1

Efficient Portfolios when Housing Needs Change over

the Life-Cycle

Loriana PelizzonUniversity of Venice

Guglielmo WeberUniversity of Padua

2

Issues1. Household wealth is made of financial wealth, human capital

and real wealth.

2. Financial wealth is liquid; housing wealth is illiquid (Grossman and Laroque (1990)).

3. Also: housing wealth is also determined by consumption motive

housing needs change with age, particularly because of demographics

4. What is the optimal financial portfolio choice, conditional on a given housing stock and considering housing needs? => Asset and liability framework

5. Empirical evidence: Are household portfolios efficient? Is there an age pattern in efficiency? How is this related to housing?

3

Financial asset allocationStatic model: no housing

• Mean-variance analysis framework:

(1)

• Where X is the vector of financial asset allocation• Jobson Korkie (1982, 1989) efficiency test: Sharpe

ratio (expected excess return/standard deviation)

1

2

20*

WUWU

XT

4

Housing• Housing is an important component of

household wealth• If we consider housing, the efficient frontier is

“better” than the standard frontier (one more asset to choose from!)

• But housing is illiquid – it cannot be changed in the short run – the relevant efficient frontier takes housing as given (conditional frontier) – Flavin and Yamashita (2002)

• People need to live somewhere! They have housing needs too (i.e. a liability)

• Housing needs change with age (demographics).

5

Estimated age profile for “rent”

Age

6

Net housing positions

• Elderly households should count most of their main residence as wealth, as they could liquidate it to buy different goods (medical care, long term care, holidays), while easily meeting their likely housing needs over their remaining years by renting. (Over-housed or long on house) exposed to house price risk! (If price falls, they lose)

• Single, young households, would be unwise to consider their main residence as wealth, given that they are likely to trade up in the future (Under-housed or short on house) exposed to rent risk! (if price/rent rises, they lose)

7

Hedging

• If the rental value of housing has a positive correlation with house prices, owning is a hedge against rent risk (Sinai and Suleles (2005)

• But still some risk remains:– Households who are long on housing or “over-housed” (the

value of their housing stock exceeds the present value of future housing needs) positive net housing exposure

– “under-housed” (vice-versa) negative net housing exposure

• Given non-zero correlation of housing with bonds and stocks, there is scope for portfolio improvement through hedging net housing exposure with financial assets

8

Model with housing• Optimal portfolios are the sum of a Markowitz portfolio and a

hedge term for housing (standard).

• We show that this optimal portfolio can be obtained in a mean-variance analysis framework, when the housing stock net of housing needs is treated as an additional constraint.

(2)

• Where: is the market value of the housing stock net of the present value of housing needs (assumed equal to rents).

bP

TDP

WUWU

X

100

1

2

20*

oPVRHPDP 0000

9

Model with housing

• Households should allocate financial assets with two objectives in mind: – to maximize the expected return of their

portfolio, given a certain risk (standard Markowitz portfolio),

– to hedge the risk in their net housing position.

10

Dynamic Model: key equations• Consumers maximize:

• Where: – C is non-durable consumption, – h are housing services (given! No response

to prices/income after time 0) that can be obtained from owning or renting housing stock, H

0

0

|, GWBedthCueE ttt

Rttt HHh

11

Model: key equations

• Total wealth is defined as:

• Where:– B denotes the risk-free asset, – X the vector of risky asset positions, – HC is human capital – V the present value of housing needs.

• The housing stock has zero depreciation (its return is net of maintenance costs)

ttttttt HCVXBHPW 1

12

Dynamic Model: key equations

Let J(W,P) be the value function. The first order conditions with respect to financial assets are:

0

1

1

1

2

2

2

TPt

TPtttt

Ttf

T

PPW

J

QhHPXW

Jr

W

J

where tttt QhHP is net housing wealth.

13

Econometric Issues

• Theoretical results => test for efficiency must be run conditionally upon net housing wealth

• Gourieroux and Jouneaux (1999) extend Jobson-Korkie (1982) efficiency tests to conditional case.

• Intuition: use Sharpe ratio (expected excess return/standard deviation) – correct for the presence of the hedge term and check if remaining portfolio is mean-variance efficient

14

How does standard portfolio analysis change when we consider housing?

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 1.00 2.00 3.00 4.00 5.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier

Risky assets efficient frontier

household portfolios

household portfolios net of hedge term

B

AA'

B'

15

Empirical evidence

1. Are household portfolios efficient?

2. Is there an age pattern in efficiency?

3. How is this related to housing?

16

Data Sources:

• Household portfolios: SHIW2002

• House Prices: Consulente Immobiliare

• Financial Assets: Datastream

• Housing needs: SHIW 1989-91-93-95-98 2000 and 2002

• Human capital : SHIW as above

17

Amounts held in financial and real assets

Asset (1)Average

(2)Median

(3)Conditional Average

Risk-free Financial Assets 12,728 5,200 15,410

Government Bonds 4,885 0 14,136

Corporate Bonds 2,638 0 7,632

Stocks 3,232 0 9,531

Total Financial Assets 23,482 7,250 46,709

Fix-rate mortgages 1,048 0 3,033

Floating-rate mortgages 1,299 0 1,334

Other debt and mortgages 949 0 2,745

Housing 132,853 100,000 204,110

Present Value of Rents 141,988 99,985 186,417

Human Capital 485,872 366,224 651,173

Total Wealth 496,924 368,242 708,282

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Financial Securities Sample first and second moments of annual asset excess returns (1989-

2003)

CORRELATIONS Government Bonds

Corporate Bonds

Stocks

Government Bonds 1 0.8404 0.0215

Corporate Bonds 1 0.1726

Stocks 1

Government Bonds

Corporate Bonds

Stocks

Expected return % 4.0981 2.2845 4.9011

Standard Deviation % 5.2383 3.2169 28.9950

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Housing returns

NW NE Centre South

Expected excess return % 3.2922 4.1883 3.2791 3.3036 Standard deviation % 5.5774 5.0755 6.5381 5.0715

NW NE Centre South

Government bonds -0.0164 -0.1169 -0.1161 -0.2036 Corporate bonds -0.0843 -0.1691 -0.2177 -0.1998

Stocks -0.5057 -0.2790 -0.4172 -0.1506

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Regressions of housing return on financial returns

Variable North West North East Centre South

Constant 2.6378(0.556)

2.8218(0.591)

2.7910(0.737)

2.8088(0.565)

rGOV. -0.0128(0.280)

0.0392(0.297)

0.1190(0.371)

-0.1461(0.284)

rCORP -0.2757 (0.477)

-0.5013(0.507)

-0.7619(0.632)

-0.3794(0.484)

rSTOCKS -0.0968 (0.028)

-0.0427(0.030)

-0.0844(0.0374)

-0.0232(0.0287)

p-value 0.001 0.030 0.015 0.012

R2 .523 .350 .390 .405

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Efficiency test – diversified portfolios

Whole country NW NE Centre South

N° % N° % N° % N° % N° %

test size = 5%

Inefficient

1623 62.98 636 72.94 405 57.37 34456.49

238 61.03

Efficient

954 37.02 23627.06

301 42.63 26543.51

152 38.97

test size = 10%

Inefficient

1820 70.62 71481.88

44863.46

412 67.65 246 63.08

Efficient

757 29.38 15818.12

25836.54

19732.35

144 36.92

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Distribution of net housing among households with risky financial assets

0.0

1.0

2.0

3.0

4F

ract

ion

-550 -450 -350 -250 -150 -50 50 150 250 350 450 550 PD - thousands of Euros

Net housing wealth position

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Proportions of efficient portfolios

Split the sample in three groups: net housing wealth > 50000; net housing wealth < -50000; net housing wealth in between. Groups have roughly equal size.

Whole country

NW NE Centre South

N° % N° % N° % N° % N° %

Over-housed 67 7.20 30 10.00 16 5.97 13 5.78 8 5.80

Negligible 388 47.67 107 41.80 114 52.78 93 53.14 74 44.31

Under-housed 499 59.98 99 31.33 171 77.03 159 76.08 70 82.35

All 954 37.02 236 27.06 301 42.63 265 43.51 152 38.97

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Proportions of efficient portfolios

• The highest proportion of efficient portfolios obtains among the Under-housed.

• Lowest proportion is found among those with a positive net housing position (likely to trade down in the future).

• Households who are Over-housed should invest more in stocks and bonds than in the standard Markowitz portfolio – apparently this is not what many of them do.

• Inefficiency for Over-housed brings about a loss of 90 basis points for 1% standard deviation. Over a twenty years time horizon, for every percentage point of risk taken, on average this group loses 20% of final wealth by failing to hedge housing.

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Under-housed

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier Risky assets E. F.

Efficient portfolios Inefficient portfolios

Negligible

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier Risky assets E. F.

Efficient portfolios inefficient portfolios

Over-housed

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier Risky assets E. F.

Efficient portfolios inefficient portfolios

Under-housed

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier Risky assets E. F.

Efficient portfolios Inefficient portfolios

Negligible

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier Risky assets E. F.

Efficient portfolios inefficient portfolios

Over-housed

0.50

1.50

2.50

3.50

4.50

5.50

6.50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

standard deviation

exp

ecte

d r

etu

rn

Efficient frontier Risky assets E. F.

Efficient portfolios Inefficient portfolios

NO

RT

H W

ES

T

SO

UT

H

26

Robustness analysis

• Risky human capital – second hedge term• Less than unit correlation between rent

and house prices• International portfolio diversification

27

Risky human capital• Optimal portfolios are the sum of a

Markowitz portfolio and two hedge terms – one for net housing, the other for human capital.

• Where HC0 is the present value of future earnings – discounted at the relevant risk-adjusted rate

TbHC

TbP

TTHCDP

TWVTWV

X

10

100

1

2

20*

28

Risky human capital• The issue is how to find the (semi-annual)

returns on human capital. We use detrended aggregate data on earnings per employee.

• The relevant hedge term is made of the regression coefficients:

• And the corresponding real discount rate is 1.39%.

St

Ct

Gt

HCt rrrr

)01.0(

025.0

)25.0(

450.0

)14.0(

425.0

)29.0(

614.0

29

Risky human capital WHOLE COUNTRY RISKY HUMAN

CAPITALRISK-FREE

HUMAN CAPITAL

  N° % N° %

Over-housed 187 20.06 67 7.20

Negligible 131 16.11 388 47.67

Under-housed 142 16.90 499 59.98

All 460 17.79 954 37.02

Key effect: more inefficient portfolios – with the sole exception of the over-housed

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Owning is less than a perfect hedge against rent risk

• If there is less than unit correlation between rent and house prices, owning is not a perfect hedge against rent risk

• Let be the hedge ratio between house returns and rents (the squared correlation coefficient)

P

31

Owning is less than a perfect hedge against rent risk

• Then the model implies that a fraction of the PV of future rents should be

subtracted from housing wealth.• This is equivalent to considering housing

needs as a fixed proportion of the present value of current and future housing services.

P

32

Owning is less than a perfect hedge against rent risk

0

10

20

30

40

50

60

70

0 0.25 0.5 0.75 1

beta

% e

ffic

ien

t

over-housed negligible under-housed

33

International Portfolio diversification• Direct stock holdings are mostly in

domestic stock, but indirect stock holdings are largely in foreign stocks.

• We take the stock return as a weighted average of domestic stocks (62%) and foreign stocks (38%).

• Efficiency portfolio has .67 (.63) in government bonds, .29 (.35) in corporate bonds, .04 (.02) in stocks.

34

International Portfolio diversification• Stronger relation to housing: stocks have

significant negative coefficients in all four areas

• But efficiency analysis is unaffected  WHOLE COUNTRY INTERNATION

AL RETURNDOMESTIC

RETURN

  N° % N° %

Over-housed 56 6.01 67 7.20

Negligible 372 45.76 388 47.67

Under-housed 525 39.50 499 59.98

All 953 29.19 954 37.02

35

Key conclusions• For most households, net housing wealth is non-zero:

Portfolios should contain a term to hedge the risk induced by future housing needs/liquidation.

• Our key empirical result is that many households do not appear to hedge housing risk in a satisfactory way.

• The largest fraction of efficient financial portfolios is found among households who are “under-housed”, and should have less in stocks than the standard Markowitz portfolio.

• The smallest fraction of efficient portfolios obtains among households who are “over-housed”:

• Even though in this group there is the highest proportion of stock-owners, their investment in stocks is often not sufficient to hedge all the housing risk.