# Housing Price-to-Income Ratio as a Way to Measure Maximum Local Affordability

Thursday, June 02 2005

**Update:** I'm now maintaining a continuously updated home affordability study over at Department of Numbers.

As with the stocks, it's difficult to find something approaching the fair value of a home in an objective manner. Even if you know how to approximately value something in either market, it's no guarantee that speculation or fear will not push prices higher or lower than their expected value. It seems though -- as evidenced by experience with the stock market -- that totally unreasonable valuations can not be sustained indefinitely. Here I have looked into what I think is a reasonable method of valuation for the housing market to try to see if certain metro areas may have risen to difficult to justify price levels.

The central assumption for this approach to home valuation is that the housing market should make a medium priced home affordable to a medium income earning family. That is, a middle of the pack income earning family should be able to afford a middle of the pack home. It's certainly arguable whether or not this is true, and there are definitely other factors to include in home valuation (such as wealth), but I think of this method as maybe a first order approximation. That is, I hope it captures the bulk of a home's value, but it probably does not capture all. Or I could be totally wrong.

If we do take this as an assumption and apply what most lenders call affordable (paying a maximum of 28% of your monthly income for your mortgage), we can figure out what medium home price to medium family income ratio is for a given down payment and mortgage interest rate. What we have then is a number that represents the *maximum* multiple of income that a home could cost and still be affordable (again by the conventional definition of affordability) to a medium income earner. Given the assumption above, this ratio is valid across the entire US housing market and allows us to *directly* compare one market to another (assuming, of course, we are using local values for median family income and median home price).

To figure out what the maximum affordable home price to income ratio is, let's assume we earn a medium family income of $1000 a year (we can assume anything and it will not change the ratio). Again, lending standards say that we can use a maximum 28% of our monthly income to service our home mortgage debt. So we have (1000/12)*.28=23.33 dollars available each month that we can use to pay the mortgage. Now we need to figure out the monthly cost for each $1000 we borrow so that we can know how much we can spend on a home. For a 7% fixed rate 30 year loan (for example), it costs $6.65 a month to borrow 1000 dollars. Therefore we can afford to borrow 23.33/6.65=3.5 multiples of 1000 dollars (i.e. 3.5*1000=3500 dollars). 3.5 is then the maximum affordable medium home price to medium family income ratio for a mortgage with 0 dollars down and a fixed 7% interest rate. Said in a more realistic way, a family making $100,000 a year can afford at most a $350,000 home (350000/100000=3.5) with this mortgage.

For rates of 6% and 8% (all other conditions the same) the ratios are 3.9 and 3.2 respectively. The ratio is larger for smaller interest rates because the cost of borrowing money is cheaper and we can do more with the 28% of our income we are allowed to use. Again, these ratios hold true for any locale given our assumptions.

If we put down some money on the home (we put down none in the previous example) we can buy something at a greater multiple because the down payment money decreases the amount of money we have to borrow. To get the ratios for a given down payment all we have to do is multiply the ratio for zero dollars down by the money (as a percentage of the home price) put down. For instance, the 3.5 ratio for a 7% mortgage rate with zero dollars down becomes 1.2*3.5=4.2 when the buyer is able to put down 20% of the price of the home.

Here's a table summarizing the maximum affordability ratio for varying interest rates and down payment percentages.

### Maximum Affordability Ratios for Different Rates & Down Payments

5% | 6% | 7% | 8% | |

0% Down | 4.35 | 3.89 | 3.51 | 3.18 |

10% Down | 4.79 | 4.28 | 3.86 | 3.50 |

20% Down | 5.22 | 4.67 | 4.21 | 3.82 |

Obviously, the parameters we have to play with here are the mortgage rate and down payment percentages. As you can see, the range of ratios is fairly broad (3.18-5.22) based on what assumptions we make about these two parameters. So, what assumption should we make? It is my opinion that the value we should choose for these parameters (the value a rational market should choose perhaps) is the future expected average mortgage rate and the future average down payment (as a percentage of the home price) that the home buyer can afford to put down. I'm going to be conservative in my guess for both and say that future rates will be around 7% and that future home buyers will be able to put down about 10% of the cost of their homes. There is plenty room for argument here, but I think this guess is somewhere in the middle of the extremes of that argument.

With these assumptions, the table above tells us that the maximum affordability ratio is 3.86. If the ratio is higher in some locale, the home buyer can do a lot of things (adjustable rate mortgages, buying cheaper, sub-median priced homes, borrowing money from family etc..) and still end up in an "affordable" home, but what is still true is that the medium priced home is not affordable for the medium income earner given the mortgage terms we assume. Opinions will likely vary, but I think that too much of a departure from this maximum affordability ratio is a sign that the local market is overvalued. If you have a different idea of what typical future rates and down payments might be you may choose a different ratio but exceeding whatever ratio you decide on says that a medium priced home is not affordable for a medium income earning family (again for our mortgage assumptions).

So, finally, now that we have a educated guess at what the maximum affordability ratio should be (3.86 or whatever you've chosen from the table), what are some actual ratios for cities in the United States? The table below shows the ratio of medium home price to medium family income for the cities listed. The medium home price comes from NAR's 1Q 2005 Housing Price Report and the medium income data comes from HUD's ~~2004~~ 2005 Median Family Income Data. This is, as far as I know, the same data that the NAR uses to compute affordability (and the most recent version of it).

### Median Home Price-to-Median Family Income Ratios for US Cities/Metros (Sorted by Home Price)

Location | Home | Income | Ratio |

San Francisco, CA | $689,200 | $83,700 | 8.23 |

San Diego, CA | $584,100 | $62,900 | 9.29 |

Honolulu, HI | $529,100 | $67,750 | 7.81 |

Los Angeles, CA | $474,700 | $59,400 | 7.99 |

New York, NY | $435,200 | $68,750 | 6.33 |

Boston, MA | $398,300 | $80,250 | 4.96 |

Washington, DC | $369,000 | $88,500 | 4.17 |

Sacramento, CA | $352,900 | $63,400 | 5.57 |

Riverside/San Bernadino, | $343,400 | $55,650 | 6.17 |

Seattle, WA | $321,100 | $69,450 | 4.62 |

Miami, FL | $315,700 | $53,650 | 5.88 |

Las Vegas, NV | $291,000 | $59,050 | 4.93 |

Chicago, IL | $243,800 | $68,950 | 3.54 |

Denver, CO | $236,000 | $71,700 | 3.29 |

Baltimore, MD | $235,300 | $72,150 | 3.26 |

Portland, OR | $223,700 | $66,300 | 3.37 |

Minneapolis/St. Paul, MN | $218,700 | $77,000 | 2.84 |

Tucson, AZ | $199,000 | $50,550 | 3.94 |

Milwaukee, WI | $198,900 | $65,200 | 3.05 |

Phoenix, AZ | $193,800 | $58,200 | 3.33 |

Colorado Springs, CO | $192,200 | $63,550 | 3.02 |

Raleigh/Durham, NC | $175,600 | $70,250 | 2.50 |

Philadelphia, PA | $164,800 | $69,100 | 2.38 |

Jacksonville, FL | $164,400 | $57,700 | 2.85 |

Atlanta, GA | $159,500 | $69,300 | 2.30 |

Salt Lake City, UT | $157,000 | $61,550 | 2.55 |

Austin/San Marcos, TX | $154,100 | $68,150 | 2.26 |

Nashville, TN | $152,100 | $59,800 | 2.54 |

Detroit, MI | $151,000 | $68,650 | 2.20 |

Albuquerque, NM | $149,700 | $53,500 | 2.80 |

Kansas City, KS/MO | $148,300 | $65,400 | 2.27 |

Lexington/Fayette, KY | $141,500 | $60,100 | 2.35 |

New Orleans, LA | $141,200 | $51,000 | 2.77 |

Columbus, OH | $140,100 | $63,850 | 2.19 |

Dallas, TX | $140,000 | $63,750 | 2.20 |

Cincinnati, OH | $139,600 | $63,750 | 2.19 |

Houston, TX | $138,100 | $59,450 | 2.32 |

Cleveland, OH | $135,400 | $60,850 | 2.23 |

Omaha, NE | $132,400 | $64,550 | 2.05 |

Memphis, TN | $131,500 | $53,600 | 2.45 |

Ft. Worth/Arlington, TX | $123,600 | $63,750 | 1.94 |

San Antonio, TX | $123,600 | $51,450 | 2.40 |

Indianapolis, IN | $116,300 | $64,000 | 1.82 |

Saint Louis, MO | $112,800 | $63,950 | 1.76 |

Oklahoma City, OK | $110,300 | $52,350 | 2.11 |

Wichita, KS | $105,100 | $58,650 | 1.79 |

El Paso, TX | $104,800 | $38,400 | 2.73 |

Buffalo, NY | $93,900 | $56,950 | 1.65 |

I won't draw conclusions about what cities are or are not in the midst of a housing bubble or heading for housing busts (if any), but I think it's safe to say that it requires some argument to justify ratios above 3.86 (and there may be some justifiable location specific arguments). However, ratios that are far above 3.86 are worrisome because they are telling us that the people that live in the city can't afford to buy a home that is placed in the same region of the distribution as their income (i.e. the median).

One final note, I got the idea to do this mini-study based on this USA Today article which quotes a Goldman Sachs economist who sites 2.7 as the historical national average median home price to median family income ratio. He says that ratios up to 3.5 might be justified by current mortgage rates and lending practices but that 2.7 is the historical average we have to compare against. Remember what we computed here was a maximum ratio based on safe lending practices. It seems historically people have been able to purchase homes with a fair bit of padding under that 28% of income ceiling (which makes the assumption that median income earners should be able to afford median priced homes seem reasonable...at least historically). In at least some markets, this will be pretty tough to do going forward.