economics forum -- october 26, 2004 santa barbara housing prices: another dot-com bubble? stephen f....

Economics Forum -- October 26, 2004

Santa Barbara Housing Prices:

Another Dot-Com Bubble?

Stephen F. LeRoy, UCSB Department of Economics


92 94 96 98 00 02 04 06 08

$210,768$243,249

$302,029

$417,700

$476,100

$634,154

$690,883

SANTA BARBARA COUNTY MEDIAN HOME PRICE

Existing Single Family


10%

15%

20%

25%

30%

35%

40%

45%

50%

96 97 98 99 00 01 02 03

SANTA BARBARA COUNTY

CALIFORNIA

Housing Affordability Index


600,000

650,000

700,000

750,000

800,000

850,000

900,000

950,000

$1,000,000

2002 2003 2004

S in g le F a m ily H o m e M e d ia n P r ic e

South Coast

2002 = $749,000

$975,000

2003 = $825,000

Aug 2003 headlines = $950,000


The March 2004 Montecito Median Home Price was$2.3 million.


2003 Median Home Pricesfor Cities in Santa Barbara County

$650,722

454,792$$481,246

$210,453

$282,563 $291,729

$557,646

Buellton Carpinteria Guadalupe Lompoc Santa BarbaraCity

SantaMaria

Solvang

All Inclusive


Recently, some signs of leveling off:

Home sales in August dropped 47% relative to a year ago.

Same with condos

Median price Jan-Aug: $1,049,000Median price August: $989,000

- SBNP, September 25


What Is A Bubble?Prices rise, then drop?Markets are irrational?

What does irrational mean?With 20-20 hindsight, of course I shouldn’t have bought all those dot-com stocksWas it obvious at the time?

Anyone could have shorted the NASDAQ …


RationalityEconomists 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


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?


Rational BubblesHere’s a definition of bubbles that doesn’t appeal to irrationalitySuppose rental income (or the service yield of a home) is I dollars per yearThe price of an apartment complex in year t is Pt

The return that the market demands (in view of risk, illiquidity) is rIf the expected value next year is Pt+1, what is Pt?


Return consists of rental income (per dollar of value) plus rate of capital gain:

Solve:

Replace t by t+1:r

PIP ttt

111

r

PIP ttt

122

1

t

tt

t

t

P

PP

P

Ir

11


Now substitute the last equation in the one before:

Keep doing this. Eventually you get:

2221

)1(1 r

PI

r

IP tttt


Present-Value

Let n go to infinity.You get that the price of the apartment complex equals the discounted value of its rents

nnt

nntt

t r

P

r

I

r

IP

)1()1(...

11


But onlyIF 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 bubbleSo price = fundamental value + bubbleExistence of a bubble is consistent with equilibrium because the rate of return equals r by construction.


The Bottom LineUnder a rational bubble, rental income per dollar is low, but price is expected to rise so as to generate the appropriate returnThis justifies the current priceTherefore I/P is decreasing, as well as lowInvestors 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.


The taskWe 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?


Special casesSuppose there’s no bubble and that I is constant. Then price is:

So if r is 10%, P=10*IThis is the constant perpetuity formula

r

IP


If I grows at rate g, this becomes

This is the growing perpetuity formulaIf r=10%, g=5%, P/I = 22. So a growing revenue stream gets a higher price multiple

gr

IgP tt

)1(


Bad NewsPrice-income multiplier is very sensitive to both r and g:

r=10%, g=5%, P/I = 22r=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…


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.


Good NewsThe constant perpetuity formula can give some guidance in interpreting changes in P/I.Changes are traceable to variations in r or g


Suppose there’s a bubble(Take g=0 for simplicity)Set Pt equal to some number greater than that implied by the constant perpetuity formulaYou can use the relation between Pt, Pt+1, Pt+2,… to calculate future prices.

If there’s no bubble, P = constant.


time

Price with bubble

Price without bubble


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.


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 1995.

WSJ, 8/31/04, p. A2


The big questionAre 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)?


Rents SB is a nice place to live

But: it was a nice place (even nicer?) in 1975, when housing prices were much lowerSo you really need to argue that people have been finding SB more attractive in the last few years


That’s possible: with telecommuting, you can trade options without living in Chicago.Supply of new housing is limitedBoomers 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).


Rents have been flat in SB since 2000 or soIt’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?


Interest rates have dropped.

Were expected to rise in the past 6 months, but they haven’t


Mortgage rate, 1971-2004

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

1 29 57 85 113

141

169

197

225

253

281

309

337

365

Series1


Mortgage rate minus CPI growth, 1971-2004

-6

-4

-2

0

2

4

6

8

10

12

1 27 53 79 105

131

157

183

209

235

261

287

313

339

365

Series1


ConclusionI 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 SBBut not this high


Past BubblesHave almost always occurred when there were genuine reasons to be optimistic1720 – South Sea bubble (East India Company had a monopoly on English trade with South America)1929 – electricity, automobilesJapanese stock prices, 1980s2000 – internetSame with SB housing


A good sign: housing prices weathered a recessionHowever, 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?


Thanks for coming!

economics forum -- october 26, 2004 santa barbara housing prices: another dot-com bubble? stephen f....

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