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Using Arbitrage Pricing Theory To
Analyse UK and USA Property Cycle
Differences
European Real Estate Society
Stockholm, Sweden
June 2009
Terry V. Grissom Ph.D.*
Jasmine L.C. Lim Ph.D.*
James L. DeLisle Ph.D.**
*School of the Built Environment University of Ulster,
Jordanstown
**College of Built Environments University of
Washington, Seattle
• Investor concerns seeking potential timing
market turnaround
• An Expectation is that an upturn in USA
property/investment market will proceed an
upturn in the UK: correlation analysis supports
this position
• However analysis of historic property and
economic cycles differences suggests alternative
scenarios
• Expectation is not supported by lead-lag
analysis
Exhibit 2: Correlation of Property Returns in the UK and US and Systematic Factors
UK
IPD
UK IPD Returns
US
GDP:UK GDP:US Unantici
NCREIF
pated
Returns
Inflation:
UK
Unantici
pated
Inflation:
US
Term Term
Struct Structu
ure:
re: US
UK
Equity
Risk
Premiu
m: UK
Equity
Risk
Premiu
m: US
1.000
US NCREIF Returns
GDP:UK
GDP:US
0.269
1.000
0.515
0.545
1.000
0.323
0.554
0.432
1.000
-0.403
-0.173
-0.424
-0.002
1.000
-0.274
-0.073
-0.296
0.113
0.943
1.000
0.206
0.112
0.291
-0.099
-0.920
-0.872
1.000
0.290
0.508
0.045
-0.893
-0.841
0.815
1.000
0.291
0.252
0.336
0.243
-0.550
-0.471
0.503
0.495
1.000
0.238
0.236
0.334
0.142
-0.579
-0.507
0.523
0.547
0.395
Unanticipated
Inflation: UK
Unanticipated
Inflation: US
Term Structure: UK
Term Structure: US
0.214
Equity Risk Premium:
UK
Equity Risk Premium:
US
1.000
.06
Comparis on of UK and US A GDP Percentage Change and Trends
UKGDP%
.04
UK Tre nd
.02
USAGDP%
.00
USA Tre nd
9-11
-.02
-.04
-.06
1980
1985
1990
1995
2000
2005
2010
Total
Returns
.04
Exhibit 3
UK, IPD Returns and US NCREIF Returns:
Monthly 1988-2009
NCREIF
.00
IPD UK
-.04
9-11
-.08
-.12
1990
1995
2000
2005
Years
.06
Exhibit 4
UK GDP Changes and IPD Return
%GDP
.04
.02
Long-term
Trend
IPD
.00
-.02
-.04
1990
1995
2000
2005
2010
Exhibit 5
US GDP Change and NCREIF Returns
.04
.00
NCREIF
GDP%
Long-term
Trend
-.04
9-11
-.08
-.12
86
88
90
92
94
96
98
00
02
04
06
08
10
• The differences in pricing/performance of cross
markets in time suggest the arbitrage potential that
may not support an equilibrium clearance of
differences.
• This suggest a limited integration and possible
segmentation of the two property/equity markets
associated with divergent regimes due to differences
in economic fluctuations.
• This suggests the use of an APT macroeconomic
variable model to address differences in the cyclical
patterns observed.
• The DCF construct of the APT model suggest pricing
differences associated with behavioural differences
observed in the two markets.
• One test of a behavioural pricing differences is
noted by Hendershott and MacGreger (2005)
• They note that investment behaviour difference
between UK and USA property markets based on
mean/trend reversion behaviour. Where:
– UK is rational reflecting trend reversion pricing
– USA is non-rational with no trend reversion
pricing noted
• The implication that differences in investor
behaviour may contribute to pricing and timing
differences defining the two markets fits the
construct of the MVM Arbitrage Price Models
• This achieved using a spline analytic for cycle
regime delineation as employed by Grissom &
DeLisle (1999). This variable assist in identifying
the potential timing and turnarounds observed and
expected for both the UK and USA property
markets.
• The theoretical constructs and the procedural steps
employed in this analysis is illustrated in the
following set of equations
E• ( Rit )  RF      UU         
Where:
R F = risk free rate (LIBOR)
  = percentage change in GDP
U


= unanticipated inflation
= term structure of interest rate
= equity asset risk premium
APT (US) with
Expected risk
free rate
E ( Rit )  RF       U U          
R2 = 75.97%
Intercept & Beta
(0.070599)
+
1.209816 () - 1.221854(U) + 0.188532() +
0.079061() + i
t statistic
-2.034205
2.439929
APT (US) with
Expected Zero
Beta
5.205751
0.021155
-12.13241
1.529515
E ( Rit )  RZ       U U          
R2 = 75.97%
Intercept & Beta
-0.008317 + 1.209816 () - 1.221854(U) + 0.188532() +
0.079061()
+ i
t statistic
-2.034205
2.439929
5.205751
0.021155
-12.13241
1.529515
APT (UK) with
Expected risk
free rate
E ( Rit )  RZ     UU        i
R2 = 93.28%
Intercept & Beta (0.070599) + 0.347208()
0.035194() + i
- 0.868562(U)
t statistic
- 17.14555
APT () with
Expected Zero
Beta
-1.769832
2.576084
7.920781
0.019971
+ 0.108614() +
E ( Rit )  RF     UU        i
R2 = 93.28%
Intercept & Beta -0.003927 + 0.347208() - 0.868562(U) +
0.035194() + i
t statistic
2.317567
-1.769832
2.576084
7.920781
0.019971
-17.14555
0.108614() +
2.317567
APT (UK)
with Expected
risk free rate
and US
Property
Performance
E ( Rit )  RF     UU        RURit | US  i
R2 = 65.66
Intercept &
Beta
(0.070599) -0.199716() - 1.101734(U) + 0.021012() +
0.029849() +0.244874Rit|US
t statistic
1.897037
0.564750
APT (UK)
with Expected
Zero Beta
reflecting US
Property
Performance
-0.652772
2.099157
- 4.355030
0.164764
E ( Rit )  RZ     UU        RURit | US  i
R2 = 65.66
Intercept &
Beta
0.022861 + -0.199716() - 1.101734(U) + 0.021012() +
0.029849() +0.244874Rit|US
t statistic
1.897037
0.564750
-0.652772
2.099157
-4.355030
0.164764
UK Returns as a function US MVM
factors
E ( Rit|UK )  RF   |USA |USA  U |USAUUSA
  |USAUSA   |USA |USA   RU Rit|USA   i
E ( Rit|UK )  RZ   |USA |USA  U |USAUUSA   |USAUSA
  |USA |USA   RU Rit|USA   i
APT (UK) with
Expected risk
E ( Rit|UK )  RF   |USA |USA  U |USAUUSA   |USAUSA   |USA |USA   RU Rit|USA   i
free rate and US
Property
Performance
R2 = 60.29
Intercept &
Beta
(0.070599) -0.151844(|US) -0.333261(U|US)+0.454337(|US)+0.065742(|US)
+ 0.191620Rit|US
t statistic
-3.129379
1.217944
-0.357658
1.309247
-2.086653
1.122048
APT (UK) with
Expected Zero E ( Rit|UK )  RZ   |USA |USA  U |USAU USA   |USAUSA   |USA |USA   RU Rit|USA   i
Beta reflecting
US Property
Performance
R2 = 60.29
Intercept &
Beta
-0.023468 -0.151844(|US) -0.333261(U|US) +0.454337(|US)
+0.065742() + 0.191620Rit|US
t statistic
-3.129379
1.217944
-0.357658
1.309247
-2.086653
1.122048
E ( Rit )  RF      UU          + knotE(Rit|)
Recessionary
Spline
UK
KnotE(Rit|)
t-Statistic
R2
-value
coefficient
1988-91
2.0958
5.5915
97.95
0.0000
1994-95
-19.1563
-1.6583
88.91
0.1358
1998-99
2.3055
1.1847
40.31
0.2738
2001-02
0.9952
31.8677
98.70
0.0000
2007-09
3.7072
1.2936
51.83
0.9465
1990-91
1.4878
5.6030
86.07
0.0000
2001-02
3.6434
6.0746
80.45
0.0000
2007-09
0.3499
1.1229
75.62
0.2818
US
Conclusions
• The UK Property investment market is at best is only
moderately integrated with the US property and capital
markets suggesting the potential for similar pricing
activities.
• However cycle investigation shows a difference in lead
lag associations across markets.
• This suggest the possibility of arbitrage across markets
and time.
• The application of the APT model shows that an
integration of the US property returns and general
economic factors however reduce the explanatory
effect of MVM factors.
Conclusions
•This suggested a difference in pricing behaviour
across the 2 markets.
•One previously hypothesized reason is that the two
markets reflect pricing differentials as a function of
mean/trend reversion behaviour, suggesting that the
UK more rationally prices general economic variables,
while the US shows a decoupling of financial and real
economic variables in the estimation of property
returns