Economics Forum -- October 26, 2004 Santa Barbara Housing Prices: Another Dot-Com Bubble? Stephen F. LeRoy, UCSB Department of Economics

Economics Forum -- October 26, $210,768 $243,249 $302,029 $417,700 $476,100 $634,154 $690,883 SANTA BARBARA COUNTY MEDIAN HOME PRICE Existing Single Family

Economics Forum -- October 26, 2004 Housing Affordability Index

Economics Forum -- October 26, , , , , , , , ,000 $1,000, Single Family Home Median Price South Coast 2002 = $749,000 $975, = $825,000 Aug 2003 headlines = $950,000

Economics Forum -- October 26, 2004 The March 2004 Montecito Median Home Price was $2.3 million.

Economics Forum -- October 26, Median Home Prices for Cities in Santa Barbara County $650, ,792$ $481,246 $210,453 $282,563 $291,729 $557,646 BuelltonCarpinteriaGuadalupeLompocSanta Barbara City Santa Maria Solvang All Inclusive

Economics Forum -- October 26, 2004 Recently, some signs of leveling off: Home sales in August dropped 47% relative to a year ago. Same with condos Median price Jan-Aug: $1,049,000 Median price August: $989,000 - SBNP, September 25

Economics Forum -- October 26, 2004 What Is A Bubble? Prices rise, then drop? Markets are irrational? What does irrational mean? With hindsight, of course I shouldn ’ t have bought all those dot-com stocks Was it obvious at the time? Anyone could have shorted the NASDAQ …

Economics Forum -- October 26, 2004 Rationality Economists like to think of people as being rational. People are doing the best they can, given limited information. They aren ’ t making mistakes that are big and obvious

Economics Forum -- October 26, 2004 Of course, a few people are irrational by any definition But if they dominated markets, there would exist obvious trading strategies by means of which rational people could exploit them Who are these rational people? What are the trading strategies?

Economics Forum -- October 26, 2004 Rational Bubbles Here ’ s a definition of bubbles that doesn ’ t appeal to irrationality Suppose rental income (or the service yield of a home) is I dollars per year The price of an apartment complex in year t is P t The return that the market demands (in view of risk, illiquidity) is r If the expected value next year is P t+1, what is P t ?

Economics Forum -- October 26, 2004 Return consists of rental income (per dollar of value) plus rate of capital gain: Solve: Replace t by t+1:

Economics Forum -- October 26, 2004 Now substitute the last equation in the one before: Keep doing this. Eventually you get:

Economics Forum -- October 26, 2004 Present-Value Let n go to infinity. You get that the price of the apartment complex equals the discounted value of its rents

Economics Forum -- October 26, 2004 But only IF the present value of its price n periods in the future (the right-most term) goes to zero! But suppose it doesn ’ t! If this term approaches a positive number, that ’ s the bubble So price = fundamental value + bubble Existence of a bubble is consistent with equilibrium because the rate of return equals r by construction.

Economics Forum -- October 26, 2004 The Bottom Line Under a rational bubble, rental income per dollar is low, but price is expected to rise so as to generate the appropriate return This justifies the current price Therefore I/P is decreasing, as well as low Investors don ’ t lose by holding an asset with a bubble That ’ s why it ’ s a rational bubble What about uncertainty? Doesn ’ t change the story much: even if the bubble may burst, the bubble may still be consistent with equilibrium, if it grows really fast when it doesn ’ t burst.

Economics Forum -- October 26, 2004 The task We have to figure out whether housing prices can be explained by the present value model without bubbles Or can we explain the price runup only by assuming that there ’ s a bubble?

Economics Forum -- October 26, 2004 Special cases Suppose there ’ s no bubble and that I is constant. Then price is: So if r is 10%, P=10*I This is the constant perpetuity formula

Economics Forum -- October 26, 2004 If I grows at rate g, this becomes This is the growing perpetuity formula If r=10%, g=5%, P/I = 22. So a growing revenue stream gets a higher price multiple

Economics Forum -- October 26, 2004 Bad News Price-income multiplier is very sensitive to both r and g: r=10%, g=5%, P/I = 22 r=8%, g=5%, P/I =37 Conclusion: given the margin of error in estimating r and g, it ’ s hard to get an exact estimate of what P/I should be in the absence of bubbles …

Economics Forum -- October 26, 2004 This checks out. In Philadelphia, P/I is around 8. In Santa Barbara, it ’ s maybe 20. Why? Nobody expects rents to grow much in Philadelphia (because they haven ’ t in the past). People do expect rents to grow in Santa Barbara (because … ). Equivalently, rental income in Philadelphia is higher than in SB per $ invested, but capital gains are expected to be lower.

Economics Forum -- October 26, 2004 Good News The constant perpetuity formula can give some guidance in interpreting changes in P/I. Changes are traceable to variations in r or g

Economics Forum -- October 26, 2004 Suppose there ’ s a bubble (Take g=0 for simplicity) Set P t equal to some number greater than that implied by the constant perpetuity formula You can use the relation between P t, P t+1, P t+2, … to calculate future prices. If there ’ s no bubble, P = constant.

Economics Forum -- October 26, 2004

If there ’ s a bubble, price rises at an accelerating rate. It must. Income per dollar invested is dropping, so capital gain rate must be increasing.

Economics Forum -- October 26, 2004 Therefore in a Rational Bubble P/I rises over time. That has happened in SB, nationally. Prices now average 20 x rents in parts of CA, Florida. Was around 10 x rents in WSJ, 8/31/04, p. A2

Economics Forum -- October 26, 2004 The big question Are people bidding up the price of real estate because Their estimates of growth rate of rental income have been revised up, or because the discount factor has dropped (no bubble) Or Just because they expect prices to rise (there is a bubble)?

Economics Forum -- October 26, 2004 Rents SB is a nice place to live But: it was a nice place (even nicer?) in 1975, when housing prices were much lower So you really need to argue that people have been finding SB more attractive in the last few years

Economics Forum -- October 26, 2004 That ’ s possible: with telecommuting, you can trade options without living in Chicago. Supply of new housing is limited Boomers are starting to retire ($) Lots of $ in LA, and many want second homes in SB But: SB economy looks a lot like the rest of California (remember those affordability indexes).

Economics Forum -- October 26, 2004 Rents have been flat in SB since 2000 or so It ’ s possible that investors revised upward their expectations of the growth rate of rental income over the distant future, even though rents are flat now. But is it plausible?

Economics Forum -- October 26, 2004 Interest rates have dropped. Were expected to rise in the past 6 months, but they haven ’ t

Economics Forum -- October 26, 2004 Mortgage rate,

Economics Forum -- October 26, 2004 Mortgage rate minus CPI growth,

Economics Forum -- October 26, 2004 Conclusion I don ’ t see fundamentals – as reflected in the growing perpetuity formula -- as justifying anything like the price runup that we have seen. Modest mortgage rate decreases, flat rents don ’ t justify price doubling in the last several years. Fundamentals justify high prices in SB But not this high

Economics Forum -- October 26, 2004 Past Bubbles Have almost always occurred when there were genuine reasons to be optimistic 1720 – South Sea bubble (East India Company had a monopoly on English trade with South America) 1929 – electricity, automobiles Japanese stock prices, 1980s 2000 – internet Same with SB housing

Economics Forum -- October 26, 2004 A good sign: housing prices weathered a recession However, interest rates will increase sooner or later. Signs of speculation: purchases of second homes. If there ’ s a price break, will owners of such properties hang on?

Economics Forum -- October 26, 2004 Thanks for coming!