Using Arbitrage Pricing Theory To Analyse UK and USA Property Cycle

Differences

European Real Estate SocietyStockholm, Sweden

June 2009Terry 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

US NCREIF Returns

GDP:UK GDP:US Unanticipated Inflation: UK

Unanticipated Inflation: US

Term Structure: UK

Term Structure: US

Equity Risk Premium: UK

Equity Risk Premium: US

UK IPD Returns 1.000                  US NCREIF Returns

0.269 1.000                GDP:UK 0.515 0.545 1.000              GDP:US 0.323 0.554 0.432 1.000            Unanticipated Inflation: UK

-0.403 -0.173 -0.424 -0.002 1.000          Unanticipated Inflation: US

-0.274 -0.073 -0.296 0.113 0.943 1.000        Term Structure: UK 0.206 0.112 0.291 -0.099 -0.920 -0.872 1.000      Term Structure: US 0.214 0.290 0.508 0.045 -0.893 -0.841 0.815 1.000    Equity Risk Premium: UK

0.291 0.252 0.336 0.243 -0.550 -0.471 0.503 0.495 1.000  Equity Risk Premium: US

0.238 0.236 0.334 0.142 -0.579 -0.507 0.523 0.547 0.395 1.000

-.06

-.04

-.02

.00

.02

.04

.06

1980 1985 1990 1995 2000 2005 2010

UKGDP%

USAGDP%

UK Tre nd

USA Tre nd

Comparison of UK and USA GDP Percentage Change and Trends

9-11

-.12

-.08

-.04

.00

.04

1990 1995 2000 2005

NCREIF

IPD UK

UK, IPD Returns and US NCREIF Returns: Monthly 1988-2009Total

Returns

Years

9-11

Exhibit 3

-.04

-.02

.00

.02

.04

.06

1990 1995 2000 2005 2010

UK GDP Changes and IPD Return

%GDP

IPDLong-termTrend

Exhibit 4

-.12

-.08

-.04

.00

.04

86 88 90 92 94 96 98 00 02 04 06 08 10

US GDP Change and NCREIF Returns

NCREIF

GDP%Long-termTrend

Exhibit 5

9-11

• 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

• URRE UFit )(

Where: FR = 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

R2 = 75.97%

Intercept & Beta

t statistic

(0.070599) + 1.209816 () - 1.221854(U) + 0.188532() + 0.079061() + i

-2.034205 5.205751 -12.13241 1.529515 2.439929 0.021155

APT (US) with Expected Zero Beta

R2 = 75.97%

Intercept & Beta

t statistic

-0.008317 + 1.209816 () - 1.221854(U) + 0.188532() + 0.079061() + i

-2.034205 5.205751 -12.13241 1.529515 2.439929 0.021155

URRE UFit )(

URRE UZit )(

APT (UK) with Expected risk free rate

R2 = 93.28%

Intercept & Beta

t statistic

(0.070599) + 0.347208() - 0.868562(U) + 0.108614() + 0.035194() + i

-1.769832 7.920781 - 17.14555 2.317567 2.576084 0.019971

APT () with Expected Zero Beta

R2 = 93.28%

Intercept & Beta

t statistic

-0.003927 + 0.347208() - 0.868562(U) + 0.108614() + 0.035194() + i

-1.769832 7.920781 -17.14555 2.317567 2.576084 0.019971

iURRE UFit )(

iURRE UZit )(

APT (UK) with Expected risk free rate and US Property Performance

 

R2 = 65.66

Intercept & Beta

t statistic

APT (UK) with Expected Zero Beta reflecting US Property Performance

 

R2 = 65.66

Intercept & Beta

t statistic

0.022861 + -0.199716() - 1.101734(U) + 0.021012() +

0.029849() +0.244874Rit|US

1.897037 -0.652772 -4.355030 0.164764 0.564750

2.099157

iRURRE USitRUUFit | )(

(0.070599) -0.199716() - 1.101734(U) + 0.021012() +

0.029849() +0.244874Rit|US

1.897037 -0.652772 - 4.355030 0.164764 0.564750 2.099157

iRURRE USitRUUZit | )(

UK Returns as a function US MVM factors

iUSAitRUUSAUSAUSAUSA

USAUSAUUSAUSAFUKit

R

URRE

||||

|||| )(

iUSAitRUUSAUSA

USAUSAUSAUSAUUSAUSAZUKit

R

URRE

|||

||||| )(

APT (UK) with Expected risk free rate and US Property Performance R2 = 60.29

Intercept & Beta

t statistic

(0.070599) -0.151844(|US) -0.333261(U|US)+0.454337(|US)+0.065742(|US) + 0.191620Rit|US

-3.129379 -0.357658 -2.086653 1.122048 1.217944 1.309247

APT (UK) with Expected Zero Beta reflecting US Property Performance R2 = 60.29

Intercept & Beta

t statistic

-0.023468 -0.151844(|US) -0.333261(U|US) +0.454337(|US) +0.065742() + 0.191620Rit|US

-3.129379 -0.357658 -2.086653 1.122048 1.217944 1.309247

iUSAitRUUSAUSAUSAUSAUSAUSAUUSAUSAFUKit RURRE |||||||| )(

iUSAitRUUSAUSAUSAUSAUSAUSAUUSAUSAZUKit RURRE |||||||| )(

URRE UFit )( + knotE(Rit|)

Recessionary Spline

KnotE(Rit|)

coefficient

t-Statistic R2 -value

UK        

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

US        

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

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