be more likely to be located closer to urban centers than for-sale homes and therefore in more expensive areas of the metro region. Using the older approach, one could erroneously conclude that buying was more attractive in some markets than it actually is. This mistaken conclusion would be driven by comparing more expensive rentals to cheaper for-sale homes. Essentially, one is comparing apples and oranges.

Table 3 presents the results of the new approach when applied across all rental properties. Note that the filter on two-bedroom homes is no longer needed since the price-rent ratio is being computed at the house level versus using two separate pools of homes (and, therefore, we don’t need to ensure that the two pools are somewhat similar). Markets with the lowest price-rent ratios (where buying is more attractive relatively) include some markets hard-hit during the housing bust such as Detroit, Miami, Orlando, Las Vegas, Tampa and Phoenix. Also included are markets that participated to a lesser extent in the housing boom such as Houston and Dallas-Fort Worth. On the other end of the spectrum, we also find some hard-hit markets such as San Francisco, Los Angeles, New York and San Diego. While home values in these markets are down significantly from their peak, they are apparently still relatively high when compared to prevailing rental rates.