Spatial Portfolio Theory

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1 Spatial Portfolio Theory C Y Yiu Researcher, REDBRIC 9 April 013 CUHK

2 Background (1) Classical Theory: Transportation improvement helps increase housing price. Housing Price We contended by a novel hypothesis: Transportation improvement helps flatten housing price gradient; absolute price change is unknown. Transportation Improvement Alonso's (1964) mono-centric bid rent curve. Dist from CBD

3 A Counter-intuitive Hypothesis Higher Demand NODE A Road Lower Demand NODE B NODE A Bridge Road Increase Demand Move in from External Decrease Demand Move from A NODE to B B 3

4 Old Theory Taken for Granted Transportation improvements may decrease housing price? People and companies may move from the originally more convenient location to the now equally convenient location due to the completion of the infrastructure. i.e. the price gradient between the nodes would be flattened, but the change of the absolute magnitude in price cannot be predicted, depending on the net increase in demand. 4

5 Developed a Price Gradient Model empirical tests on the transportation improvement effects on housing price gradient, rather than on price; Developed a novel empirical regression model with interactive terms to identify the gradient changes of housing price. Details see Yiu, C.Y. and Wong, S.K. (005), The Effects of Expected Transport Improvements on Housing Prices, Urban Studies, 4(1), Dec., ; and Yiu, C.Y. (010) Differential Economic Benefits of Transportation Infrastructure at Two Transport Nodes, ISSF Conference. 5

6 Micro Empirical Evidence ln( PRICE ) = β 1 TY BEF + α 1 β + α AGE + α TY AFT + 3 β GFA + α 3 FLR ST AFT + ε 4 + α 5 SV + Housing transaction data: 14,767 transactions 6

7 Background () Classical Theory: one-workplace model - traveling frequency determines housing location choice. But how about two-workplace? workplaces for husband and wife; cross-border HQs and factory; Developed a two-workplace (with known traveling frequency) model: the housing price gradient between two workplaces will become flattened when the visiting frequency to the workplace increases relatively. Details see Yiu, C.Y. and Tam, C.S. (007) Housing Price Gradient with Two Workplaces - an empirical study in Hong Kong, Regional Science and Urban Economics 7,

8 Two Workplaces (wkf) Model 8

9 A Novel Temporal-Spatial Differencing Empirical Model Micro-economics Housing Price Gradient between the terminals, S & N Differences in the Traveling Frequencies between S & N Macro-economics 9

10 A Macro Empirical Evidence HK-Macau The 1st paper on Macau housing market; better data controls on cross-border proxies; Details see Yiu, C.Y. (008) Housing Price Gradient between Macau and Hong Kong - a neighboring city effect, International Journal of Housing Markets and Analysis 1(),

11 Motivations Classical models are uncertainty-free; Previous studies on uncertain transportation cost, uncertain housing price, etc. How about two-workplaces, with uncertain traveling frequency? A new housing centre can be emerged! details see Yiu, C.Y. (011) A Spatial Portfolio Theory of Household Location Choice, Journal of Transport Geography, 19,

12 Why Multiple Workplaces? Globalisation Trend; Contemporary office strategies: Multi-site Shared space Hotel space Just-in-time offices Free address model cater for more than one workplace with uncertain traveling frequency! Langston, C. and Lauge-Kristensen, R., 00, Strategic Management of Built Facilities (Butterworth-Heinemann, Oxford). 1

13 Theoretical Framework This paper develops a two-centre two-workplace with stochastic (uncertain) traveling frequency model i.e. a (--0) model of a linear bi-centric city of two workplaces I II III (0,0) D 1 D D

14 Expected Commuting Cost The expected commuting distance E(d) at any point (z,0) weighted with the frequency, u Assuming fixed unit cost of commuting c, the expected commuting cost E(c) at any point (z,0) is then:

15 Variance of E(c) The variance of the expected commuting cost is: Since Corr(D1, D) = -1

16 Household's Utility Maximization where x is the non-housing composite goods with price equal to one; h is the quantity of homogeneous housing consumption. The household s utility increases with x, h and decreases with c, i.e. Ux, Uh > 0 and Uc < 0; subscripts are the corresponding partial derivatives. Y is the household s income per period, R(.) is the function of unit housing rent, and c is the fixed unit commuting cost.

17 Lagrangian of the Maximization

18 Consider the sign of the terms inside the bracket, then ( ) ( ) [ ] = b a c D z c z ( ) ( ) [ ] θ = D z D z b a Differentiate the variance wrt z Differentiate the variance wrt z Differentiate the variance wrt z Differentiate the variance wrt z

19 a simple case of 1 = 1 = θ ( ) ( ) [ ] < = > < = > = 1/ 1/ 1/ D z when D z c z b a c A Simple Case A Simple Case A Simple Case A Simple Case

20 Intuitive Interpretations 1. If the traveling frequency is certain, i.e. the nd term = 0,. then the 1st term tells that the unit housing rent is decreasing with the commuting distance; 3. i.e. Alonoso's bid rent curve. 4. But when trevling frequency is taken into consideration; 5. the sign of the rent gradient is NOT necessarily negative; 6. There are 3 possible cases.

21 Intuitive Interpretations (Cont'd) 1.Even if the expected traveling frequency to centre D1 is higher than that of centre D;. If the commuter dislikes any losses due to the uncertain frequency traveling to centre D; 3. then the sum of the two terms become positive; 4. i.e the commuter would prefer living closer to the mid point rather than closer to centre D1.

22 Intuitive Interpretations (Cont'd) R(z.) μ a1 >= μ b a1 = b Cov (D1a, Db) = -1 μ U is small 1 = = 0 Bicentric with certainty of frequency μ U is large 1 and > 0 Bicentric with D 1 uncertainty of frequency z =D/ D A New Centre can be Emerged between the Two Original Centres!

23 Empirical Evidence

24 HK Households work in China within a year

25 Data and Methodology transaction data of housing units along the East Rail over the last decades, from 1991 to 008. Using standard BMN repeat-sales model

26 Empirical Model - Repeat Sales control the original price differences among stations Pit ln( P it ) ( b x + S λ x ) 1 T 7 = t it t = 1 l = 1 where P is transaction price of dwelling, b is the base index, x is equal to 1 when t = t and is equal to 1 when t = t1, λ is the logarithms of the location factor of location, S = 1 if dwelling is located at location l; 0 otherwise, l = 1 for Tai Wai station, for Sha Tin station 7 for Sheung Shui station, T = the total number of months in the sample period ( ). µ is the stochastic term. il lt it + u it 1 t

27 Empirical Findings (SZ) the housing price in the middle part of the East Rail has been increasing relative to other terminus.

28 Empirical Findings (HK)

29 Price Contour of Different Locations locat ion f a c to r dat e st at io n

30 Implications A spatial portfolio theory in analogous with the portfolio theory in finance. Living in the mid point (choosing the ease of travel to the two workplaces in a portfolio) of two workplaces of uncertain traveling frequency acts the role of hedging the risk of changing traveling frequency. A new city centre can be emerged between frequently travel workplaces. 30

31 Predictions The Spatial Portfolio Theory predicts: A new centre at the border between HK and Shenzhen. (a new city is to be built) A new centre to be emerged at Tung Chung when the HK-ZH-MA link bridge is built. The housing price gradient between HK and Macau would be flattened. How about the Express Rail? Would Chongquin become a new centre for frequent travelers between HK and Shanghai?

32 The End Contacts: blog: Download: homepage: 3

STUDY ON RELATIONSHIP BETWEEN CATCHMENT AND BUILT ENVIRONMENT OF METRO STATIONS IN HONG KONG AND SHENZHEN. Yin Ziyuan

STUDY ON RELATIONSHIP BETWEEN CATCHMENT AND BUILT ENVIRONMENT OF METRO STATIONS IN HONG KONG AND SHENZHEN Yin Ziyuan DOCTOR OF PHILOSOPHY CITY UNIVERSITY OF HONG KONG JUNE 2014 CITY UNIVERSITY OF HONG