1
Valuation of Properties and Economic
Models of Real Estate Markets
Rainer Schulz
CASE – Center for Applied Statistics and Economics
Institut für Statistik und Ökonometrie
SFB 373
Humboldt-Universität zu Berlin
Real Estate Valuation
Introduction and motivation
Introduction and motivation
Real estate valuation is important at the micro level for
• investment decisions like buying or selling a property,
• lending decisions where a property serves as collateral.
Real estate valuation is also important at the macro level for
• measurement of real estate price trends via appraisal based indices
like the NCREIF or the DIX,
• measurement of real estate wealth.
Real Estate Valuation
1-1
Introduction and motivation
What is property valuation?
Valuation is the process of estimating the market value of a property.
Valuation consists of physical and legal identification of property
(rights), gathering and analyzing of market data, and applying the
convenient valuation approach.
Major valuation approaches:
– sales comparison approach
– cost approach
– income approach
Real Estate Valuation
1-2
Introduction and motivation
1-3
A valuation approach is based on an economic market model and may
have different techniques to calculate indicated values.
Indicated value = VA(xn,t , Ωt )
(1)
xn,t vector with characteristics of the property
Ωt set with market information
Adjustment for general market conditions gives
a
Vn,t
= Mt VA(xn,t , Ωt )
a
Vn,t
ascertained market value
Mt general market conditions
Real Estate Valuation
(2)
Introduction and motivation
Focus: income valuation in Germany
codified valuation technique, specified in Regulation on Valuation
(WertV) and Guidelines on Valuation (WertR 91),
enhancing the economic understanding of the valuation approach,
assessment of the appraisals compared with transaction prices,
influence of characteristics and market indicators,
results are of interest for the discussion on valuation approaches, see
RICS (2002); IVSC (2002); Dotzour (1988); Chinloy, Cho, and
Megbolugbe (1997); Graff and Young (1999); Crosby (2000)
Real Estate Valuation
1-4
Income approach according to WertV
2-1
Economic rationale of the income approach
No investor will pay more for an existing property than he will retrieve by
holding the property.
Market value is the present value (Cochrane, 2001)


∞
X
Dn,t+j

Vn,t = Et 
Qj
i=1 (1 + Rt+i )
j=1
def
Et [·] = E[·|xn,t , Ωt ]
Dn,t+j net operating rent
Rt+i required returns from comparable investments
Real Estate Valuation
(3)
Income approach according to WertV
2-2
WertV valuation technique
Income value (Ertragswert) according to §§ 15, 16 WertV is
En,t
τn,t τn,t
1
1
1
=
1−
Dn,t +
Ln,t
θt
1 + θt
1 + θt
τn,t remaining time of usage
θt discount rate (Liegenschaftszins)
Dn,t net operating rent
Ln,t approximate value of the lot
Real Estate Valuation
(4)
Income approach according to WertV
2-3
Adjustment of En,t gives
a
Vn,t
= Mt En,t
(5)
General market conditions Mt reflect the current situation on the real
estate market, the capital market and the regional situation.
§ 3 Abs. 3 WertV and 1.5.3 WertR 91 imply that
E[Mt ] = 1 .
Real Estate Valuation
(6)
Income approach according to WertV
2-4
Statistical model
Transaction price is market value influenced by proportional unusual
circumstances
Pn,t = Vn,t Un,t
with Et [Un,t ] = 1. With
Vn,t = Mt En,t
def
Qn,t =
Pn,t
En,t
one obtains
Qn,t = Mt Un,t .
Real Estate Valuation
(7)
Income approach according to WertV
2-5
Implications from the statistical model
1. long-run: expected deviations between Pn,t and En,t disappear
E[Qn,t ] = 1 ,
i.e. income valuation according to WertV is unbiased.
2. short-run: expected deviations between Pn,t and En,t are
Et [Qn,t ] = Mt ,
i.e. all property specific information has to be incorporated in En,t .
Real Estate Valuation
Empirical investigation
Empirical investigation
Data are provided by the Gutachterausschuss für Grundstückswerte in
Berlin
• transaction prices and property characteristics of apartment houses
in Berlin between 1980:1 and 2000:5, 4150 observations
• indicated values are income values (Ertragswerte) calculated
according to WertV for internal purposes
Data are stored in the non-public sector of MD*Base, www.mdtech.de.
Real Estate Valuation
3-1
Empirical investigation
3-2
Table 1: Summary statistics for transacted apartment houses in Berlin,
Germany between 1980:1 to 2000:5.
Mean
Median
Std. Dev.
Min
Max
Units
982.2
767.0
1920.8
186.0
56332.0
Square metres
2168.9
1867.5
2637.2
128.0
89614.0
Square metres
Age
73.9
81
29.2
0
186
Years
Price
721.2
496.0
1120.9
53.7
40900.0
Thsd. EUR
Income value
662.2
455.6
1451.8
48.1
72800.0
Thsd. EUR
Gross rent
54.8
43.3
90.0
6.2
4260.5
Thsd. EUR
Net rent
61.9
33.6
131.0
3.6
1610.7
Thsd. EUR
Lot size
Floor space
Note: 3835 observations have information on the gross rent and 315 on the net rent.
Real Estate Valuation
Empirical investigation
25.00
22.50
3-3
finely dashed: all objects built before 1949
dashed: all objects built after 1948
solid: all objects
20.00
17.50
15.00
12.50
10.00
1980
1985
1990
1995
2000
Figure 1: Average yearly price-rent ratios from 1980 to 2000. Calculated with all 3835 observations with information on gross rents.
REVincome1.xpl
Real Estate Valuation
Empirical investigation
3-4
Table 2: Summary statistics for ratios of prices and income values.
Panel A: Ratios of Price to Income Value
Mean
Standard deviation
Minimum
Median
Maximum
1.133
0.392
0.247
1.058
4.941
10% Quantile
90% Quantile
Skewness
Kurtosis
Number of obs.
0.773
1.577
2.726
19.178
4150
Panel B: Ratios of Income Value to Price
Mean
Standard deviation
Minimum
Median
Maximum
0.968
0.294
0.202
0.945
4.044
10% Quantile
90% Quantile
Skewness
Kurtosis
Observations
0.634
1.294
1.562
12.147
4150
REVincome2.xpl
Real Estate Valuation
Empirical investigation
Result I
Income values according to WertV are biased predictors for prices in the
long run
– reject hypothesis E[Q] = 1 with
√
N (Q − 1)
= 21.8
sQ
– reject hypothesis E[1/Q] = 1 with
√
N (1/Q − 1)
= −7.06 .
s1/Q
Income values understate transaction prices on average.
Real Estate Valuation
3-5
Empirical investigation
Recall income value according to WertV is
τn,t τn,t
1
1
1
Dn,t +
Ln,t
En,t =
1−
θt
1 + θt
1 + θt
(Complementary) explanations for understatement of prices:
– discount rates θt are too large on average
– assessed net operating rents Dn,t are too low on average
– approximate lot values Ln,t are too low on average
– remaining times of usage τn,t are too low on average
Real Estate Valuation
3-6
Empirical investigation
3-7
Table 3: Linear regression for q on object-specific characteristics.
Coefficient
t-Statistic
P-Value
0.034
2.89
0.004
Log lot size
-0.027
-2.01
0.045
Age
-0.001
-4.89
0.000
Log real gross rent
Diagnostics
R2
0.218
R̄2
0.166
F-Statistic
4.197
0.000
Observations
3835
P-Value(F-Stat.)
cε2
σ
0.069
Notes: Coefficients for overall constant and time dummies are not reported. Gross
rents are deflated with StaLa consumer price index for households comprising four
persons with average income in Berlin West, base year is 1995.
REVincome3.xpl
Real Estate Valuation
Empirical investigation
3-8
Capitalization technique
Multiple technique (Maklermethode) simply capitalizes current gross
g
rent Dn,t
(Gottschalk, 1999)
a
Vn,t
g
Dn,t
= g
θ
(8)
θg is derived from comparable sales.
We calculate θg ’s for all 3835 properties with information on gross rents,
so that
– average ratio of price to capitalized income value is one, θP M
– average ratio of capitalized income value to price is one, θM P
Real Estate Valuation
Empirical investigation
3-9
Table 4: Comparison of income valuations according to WertV and
multiple technique.
Panel A:
Variance
Bias
MSPE
WertV price to income value
0.129
0.135
0.147
θP M price to income value
0.167
0
0.167
WertV income value to price
0.079
-0.042
0.080
θM P income value to price
0.126
0
0.126
MAPE
Percentage within 15%
WertV price to income value
25.72%
44.64%
θP M price to income value
29.56%
31.94%
WertV income value to price
21.17%
45.35%
θM P income value to price
27.80%
32.46%
Panel B:
REVincome4.xpl
Real Estate Valuation
Empirical investigation
Recognize that the “economic loss associated with a forecast may be
poorly assessed by the usual statistical metrics” (Diebold and Mariano,
1995)
Example: unbiased valuation approach that exhibit large positive outliers
might be inferior for lending purposes compared with a biased, but
“conservative” valuation approach (Shiller and Weiss, 1999).
Investors are interested in valuation approach that minimizes their loss
function.
Real Estate Valuation
3 - 10
Empirical investigation
3 - 11
1.75
ratios of price to income value, multiple technique
ratios of price to income value, WertV
1.50
1.25
1.00
0.75
0.50
0.25
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
Figure 2: Nonparametric density estimates for ratios of price to income
value. Uniform confidence bands are at the 95% level (Müller, 2000).
REVincome5.xpl
Real Estate Valuation
Empirical investigation
3 - 12
1.75
ratios of income value to price, multiple technique
ratios of income value to price, WertV
1.50
1.25
1.00
0.75
0.50
0.25
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Figure 3: Nonparametric density estimates for ratios of income value
to price. Uniform confidence bands are at the 95% level.
REVincome6.xpl
Real Estate Valuation
Empirical investigation
Result II
Multiple technique is a simpler technique than income valuation
according to WertV.
Regarding MSPE and MAPE, outcomes from multiple technique are
inferior compared with the outcomes from the WertV technique.
Density estimates reveal that investors and lenders may generally prefer
income valuations according to WertV if
– “conservative” valuation is associated with smaller loss
– loss increases with size of absolute prediction errors
Real Estate Valuation
3 - 13
Empirical investigation
General market conditions
Valuation according to WertV is a two step procedure.
Second step is adjustment of En,t with market conditions Mt .
Mt is influenced by (§ 3 WertV, GAA reports)
– five-year mortgage rates
– interest rates for credits
– building permissions
– inflation
– market volume
Real Estate Valuation
3 - 14
Empirical investigation
3 - 15
Rationale for Mt
Ascertained market value is
a
Vn,t
= Mt En,t
and market value is
Vn,t


∞
X
Dn,t+j
 .
= Et 
Qj
i=1 (1 + Rt+i )
j=1
Income value is calculated with constant discount factor.
Thus, Mt may account for time-varying discount rates.
Real Estate Valuation
Empirical investigation
3 - 16
Approximation of the market value (Campbell, Lo, and MacKinlay, 1997;
Cochrane, 2001)
log Vn,t ≈
∞
X
ρj {k + (1 − ρ)Et [dn,t+1+j ] − Et [rt+1+j ]} ,
j=0
where
def
dn,t = ln Dn,t
def
rt+j = ln (1 + Rt+j )
k and ρ are approximation constants
0<ρ<1
Real Estate Valuation
(9)
Empirical investigation
3 - 17
En,t is market value ascertained with constant discount factor r.
Thus
qn,t = κ −
∞
X
ρj Et [rt+1+j − r] + εn,t
(10)
j=0
and
def
mt = κ −
∞
X
ρj Et [rt+1+j − r]
(11)
j=0
gives
qn,t = mt + εn,t .
mt accounts for time-varying discount rates.
Real Estate Valuation
(12)
Empirical investigation
3 - 18
Expected return deviations will be influenced by market indicators
Φ(L)mt = κ̃ + s>
t γ + ξt
(13a)
qn,t = mt + εn,t .
(13b)
and
Φ(L) = 1 − φ1 L − φ2 L2 − . . . − φp Lp and Lj xt = xt−j
st is a vector that collects the market indicators
γ are coefficients of the indicators
The above system represents a state space model (SSM).
Real Estate Valuation
Empirical investigation
3 - 19
Table 5: Estimated SSM for the general market conditions for 1982:6
to 2000:5.
Coefficient
t-Statistic
P-Value
0.925
32.26
0.000
θ̂
[
ln
σξ
-0.689
-6.07
0.000
-2.892
-20.56
0.000
[
ln
σε
-1.265
-104.87
0.000
Spread5
-3.953
-2.90
0.004
5.759
1.68
0.092
-0.027
-1.55
0.121
0.015
2.52
0.012
-0.986
-0.94
0.349
φ̂
Real interest
Building permissions
Log number of transactions
Rent index
continued on the next slide
Real Estate Valuation
Empirical investigation
3 - 20
Table 5: continued
Coefficient
t-Statistic
P-Value
0.168
2.44
0.015
Log lot size
-0.015
-1.66
0.097
Age
-0.001
-2.67
0.008
ˆ
κ̃
Diagnostics
Log likelihood
Observations
Real Estate Valuation
2720.192
3629
cε2
σ
cq2
σ
0.080
0.096
Empirical investigation
3 - 21
0.50
0.25
0.00
-0.25
-0.50
1985:1
1990:1
1995:1
2000:1
Figure 4: Smoothed general market conditions 1982:6-2000:5. Confidence bands are at the 95% level.
REVincome7.xpl
Real Estate Valuation
Conclusion
Conclusion
Present value is economic rationale of income valuation according to
WertV.
Two step valuation technique with constant discount rate, second step
adjusts for short-run variations of the discount rate.
Outcomes are biased, but better than outcomes from the simpler
multiple technique according to MAPE and MSPE.
Ranking of valuation techniques depends on whole distribution of
outcomes and loss function of investors.
Real Estate Valuation
4-1
Conclusion
General market conditions account for about 17% in systematic variation
of valuation ratios.
Explanatory factors for general market conditions are sensible and should
be included systematically into the valuation process.
Tax treatment of real estate investments is neglected in the economic
model and the valuation process.
Real Estate Valuation
4-2
References
References
Campbell, J. Y., A. W. Lo, and A. C. MacKinlay (1997): The
Econometrics of Financial Markets. Princeton University Press,
Princeton, New Jersey.
Chinloy, P., M. Cho, and I. F. Megbolugbe (1997):
“Appraisals, Transaction Incentives, and Smoothing,” Journal of Real
Estate Finance and Economics, 14:1–2, 89–111.
Cochrane, J. H. (2001): Asset Pricing. Princeton University Press,
Princeton, New Jersey.
Crosby, N. (2000): “Valuation Accuracy, Variation and Bias in the
Context of Standards and Expectations,” Journal of Property
Investment & Finance, 18, 130–161.
Real Estate Valuation
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References
Diebold, F. X., and R. S. Mariano (1995): “Comparing Predictive
Accuracy,” Journal of Business & Economic Statistics, 13, 253–263.
Dotzour, M. G. (1988): “Quantifying Estimation Bias in Residential
Appraisal,” Journal of Real Estate Research, 3(3), 1–11.
Gottschalk, G.-J. (1999): Immobilienwertermittlung. C.H. Beck,
München.
Graff, R. A., and M. S. Young (1999): “The Magnitude of
Random Appraisal Error in Commercial Real Estate Valuation,”
Journal of Real Estate Research, 17(1-2), 33–54.
IVSC (2002): “Exposure Draft of Proposed International Valuation
Application—Mass Appraisal of Real Property,” International
Valuation Standards Committee (IVSC), London, www.ivsc.org.
Real Estate Valuation
5-2
References
Müller, M. (2000): “Smoothing Methods,” in XploRe Learning
Guide, ed. by W. Härdle, S. Klinke, and M. Müller, pp. 169–204.
Springer-Verlag, Berlin.
RICS (2002): “Property Valuation: The Carsberg Report,” Royal
Institution of Chartered Surveyors, www.rics.org.uk.
Shiller, R. J., and A. N. Weiss (1999): “Evaluating Real Estate
Valuation Systems,” Journal of Real Estate Finance and Economics,
18:2, 147–161.
Real Estate Valuation
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