Factor Modelling of UK Unlisted Funds: Panel Data Analysis of Performance Drivers
Kieran FarrellyCBRE Investors & Henley Business School, University of Reading
& George Matysiak
Henley Business School, University of Reading
JUNE 2011
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Table of Contents
Research questions and objectives
Sources of risk and return in unlisted funds
Prior literature
Data
Panel unit root testing
Panel regression analysis
Conclusions and next steps
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Research Questions & Objectives
CAPM (market model) is based on the assumption that there are no additional factors present which are correlated with the market return
Inclusion of other factors has been found to better explain the cross section of asset returns Ross (76): macroeconomic factors – Arbitrage Pricing Theory Fama & French (92), Jegadeesh & Titman (1993), Carhart (97) : fundamental factors – value/growth/momentum
Multifactor models employed extensively in equities for risk management and performance attribution purposes
Generally the property investment industry has been unable to quantify well the key sources of risk in property portfolios
Unlisted property funds have become a significant conduit in the real estate investment landscape
Purpose of this study is to identify which direct property portfolio and unlisted fund ‘structure’ characteristics/factors explain the cross section performance of unlisted property funds
End goal is to develop a multifactor model and subsequent portfolio management tool for understanding portfolio risk of both property funds/ and funds-of-funds
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Sources of Risk and Return in Property Funds
Property FundRisk & Return
Portfolio Structure /
Market RiskStock Risk Fund Structure
Structure (market risk): Allocations to more volatile sectors Macro risks
Stock risk: Asset level (operating) leverage Risk continuum from ground rents to speculative
developments Age, structure
Fund Structure: Financial leverage risk where used Vehicle characteristics: age, structure, fees/costs
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Prior Studies: Multifactor Modelling of Property Market/Portfolio/Fund Returns
Market Risk Macroeconomic factors (APT):
Ling & Naranjano (90,97) – per cap consumption, real govt bond yields, term structure, unexpected inflation Liow (94) – industrial production, unexpected inflation significant predictors of expected risk premia Marcato & Tira (10) – GDP, stock market
Property markets Pai & Geltner (07) location (Tier I & III location performance differential), Fuerst & Matysiak (08 ) - weighted direct market
return, IPF (11) – UK region exposure, property type tracking error/concentration
Stock risk – direct portfolio assets’ characteristics Yield – Fuerst & Marcato (09) high/low yield return differential, Bond & Mitchell (09) equivalent yield, IPF (11) relative
equivalent yield Size – Zieiring & McIntosh (99) – size positively related to risk and return, Pai & Geltner (07) + Fuerst & Marcato (09) -
performance differential between asset sizes, IPF (11) – average lot size, asset concentration Income: Pai & Geltner (07) - performance differential between assets with short/long ease lengths, IPF (11) - void rate,
covenant strength, % income from top 10 tenants Development/Vacancy: IPF (11)
Fund structure Financial leverage: Fuerst & Matysiak (08), Marcato & Tira (10), IPF (11) all found financial leverage to be significant Liquidity: Lee (00) found no evidence, Marcato & Tira (10) found evidence Cash exposure : Marcato & Tira (10) Style: Fuerst & Matysiak (08) – core/value added/opportunisitc styles impacted performance Performance Persistence: Fuerst & Matysiak (08), Marcato & Tira (10), IPF (11)
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Dataset
Unique sample of UK unlisted funds Quarterly returns from 2003:Q4-2010:Q4 Good depth in terms of fund/portfolio characteristics (x
variables) Data runs over what we’d consider to be a full cycle
Sources: CBRE Investors database 2003:Q4 – 2004 Q3 – collated
by HSBC/IPD IPD UK Property Funds Vision data 2004:Q4 to 2010:Q4 Consistently collected data via quarterly questionnaire
Unbalanced panel with sample of funds with sufficient data points growing through time
Commences with data on 28 funds Maximum of 75 funds in any given period
Large proportion of the sample are open-ended funds and would be considered as having a core risk profile
– Both balanced/diversified and sector specialist vehicles
Source: IPD
UK Pooled Property Fund Indices Performance 2003:Q4 = 100
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Sample Statistics
Mean Median
Maximu
m
Minimum Std. Dev Skew Kurtosis
3 Month Excess Returns -3.1% -1.3% 52.5% -61.3% 8.9% -0.86 9.41
Cash % Assets 5.4% 3.0% 45.7% -0.4% 6.4% 1.78 6.44
% Development (%ERV) 1.5% 0.0% 45.3% 0.0% 4.2% 5.23 38.39
Lease Length Conc 17.3% 12.8% 100.0% 0.4% 14.7% 2.44 11.37
Initial Yield 5.8% 5.7% 10.2% 1.6% 1.3% 0.21 3.06
Number of Assets 50.27 35.00 397.00 1.00 58.17 3.33 17.07
LTV 18.7% 8.0% 98.8% -0.3% 22.5% 1.04 2.89
Reversionary Yield 6.6% 6.4% 11.9% 2.6% 1.5% 0.50 3.65
OFFICE Exposure 26.6% 25.6% 100.0% 0% 27.5% 1.29 4.31
IPD PAS Concentration 36.0% 11.6% 100.0% 1.5% 36.9% 0.77 1.99
Rental Reversion 1.19 1.15 2.96 0.89 0.20 4.20 29.38
Void Rate 7.0% 5.9% 37.5% 0.1% 5.1% 1.62 7.42
% Top 10 Tenants 38.3% 36.0% 100.0% 8.8% 16.7% 0.69 3.25
0
100
200
300
400
500
600
700
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
Series: _3MTREXCSample 2003Q1 2010Q4Observations 2053
Mean -0.027756Median -0.011457Maximum 0.618576Minimum -0.865614Std. Dev. 0.087015Skewness -1.068804Kurtosis 14.15131
Jarque-Bera 11028.13Probability 0.000000
0
100
200
300
400
500
600
700
800
900
0.0 0.2 0.4 0.6 0.8 1.0
Series: LTVSample 2003Q1 2010Q4Observations 1880
Mean 0.191935Median 0.072660Maximum 0.988157Minimum -0.002544Std. Dev. 0.234371Skewness 0.966539Kurtosis 2.641104
Jarque-Bera 302.8050Probability 0.000000
0
40
80
120
160
200
240
280
0.02 0.04 0.06 0.08 0.10 0.12 0.14
Series: NIYSample 2003Q1 2010Q4Observations 1704
Mean 0.058339Median 0.057350Maximum 0.137800Minimum 0.015800Std. Dev. 0.012738Skewness 0.340379Kurtosis 3.835869
Jarque-Bera 82.50971Probability 0.000000
Histogram – 3 Month Excess Total Returns
Histogram – Initial Yield
Histogram – Loan to Value Ratio
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Identifying Factors: Panel Approach
First stage of multifactor modelling is the identification of statistically significant factors
We have employed a panel data approach to do this
This approach allows us to identify and test parameters without restrictive assumptions e.g. do investment styles have differential impacts ?
Firstly we used a number of panel unit root tests to assess whether the variables are trend stationary
We then tested for the presence of fixed and/or random effects
Fixed effects: used when we want to control from omitted /unobserved variables whose impact will differ between cases
Random effects: used when we want to control from omitted /unobserved variables whose impact will have the same constant impact but vary randomly between cases. Hausman test used to assess whether random effects are present
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Panel Unit Root Tests Summary
Panel unit root tests are statistically more powerful than individual unit root tests
Panel unit root tests show both yield variables and ‘number of assets’ are I(1)
Otherwise other variables can be deemed I(0)
Method
3 Month Excess
Returns Cash % Assets
Lease Length Conc
Initial Yield
Reversionary Yield
Number of Assets LTV
Office Exposure
IPD PAS Concentration
Reversionary Potential
Void Rate
% Top 10 Tenants
Null: Unit root (assumes common unit root process) Levin, Lin & Chu t* -2.66 -14.09 -2.57 -2.79 -2.20 0.04 -4.18 -3.90 -8.99 -1.59 -2.87 -2.56Prob 0.00 0.00 0.00 0.00 0.00 0.52 0.00 0.00 0.00 0.06 0.00 0.00
Null: Unit root (assumes individual unit root process)
Im, Pesaran and Shin W-stat -2.60 -8.69 -2.28 0.40 0.01 2.22 -3.66 -2.13 -7.57 -1.19 -3.39 -2.97Prob 0.00 0.00 0.01 0.65 0.51 0.99 0.00 0.02 0.00 0.12 0.00 0.00ADF - Fisher Chi-square 203.52 322.31 192.67 123.54 140.66 125.97 203.28 137.14 287.20 178.62 211.96 231.35Prob 0.03 0.00 0.01 0.93 0.61 0.91 0.00 0.00 0.00 0.06 0.00 0.00PP - Fisher Chi-square 232.05 506.31 291.37 88.90 124.49 164.80 198.49 186.35 324.68 212.84 263.59 392.51Prob 0.00 0.00 0.00 1.00 0.90 0.16 0.00 0.00 0.00 0.00 0.00 0.00
Conclusion I(0) I(0) I(0) I(1) I(1) I(1) I(0) I(0) I(0) I(0) I(0) I(0)
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Fixed Effects Regression – 2004:Q1 to 2010:Q4
Dependent Variable: _3MTREXC Coefficient Std. Error t-Statistic Prob. C 0.05 0.03 1.76 0.083MTREXC(-1) 0.71 0.02 35.07 0.00LOAN TO VALUE(-1) 0.21 0.02 8.62 0.00% OFFICE EXPOSURE (-1) -0.13 0.04 -3.49 0.00REVERSIONARY POTENTIAL (-1) -0.08 0.02 -4.30 0.00% TOP 10 TENANTS (-1) 0.06 0.03 1.77 0.08R-squared 0.55 Mean dependent var -0.03Adjusted R-squared 0.53 S.D. dependent var 0.09S.E. of regression 0.06 Akaike info criterion -2.64Sum squared resid 5.68 Schwarz criterion -2.36Log likelihood 2077.72 Hannan-Quinn criter. -2.54F-statistic 22.17 Durbin-Watson stat 1.89Prob(F-statistic) 0.00
Fixed effects regression was found to be the appropriate – model has good explanatory power
Thus there are significant differences between funds and over time periods
Not surprising given there are a range of fund structures and styles
0
5
10
15
20
Cross Section Fixed Effect
Frequency
Distribution of Cross Section Fixed Effects
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Panel GMM Regression
Dependent Variable: _3MTREXC
Panel Fixed Effects
Coefficient Prob. Panel GMM Coefficients 1 Prob.
Panel GMMCoefficients 2 Prob.
C 0.05 0.083MTREXC(-1) 0.71 0.00 0.67 0.0000 0.69 0.0000
LOAN TO VALUE(-1) 0.21 0.00 0.26 0.0005 0.25 0.0002
% OFFICE EXPOSURE (-1) -0.13 0.00 -0.22 0.0177 -0.24 0.0076REVERSIONARY POTENTIAL (-1) -0.08 0.00 -0.10 0.0061 -0.07 0.0273% TOP 10 TENANTS (-1) 0.06 0.08 0.04 0.5550Mean dependent var -0.03 -0.00 -0.00S.D. Dependent var 0.09 0.05 0.05S.E. of regression 0.06 0.08 0.08Sum squared resid 5.68 9.84 10.17
• As there is a lagged dependent variable (momentum) in the preferred specification we have used the Panel GMM estimator
• Coefficients magnitude have changed though signs and significance remain for 4 of the variables - but %top ten tenants variable is no longer significant (but note that Arellano-Bond standard errors can be very unreliable!)
• Second GMM discards this variable and significant variables remain similar
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Provisional Conclusions
Identified the key fundamental factors which best determine the cross section of unlisted property funds over time
Factors found amongst what we consider to be the three key sources of risk-returns in funds
Presence of fixed effects points to differences across funds and over time
Next steps:
Continue to test additional factors
Creation of ‘factor returns’ via cross section regressions
Use these as a basis for estimating a factor covariance matrix which can then be used to create portfolio construction/optimisation tools
Risk budgeting via factors
These will also be used for performance attribution purposes
Estimate asymmetric impacts of factors upon performance