Electronic copy available at: http://ssrn.com/abstract=1691924

Journal of Real Estate Portfolio Management 17

Dynamic Correlation: A Tool for HedgingHouse Price Risk?

Executive Summary. Dynamic correlation modelsdemonstrate that the relationship between interest ratesand housing prices is non-constant. Estimates reveal sta-tistically significant time fluctuations in correlations be-tween housing price indexes and Treasury bonds, theS&P 500 Index, and stock prices of mortgage-relatedcompanies. In some cases, hedging effectiveness can beimproved by moving from constant to dynamic hedge ra-tios. Empirics reported here point to the possibility thatincorrect assumptions of constant correlation could leadto mis-pricing in the mortgage industry and beyond.

*University of Texas–Dallas, Richardson, TX 75083 andMax Planck Institute for Human Development, Berlin ornberg@utdallas.edu.

**State University of New York, Geneseo, NY 14454 oragu@geneseo.edu.

***University of Texas–San Antonio, San Antonio, TX 78249-0633 or don.lien@utsa.edu.

by Nathan Berg*Anthony Y. Gu**Donald Lien***

This study estimates bivariate dynamic correlationmodels for housing price indexes and financialmarket time series. The latter include Treasurybond rates, the S&P 500, and individual commonstocks sensitive to defaults on residential homemortgages. The primary motivation for analyzingthese correlations is twofold: first, to provide aquantitative description of time patterns in the lin-ear relationships between housing market varia-bles and financial markets; and, second, to look forpotential cross-hedging instruments against hous-ing price volatility in different regions of theUnited States. No attempt is made to estimate astructural model. Rather, the goal is to see whethercorrelations used in previous studies of hedging inhousing markets are statistically constant with re-spect to time and, if not, whether dynamic corre-lations can be predicted (in a forecasting ratherthan structural sense) using highly liquid securi-ties that are easily used as hedging instrumentsand thought to be structurally linked to homeprices.

The consequences of homeowners’ lack of access toinsurance against declines in home values and thebroader economic impact of sharp movements inmortgage default rates have been described byCase, Shiller, and Weiss (1996). This paper relaxestheir assumption that correlations between homevalues and other assets are constant with respectto time, a maintained assumption in nearly all theliterature in this area. There would likely be shiftsin policy for mortgage industry decision makers,whose job it is to price risk, if real and financial

Electronic copy available at: http://ssrn.com/abstract=1691924

Nathan Berg, Anthony Y. Gu, and Donald Lien

18 Vol. 13, No. 1, 2007

asset markets were found to have systematicallytime-varying correlation. Difficult-to-forecast dy-namic correlation may also help explain whyfinancial-market innovators have so far providedfew practical hedging instruments for averagehomeowners.

The major stakeholders in developing new hedginginstruments include homeowners, builders, mort-gage holders, insurers, and mortgage-backed se-curities companies. Although major home financefirms such as FNMA and FHLMC have ‘‘risk shar-ing’’ operations, these transactions are all over-the-counter, creating significant transaction costs andilliquidity. Case, Shiller, and Weiss (1996) havesuggested the establishment of futures or optionsmarkets for residential real estate prices, but liq-uid markets for options based on region-specific in-dexes seem unlikely to emerge in the foreseeablefuture.1

There is a possibility, however, that existing fu-tures and options markets for the S&P 500 andU.S. Treasury Bonds might provide a partial so-lution because of their correlations with homeprices. With the aid of dynamical correlation mod-els, one hopes to discover cross-hedging strategiesthat could be built using relatively liquid instru-ments, such as the S&P 500 and T-bond futuresand options, based on their predicted time pathsand the relevant correlations. In this paper, thesefrequently studied hedging instruments are aug-mented by the inclusion of publicly traded real es-tate investment trusts (REITs) and the commonstocks of firms in the homebuilding and mortgageinsurance industries.

A small but growing collection of empirical studieson the relation between housing prices and thestock market indexes has emerged in recent dec-ades. Research examining the relation between se-curitized real estate indexes (REITs) and the stockmarket has produced conflicting views. Okunevand Wilson (1997) report that securitized REITsand stock markets are segmented when examinedusing conventional cointegration tests, and arefractionally integrated when examined with anonlinear model. Wilson, Okunev, and Du Plessis(1998) report that property and stock markets are

not cointegrated in Australia but are somewhatcointegrated in South Africa. Gyourko and Keim(1992) and Eichholtz and Hartzell (1996) reportthat lagged values of real estate stock portfolio re-turns help predict the returns of appraisal-basedreal estate indexes. Takala and Pekka (1991) sug-gest that using lagged changes in the stock indexcan improve house price prediction in Finland. Us-ing repeat-sales price indexes, Goetzmann (1993)finds negative correlation between housing andbond returns, and small negative correlations withthe S&P 500.

Several recent studies investigate the correlationbetween different financial markets using dy-namical correlation models. For example, usingGARCH models, Christofi and Pericli (1999), Engle(2000), and Tse (2000) demonstrate time-varyingcorrelations between stock markets. Tse reportsconstant correlation for spot futures and foreignexchange data. Ball and Torous (2000) use anintegration-based filtering method to uncover dy-namic correlations between stock markets. Berg(2003) investigates changes in correlation struc-ture within a single city’s housing market.

This paper tests dynamic conditional correlation(DCC) models against the null hypothesis of con-stant correlation. The second step of this empiricalinvestigation is to forecast estimated DCCs usinga basket of housing-related equities and financialmarket indexes. Forecastability is a pre-conditionfor DCCs to have any utility in illuminating rela-tionships needed for hedging housing risk. Thepredictors include volatility measures, seasonality,and macroeconomic variables. Nonstructural fore-casting models reported here are intended toprovide evidence concerning whether the pre-condition of DCCs’ forecastability holds sufficientlywell to think that further work with DCCs mightprovide practical hedging tools. To pursue the is-sue, measures of hedging effectiveness are com-pared for dynamic hedging portfolios, whose hedgeratios change each period based on a covariance/variance ratio from the period before, versus statichedging strategies, whose hedge ratio is estimatedby linear regression as is standard in the hedg-ing literature. Ultimately, methodological improve-ments in risk management for the housing and

Dynamic Correlation: A Tool for Hedging House Price Risk?

Journal of Real Estate Portfolio Management 19

home-finance industry are intended to help im-prove housing market and financial market effi-ciency together with the economic well-being of in-dividual homeowners.

Data and Method

The Data

The house price data is published by Fannie Mae(Federal National Mortgage Association) and Fred-die Mac (Federal Home Loan Mortgage Corpora-tion). The data includes quarterly housing price in-dexes for 163 metropolitan areas, the 50 statesplus the District of Columbia, the nine Census Di-visions, and the United States as a whole from thefirst quarter of 1975 to the last quarter of 2001.Owing to space considerations, only results thatincorporate regional indexes from the five mostpopulous states are reported. The indexes are builtas repeat-sales weighted averages. Details aboutthe building of the indexes have been described byWang and Zorn (1997). The repeat-sales method isbased on the approach of Bailey, Muth, and Nourse(1963). Successful applications and modificationsof the method are provided by Case and Shiller(1987), Shiller (1991), and Wang and Zorn (1999).The method takes differences in prices of the samehouse at different times of sale. Once constructedfrom the Fannie Mae and Freddie Mac data, theindex represents the largest and best data availa-ble for this study. The data are immune to thewell-known problem of seasonal bias that afflictsappraisal-based house price indexes. The returnsof composite REITs, equity REITs, mortgageREITs, and hybrid REITs are from the NationalAssociation of Real Estate Investment Trusts(NAREIT). One finds methodological details for thecalculation of these indexes at the NAREIT web-site: www.nareit.com. House-related firms includeCentex Corporation (CTX, NYSE), Heady Lennar(LEN, NYSE), Fannie Mae (FNM, NYSE), FreddieMac (FRE, NYSE), NVR, Inc. (NVR, AMEX), andPulte Homes, Inc. (PHM, NYSE). Data for U.S.Treasury bond rates, GDP growth, and employ-ment growth are from ‘‘International FinancialStatistics’’ published by the International Mone-tary Fund.

Methods

Constant Correlation. In order to determine the op-timal hedging portfolio within a standard mean-variance framework, a hedger needs to know thecorrelation between returns on potential instru-ments and returns on home values, along with theexpected return for instruments and home values.Under the assumption that instrument and homeprice correlations are constant with respect totime, they can be estimated from the followingequation:

R � � � �R � � , (1)H,t I,t�j t

where RH,t represents the period-t return on ahouse price index, RI,t�j represents returns on apotential instrument at time t � j, j � �1, 0, 1,and t is a zero-mean error term. Constant correla-tion is estimated by the expression �(var(RH t) /var(RI))5. Return is calculated as differenced nat-ural logarithms of consecutive quarters’ index val-ues. Defining P as the value of an individual’shouse or portfolio of housing, and A as the currentvalue of the assets underlying a single futures con-tract, the number of contracts (shares) to long orshort can be expressed as �*(P /A).

Whether homeowners take long or short positionsdepends on the direction of the correlation. For ex-ample, suppose the expected (constant) correlationbetween house price returns and the S&P 500returns is �1.0. Also suppose a home is worth$300,000 and the value of the S&P 500 Index is1,000. Then the homeowner can obtain insuranceagainst fluctuations in the value of the home overthree- and six-month time horizons by buyingthree call option contracts (100 futures per con-tract) with a strike price of 1,000. If the expectedcorrelation is 0.333, only one contract should bebought.

Dynamic Correlation. The constant correlation ap-proach assumes that the variance-covariance ma-trix is constant. For the dynamic correlation ap-proach, the dynamic conditional correlation (DCC)model proposed by Engle (2000) is applied. TheDCC model is a multivariate GARCH estimatorwith the following specification:

Nathan Berg, Anthony Y. Gu, and Donald Lien

20 Vol. 13, No. 1, 2007

E (r r�) � H � D R D , (2)t�1 t t t t t t

where rt is an nx1 vector of mean zero residualsobtained from the AR models and Dt is a diagonalmatrix given by:

2D � diag{�E[r ]}. (3)t it

The steps for estimating the DCC are as follows:

Step 1: Estimate a univariate AR-GARCH(1,1)model of each variable. This produces consistentestimates of the time-varying variance (Dt) for thehedging instrument.

Step 2: Calculate the standardized residuals �t �rt, where rt is the residual from the AR-GARCH�1Dt

model.

Step 3: Estimate an ARMA(1,1) model on ei,j,t ��i,t�j,t, ei,i,t � �i,t�i,t, and ej,j,t � �j,t�j,t jointly:

e � � � � e � u � � u . (4)i,j,t 0 1 i,j,t�1 t 1 t�1

The parameters for the covariance and varianceprocesses are assumed to be the same. Thus theparameters in Equation 3 are estimated by stack-ing the variance and covariance series of ei,i,t to-gether. Equation 3 is derived from the followingGARCH(1,1) process of the covariance between in-struments i and j:

q � � � �(e � � ) � �(q � � ), (5)i,j,t i,j i,j,t�1 i,j i,j,t�1 i,j

where � �0/(1 � �1), � � �1 � �1, and � � �1.�i,j

Step 4: Calculate the variances of instruments iand j and the covariance between instruments iand j (qi,j,t).

Once the parameters in Equation 3 are estimated,one can calculate the covariance from Equation 4using initial values of qi,j,t set to �0 /(1 � �1).

Step 5: Calculate the correlation between instru-ments i and j.

qi,j,t� � .i,j,t �q qi,i,t j,j,t

Estimated Models

Estimated Constant Correlation

Exhibit 1 presents estimated constant-correlationregressions of U.S. and state-specific house priceindexes on potential hedging instruments. Repre-sentative results were chosen from a much largerlist of combinatorial possibilities involving regionalhouse price indexes and potential hedging instru-ments. The tabled results are bivariate regressionsof house price returns on a single financial marketvariable’s return at lags of �1, 0, and �1. For ex-ample, the first entry of Exhibit 1 indicates thatthe regression coefficient of U.S. Treasury bond re-turns on aggregate U.S. house price returns is�0.16 and statistically insignificant.

The results in Exhibit 1 imply that the relationbetween house price indexes and potential hedginginstruments is generally weak and geographicallyunstable. Standard correlation computations basedon the data show that REITs have only modestpredictive power for U.S. and Florida indexes.There are also several statistically significant non-dynamic correlations for Texas and Illinois in-dexes. Even where statistical significance prevails,however, the magnitudes of estimated correlationsare rather small, ranging from 0.002 to 0.10.Therefore, these potential instruments cannot beefficient and effective for hedging house price risk.

When multiple hedging instruments are combined,their joint predictive power remains weak. If thesenon-dynamic correlations were stronger, Treasurybonds and the S&P 500 would be convenient in-struments because of their well-developed optionsmarkets. Dynamic correlation models are exam-ined next to look for possible improvements inhedging strategies.

Estimated Dynamic Correlation

The estimated dynamic correlation models indicatethat most of the bivariate relationships consideredin Exhibit 1 fluctuate significantly through time.Exhibits 2a–f show the time paths of dynamic cor-relations between Treasury bonds and house pricereturns for the U.S. as a whole and for the fivelargest states by population (Florida, Illinois,

Dynamic Correlation: A Tool for Hedging House Price Risk?

Journal of Real Estate Portfolio Management 21

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Nathan Berg, Anthony Y. Gu, and Donald Lien

22 Vol. 13, No. 1, 2007

Exhibit 2aCorrelation between U.S. House-Price Return and T-Bond Rate

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Dynamic Correlation: A Tool for Hedging House Price Risk?

Journal of Real Estate Portfolio Management 23

Exhibit 2dCorrelation between Texas House-Price Return and T-Bond Rate

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Nathan Berg, Anthony Y. Gu, and Donald Lien

24 Vol. 13, No. 1, 2007

Texas, New York, and California). According to Ex-hibit 2a, U.S. housing and bond prices are posi-tively correlated from 1979 to 1982 and from 1991to 1997, but negatively correlated, with large-magnitude correlation coefficients, from 1983 to1985 and from 2000 to 2002. The time pattern ofhousing and T-bond correlation is clearest in Ex-hibits 2a and 2f, which correspond to the U.S. andCalifornia house price indexes. Treasury bond cor-relations for Florida and New York (Exhibits 2band 2e) exhibit fewer negative values. The T-bondcorrelation for Illinois (Exhibit 2c) is mostly nega-tive before 1987 and mostly positive after 1987.The dynamic correlation path for Texas (Exhibit2d) is the most volatile. Correlations betweenhouse price returns and next (t � 1) period’s T-bond rate are generally the largest (except for NewYork and Texas), consistent with the idea that ex-pected interest-rate changes are a driving sourceof variation in home prices.

Correlations between house price returns and in-dividual stocks (not presented in the exhibits) alsofluctuate over time and across region. Those cor-relations tend to be significantly negative around1980 and then positive in the early 1980s and early1990s. The correlation between housing and theS&P 500 Index is significantly negative from thelate 1990s onward, possibly indicating that inves-tors use real estate as a broad-based hedge againstfinancial equity risk.

Overall, no clear and consistent pattern character-izes the estimated dynamic correlations aside fromthe fact that they appear strongly non-constant.The question then is whether the dynamic corre-lations are predictable. Predictability is requiredfor hedging to be possible.

Predictors of Dynamic Correlation

It is generally expected that interest rates, eco-nomic growth, employment growth, and stock-market growth are closely related to housingprices. House price increases have often been ob-served during low-interest-rate periods, which of-fer lower borrowing costs to home buyers. Becausewillingness to pay for housing probably goes up

with home buyers’ income, ceteris paribus housingprices should be positively correlated with eco-nomic growth and employment growth in lockstepwith demand for housing. Also, housing prices andthe stock market should be positively correlatedsince stock market growth increases households’wealth and enables them to buy more housing.

These factors interact in determining the level andvolatility of the correlations (i.e., one can observealternatively negative and positive, and alterna-tively significant and insignificant correlations be-tween house prices and these macroeconomic fac-tors during different time periods). The literaturehas not produced stable or consistent estimates ofthe relationships among these variables. One can,however, say that housing demand generally in-creases during periods of economic growth and lowinterest rates.

Regression analyses of the correlations on macro-economic time series were conducted to reveal therelations between dynamic correlations and mac-roeconomic factors over time. In the regressions,the estimated DCC (between housing prices andone potential hedging instrument) is the depen-dent variable. As for the independent variables, itis hypothesized that when interest rates are risingfaster than GDP growth and when interest ratesare declining faster than GDP is declining, nega-tive correlation between house prices and interestrates should be observed. When interest rates arerising slower than GDP growth and when interestrates are declining more slowly than GDP is de-clining, positive correlation between house pricesand interest rates should be observed. Hence, thefirst independent variable in the regression is theabsolute value of the difference between the rateof interest rate and the rate of GDP growth, andthe coefficient of the variable is expected to have anegative sign. The second independent variable isthe rate of employment growth, and the third in-dependent variable is the return of the S&P 500Index.

The estimated regressions are reported in Exhibit3. As expected, the difference between interest rategrowth and GDP growth is negatively related to

Dynamic Correlation: A Tool for Hedging House Price Risk?

Journal of Real Estate Portfolio Management 25

Exhibit 3Estimated Prediction Models

Intercept i - gGDP gEmploy gS&P500 Adj. R 2

U.S. 0.19 �2.93 �8.15 0.68 0.03t-Stat �1.6 (�1.9)* (�1.1) �1.5

California 0.40 �3.80 �19.41 0.29 0.01t-Stat �2.0 (�1.5) (�1.6) �0.4

Florida �0.01 0.42 2.50 0.59 0.01t-Stat (�0.2) �0.4 �0.5 (2.0)**

Illinois 0.36 �4.98 �5.24 0.44 0.12t-Stat �3.6 (�4.0)*** (�0.9) �1.2

New York �0.09 2.81 20.50 0.58 0.12t-Stat (�1.0) (2.4)** (3.7)*** (1.8)*

Texas 0.01 0.09 �14.40 0.27 0.05t-Stat �0.1 �0.1 (�2.6)** �0.8

Notes: This table presents the estimated predictive effects of the in-dependent variables (difference between real interest rate and GDPgrowth, employment growth, and S&P500 growth) on the dynamicconditional correlation between returns of house-price indices (U.S.national and five states) and T-bond rates.*Significant at the 10% level.**Significant at the 5% level.***Significant at the 1% level.

the dependent variable for the U.S. national, Cal-ifornia, and Illinois housing price series. The con-nection is significantly positive for New York, per-haps because higher interest rates benefit parts ofthe finance industry, which are concentrated inNew York City. The predictive effect of employmentgrowth on the dependent variable also varies byregion with surprisingly negative effects in Texasand Florida and effects conforming to expectationsin New York and elsewhere. The predictive rela-tionships between growth in the S&P 500 and theDCCs are positive across all regions as expected.

Dynamic versus Static Hedging

Correlations between housing market indexes andfinancial-market indexes are clearly dynamic. Pre-vious literature and the data considered in this pa-per both suggest that housing markets present in-dividual investors and portfolio managers withrisks that are difficult to hedge against. It may ap-pear that dynamic correlation makes that diffi-culty even worse. Insofar as the search for hedgingtools is restricted to a space spanned by modelsthat assume constant correlation, the performance

of resulting hedging strategies will be limited,since those models impose a restriction clearly fal-sified by time-varying correlations in the data.

One measure of potential value as a practical toolis hedging effectiveness, i.e., the percentage of var-iance in the housing index return xt that can bereduced by constructing a hedging portfolio usingthe hedging instrument yt. To pursue the questionof DCC’s value as a hedging tool, an attempt wasmade to run a horse race between regression-basedhedging strategies in which the hedge ratio �reg ��cov(x,y) /var(y) is constant, versus dynamic hedg-ing strategies, in which the hedge ratio is based ontime-varying covariances and variances estimatedby the DCC: �tDCC � �covt�1 (x,y) /vart�1 (y).

The regression-based hedging portfolio is definedas xt � �regyt, whereas the DCC hedging portfoliois defined as xt � �tDCC yt. Hedging effectivenesscan be computed for both strategies: hereg � 1-var(xt � �regyt) /var(xt), and heDCC � 1-var(xt ��tDCCyt) /var(xt).

The more effective a hedging strategy is, thesmaller is var(xt � �tyt) relative to var(xt), and thegreater the percentage reduction is, as measuredby hereg and heDCC, with a maximum of 100%.

Exhibit 4 reports values of hereg and heDCC in thethird and fourth columns for the six housing mar-ket indexes whose DCCs were shown in Exhibits2a–f. In each case, the hedging tool yt (i.e., theother asset in the bivariate hedging portfolio) isU.S. Treasury bonds, either contemporaneous withhousing prices or lagged by one period so thattreasuries are used to predict one-period-aheadhousing market returns. Of the six housing-priceindexes for which the hedging effectiveness of T-bonds is reported in Exhibit 4, there is one case,Florida, in which the DCC would appear to providean economically significant reduction in volatility.For the Florida time series, dynamic hedging withthe DCC leads to a 28% reduction in variance,whereas a hedging portfolio based on static regres-sion reduces volatility by, at most, one-tenth of 1%.In other cases, such as the U.S. series and Texas,where the absolute magnitude of reduction issmaller, the relative reduction, heDCC /hereg, is still

Nathan Berg, Anthony Y. Gu, and Donald Lien

26 Vol. 13, No. 1, 2007

Exhibit 4Hedging Effectiveness Using Bivariate DCC Versus Constant Regression to Hedge Home-Price

Indexes with Treasuries

HousingPrice Index

hereg

(Constant Hedge Ratio)heDCC

(Dynamic Hedge Ratio)Dynamic Stabilityof the DCC

U.S. contemporaneous 0.0094 0.0478 1.211-step ahead 0.0009 0.0519

Florida contemporaneous 0.0003 0.2834 1.391-step ahead 0.0012 0.2842

Illinois contemporaneous 0.0298 0.0107 1.091-step ahead 0.0216 0.0168

Texas contemporaneous 0.0019 0.0317 1.141-step ahead 0.0121 0.0323

New York contemporaneous 0.0317 0.0036 1.081-step ahead 0.0346 �0.0022

California contemporaneous 0.0018 �0.0038 0.791-step ahead 0.0003 0.0038

quite large. Exhibit 4 also shows cases where dy-namic hedging increases volatility relative to theunhedged housing price index, indicated by nega-tive values of hedging effectiveness. With that ca-veat in mind, Exhibit 4 provides at least tentativeevidence that DCC has potential as a volatility re-duction tool.

This is not overwhelming progress, of course, be-cause the daunting challenge of regional hetero-geneity remains as before. Therefore, the issue ofregional heterogeneity was further investigated totry understanding whether something more sys-tematic could be said about why, for instance, Flor-ida appears so different than, say California, interms of the hedging effectiveness of the DCC.Rather than classical statistics, one further statis-tic is reported that seemed potentially interestingafter visually inspecting the DCCs at differentleads and lags, as shown in Exhibits 2a–f. Thedevelopment of quantitative measures motivatedby visual inspection of data follows the data-to-statistical-tools methodology advocated by Tukey(1977). In Exhibits 2a–f, it appears that caseswhere hedging effectiveness is high, e.g., theU.S. and Florida series in Exhibits 2a and 2b, theDCCs at different lags look approximately likehorizontally-shifted translations of each other. Onthe other hand, in cases where hedging effective-ness is low, e.g., California and New York in Ex-hibits 2e and 2f, the DCCs at different lags appear

much more unstable, crossing at many irregularspots. Because the DCCs appear to track one an-other more closely at different lags in cases whereDCC hedging effectiveness is large, the stabilityof dynamic correlation was determined by twocriteria:

� Correlations at different lags are differentby a meaningful magnitude; and

� Differences in correlation at different lagsdo not change much through time.

If correlation were constant and the DCC weretherefore wrong, then cort (xt,yt�1) � cort (xt,yt) �cort (xt,yt�1), and the first criterion would be vio-lated. For dynamics to matter, time-dependent cor-relations must be different to an appreciable ex-tent. Second, insofar as dynamical correlation canbe captured with a parsimonious parametricmodel, the time paths of cort (xt,yt�1) andcort(xt,yt�1) should be linked in a simple way, im-plying that their difference should not varyerratically.

To measure these features simultaneously, theabsolute difference in lag-differenced correlationswere computed at each point in time: dt � �cort

(xt,yt�1) � cort(xt,yt�1)�. And then, for each pair ofindexes, computed the coefficient of variation fordt, referring to the result as dynamic stability: dy-namic stability � mean(dt) /var(dt).

Dynamic Correlation: A Tool for Hedging House Price Risk?

Journal of Real Estate Portfolio Management 27

The last column of Exhibit 4 reports dynamic sta-bility for the six price series, each paired with theTreasury bond time series. Ranking housing priceindexes by dynamic stability reveals an orderingthat matches almost perfectly the same variables’ranking by hedging effectiveness, depending onwhether one looks at contemporaneous or 1-period-ahead measures of hedging effectiveness. The find-ing admittedly leaves one with an as yet incom-plete picture of the structural causes of DCChedging effectiveness. Nevertheless, the pattern issuggestive of an implementable diagnostic for un-derstanding regional heterogeneity and predictingthe effectiveness of dynamic hedging.

Conclusion

This study reports dynamic correlations betweenthe returns of house price indexes and certain se-curities at leads and lags and during various timeperiods. The level and direction of the correlationschange markedly over time. Although some of theestimated correlations are statistically significant,they are not economically significant because thecorrelation is too small for effective and efficienthedging of house price risk. Furthermore, the in-struments considered would serve as effectivehedging tools only if historical patterns of dynamiccorrelation are themselves fairly stable throughtime, which is not yet known. Thus, there is still along way to go for hedging house price risk. Nev-ertheless, the large magnitude of the dynamic cor-relations, which are considerably larger than thoseestimated in the constant-correlation models, sug-gests some hope of leveraging time variation incorrelations to better hedge against housing risk.

Macroeconomic factors such as the interest rate,GDP growth, employment rate, and stock marketgrowth are statistically significant predictors ofthe estimated dynamic correlations between houseprice returns and the T-bond rate. The predic-tive relationships vary, however, across differentregions. Further study is needed to understand thefactors that drive the dynamics of correlation be-tween house prices and potential hedging instru-ments. In particular, there needs to be furtherexamination of whether the lead and lag rela-tionships or the simultaneous correlations are

more important, and which of these could bestbe exploited using existing financial derivatives.Historical analysis of the dynamic correlationswould also provide a useful check on the reliabilityof estimated dynamic correlations.

Correlation analyses of potential hedging instru-ments have been published ad nauseam in manyareas of asset pricing and risk management. Cor-relation itself is not novel; however, the correla-tions presented in this paper do effectively arguefor the structural claim that constant-correlationmodels used in the vast majority of empirical stud-ies of hedging possibilities are incorrect for hous-ing markets, because they impose a static con-straint on an inherently dynamic structure. TheDCC is used here as a tool for observing whetherthe correlation between house price and financialmarket returns fluctuates through time. Indeed itdoes.

The first implication of dynamic correlation is todrop the search for static correlation hedging strat-egies that predominate in much of the portfoliohedging literature. A second implication based onthese data is that, at least in select cases, DCC canbe used as a tool for variance reduction. Dynamichedging strategies would appear to work bestwhen dynamic effects are sizeable (i.e., changes incorrelation through time are of large magnitude),and when those differences are relatively stablethrough time, so that they can be effectively ex-ploited with a minimum of statistical parameters.

Endnotes1. An encouraging development in the form of newly available

hedging instruments is the ‘‘hedgelet’’ (see hedgestreet.com),which allows individual investors to bet on upward or down-ward movements in six city-specific real estate indexes. Theindexes for which options trading are now available are theNational Association of Realtors’ (NAR) Median Sales Pricesof Existing Single-Family Homes for Chicago, Los Angeles,Miami, New York, San Diego, and San Francisco.

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