An Analysis on Property Price Fluctuation YEUNG Yan Ho 260591446

8/13/2019 An Analysis on Property Price Fluctuation YEUNG Yan Ho 260591446

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An Analysis on Property price fluctuation:

Application to and implication from Hong Kong as an Example

Yeung Yan Ho

Abstract

This paper provides a systematic way to access to estimation of property price and corresponding

volatility. Due to relatively high market friction and transaction cost, property market can be regarded as

an inefficient market compared to other asset classes. I made the following hypothesis: the actual price

movement is generally aligned with macroeconomic factors, while the implicit equilibrium is determined

by microeconomic factors. Deviation (DEV) between them is supported by inefficiency and information

asymmetry. Such deviation corresponds to the risk of bubble burst or price jump. The critical deviation is

determined by volatility of price which is affected by social-economic factors. Equilibrium price is

estimated from a microeconomic model which equate equivalent cash flow. Then, I use a macroeconomic

fundamentals to generate price trend through linear regression. I analyze the residual and explained the

volatility with social-economic factors. After considering the above result, a risk test is constructed.

Finally, I use Hong Kong as an empirical example to examine the current situation in Hong Kong.


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I. Introduction

Purpose: Investigate the factors affecting the housing price in Hong Kong. Build a model to

simulate the property price trend. After understanding the mechanism, estimate the bubble risk

with respect to the factors.

Being one of the most crowded city in the world, the housing market in Hong Kong is interesting

to investigate. Several factors making Hong Kong a special place: high population density, low

land supply and corresponding government policies, monopoly among developers and prosperity

of real estate brokerage business, high sensitivity to international and China economies. Due to

the high contribution of properties to the Hong Kong economy, macro-factors exhibit a high

correlation with it. Property price is always a hot topic in the news and peoples life.

In this dissertation, price mechanism will be studied. A classic demand-supply theory will be

adopted. Demand-side factors, including fundamental need (population rise), mortgage rates

(public credit rating and interest rates), income level (tolerance and affordability), current and

expected rental income, substitution among different assets (consumer confidence and

preferences among different investment), and tradition of property speculation (expected price

movement), will be investigated. Supply-side factors include low elasticity and growth of land

supply, public housing scheme, effect of stamp-duty and related tax policies, behaviors of

developers (first-hand) and owners (second-hand). Macroeconomic factors including inflation,

Fed rate (linked currency system) and unemployment rate, stock market and other asset classes

(investment atmosphere) will also be considered. After quantifying the above data, regression

will be applied and an appropriate time-series model will be used for smoothing purpose.

Hopefully, an equilibrium model is generated.


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After figuring out the key factors affecting the current price, a risk estimate would be proposed.

That is, a measure of degree of irrational behaviors in the market. A traditional NVP and return

period model will be first adopted and adjustment will be made based on the result of the first

part. Hypothesis include price momentum and investment decisions of land developers. We then

try to combine the data together and investigate the identification of a housing bubble and

predictability of bubble burst.


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II. Literature Review

There is a lot of literature concerning real estates and property market. I concentrate my research

on possible pricing model and list out the following problems.

A. What are the existing models?

a) Explaining price with demand-supply model

The traditional demand-supply model involve estimating demand and supply with affordability,

production costs etc. However, literatures using demand and supply to explain price movements

tend to be statistically less significant than macro model.

b) Price tracking with macroeconomic model

It is one of the easiest yet accurate method to estimate the price. Putting macroeconomic factors

into a regression model, one can generally proxy the influence of local and global economic

trend to the property market. However, the selection of independent variables is critical to the

result.

c) Risk measure by deviation between actual price and model-generated price

B. What is missing?

a) The micro model has some difficulty identifying rental and owning market.

b) There is no integrated version of models in respective microeconomic aspect and

macroeconomic aspect. Not only the selection of independent variables matters, but also there

exist different format of specific equations and regressions within the category.

c) There is no relationship explained between the micro and macro models.


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d) There is no explanations and model for the volatility of price movement

d) Only incomprehensive explanations for the price deviation

e) Missing criteria for critical deviation before price collapse or jump

C. What is new in this dissertation?

a) In each of the micro and macro aspect, construct respective model by choosing significant

variables from the existing those.

b) Using information asymmetry to merge the two aspect together: People tend to rely on easily

accessible macro-information to set the purchase or selling price, while tend to ignore or have

certain barrier or distortion in accessing micro information like rent, construction cost etc. And

thus there exists certain deviation between them. The micro price usually is the price floor in

blooming economy and price ceiling under depression.Macro price move above or below the

micro equilibrium in different stages. The degree of deviation depends on the volatility. The

volatility is then a function of other social-economic factors, including those affecting

consumption, investment behavior, wealth distribution etc. Note that all the parameters vary with

time and location. The graph below shows the draft idea of the hypothesis.


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c) Propose a risk measure using the ratio of deviation (DEV) from benchmark to volatility. It is

different from the existing one, which only consider absolute value of the DEV. There are two

versions of existing tests, one uses regression and considers the standard score of each actual

price point (a probabilistic approach). Another one is similar, but it calculates the DEV from

benchmark and finds international comparison. Although the first model accounts for volatility,

it may mistake the risk. It is because for a more aligning model there exist more macro factors

but then it will have less proportion of micro information.Note that the micro and macro trend

can be different. The second model should be able to realize the logical deviation but fail to

impose relative measure. I introduce a ratio method because I propose volatility is relevant to the

DEV and volatilities vary cities from cities.

d) The steps are as follow. In order to know the volatility of the price, we have to build a model

to estimate the price to eliminate predictable price movement and isolate the error term. The

error should look like some white noise. It is observed that the price follows more on macro

factors. So I choose macro to be the regression model. Note that the fluctuation along the macro

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1 2 3 4 5 6 7 8 9 10

Property Market

Micro Equilibrium Macro Model

DEVActual price


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line is assumed to be a normal distribution and generally is smooth (no sharp jump) along the

macro-line. That means, usually it is irrelevant to jump or bubble burst. This paper introduces a

concept of information bottleneck. As mention, the implicit true value of property follows micro

factors, where exist certain information barriers to the investors. If the price is misaligned with

the micro line very much, then it will induce a price jump. If the volatility is generally high

within a period of time and region, people will not take action to seek information until the DEV

grows larger than expected implied by the volatility. Simply putting, a high volatility allow a

largerDEV. Note that the macro line is there only for calculating the white noise variance. It is

necessary to build such a model because the micro and macro line may not follow the same trend.

e) Imagine the following metaphor. In a booming economy, the actual price usually lies above

the micro equilibrium. The actual price is a ball on the graph, and there is a spring connecting it

to the micro equilibrium. There is a string pulling the ball up (representing information

asymmetry), thus generate a gap. Certainly, when the gap size increases, the tendency for the ball

to go back to the micro equilibrium increases. But it does not imply that it will definitely go back.

When the pull is too strong the string will break and the ball will then jump back to the micro

equilibrium. I consider the strength of the string the volatility. When the volatility is high, it

allows a larger gap, and at the same time sharper jump. In an economy of low volatility, the

string break continuously, showing smaller gaps in long run. Here I also provide a method to

estimate the volatility by social-economic factors. That explains why some places have a strong

string while other have a weak one.

D. What are the empirical results?


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My model is originally built on my observation on Hong Kong property market, where I want to

generalize the result to other cities. The hypothesis is moderately aligned with the empirical tests

in Hong Kong. Some of the propositions are evident in UK and US.

E. Is there any limitation?

As most of the statistical experiment, the problem is the sample size. In order to show the theory

is significant, we need to have a larger sample of price fluctuation and varying conditions.


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III. Market Equilibrium-A Microeconomic approach

A. Demand-Supply Model

We will first focus on the connection between property price and the rental market. The linkage

is the expected rates of return, which is under the influence of several factors including inflation,

interest rate and the loan-to-value ratio. We can see that the initial property price and the rental

income of the property are exogenous. Then, we will use the classic optimization equilibrium of

property market to determine the property price.

a) Optimal Aging Period and Risk Analysis

From the perspectives of an investor, the expected return is mainly composed of rental income as

well as capital gain. A cash flow model assuming perpetuity of rental income is not

comprehensive as the house owner may resell the property in the second-hand market. Here, a

net profit function is constructed as a way to determine the optimal condition.

= 0 + 1 + 0

Which is the discounted cash flows of initial price, 0, Rental income net of tax at time, 1and price at time N,H(N).To optimize the holding period, we take the derivative of P with respect to N and make it to zero.

= 1 + = 0

,which implies

(1 )() + = 0


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Or equation (1):

= 1 +

The intuition of the above equation is the rate of time preference should be equal to the sum of

rental income net of tax and the expected growth rate of the property.

Taking the second derivative, yields

22 = 1 + 1 +

Setting it to negative for maximum optimization, and combining equation (1),

1 + 2 < 0The aging period affects the change of the rate of time preference. To investigate the effect, we

differentiate equation (1)

dN

dk=

H2

1 THRHR+ HH H2 < 0

The implication from the above equation is the inverse proportion between subjective rate of

time preference and holding period.

It is proposed that there exists correlation between rate of time preference and rates of return on

other competing assets. Both theoretical and empirical results show that return on property

declines when interest rates rise. Consequently, investors prefer a portfolio of higher return

assets to houses. The rate of return on property depends mainly on two factors, rental income and

capital gain (illustrated in equation (1)). Despite a low rent-to-value ratio, Investors may be still


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willing to hold the property if appreciation is expected. In a situation that price growth is low,

investors would demand a higher rental income or otherwise resell the property.

Property sometimes is considered as a way of inflation hedge, but at the same time holding

property introduce other risks. For example, the wide price fluctuation due to immobility and

political uncertainty. Risk elements can be incorporated in the expected capital growth rate.

When risk increases, investors demand a higher rate of return, thus property price declines. This

equilibrium mechanism brings out that property price tend to decline relative to the rentals. In

booming economy, an unreasonable high price level is attained because of high expected capital

growth rate, despite low rent-to-value ratio.

A revised arbitrage condition proposed by L. H. Goulder (1989),

1 + = + In equilibrium the risk-adjusted rate of return would be equal to +

Under the expectation of the future interest rate and inflation rate, the estimated nominal rate of

return reflects the return of discounted value of the net after-tax service flows of the asset.Owing to the importance of expectation of the future property price movements, we make further

revision on the formula,

+

= +

This imposes that investors are willing to accept a lower current rate of return if the future price

expectation is high, vice versa. (/)may also interact with since investors adjust the


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expectation incorporating information on risks. For each equilibrium values, take the derivative

with respect to ,

= 1 Where is assumed to be independent of can be interpreted as the sensitivity of price expectation with respect to risk. With the

assumption that expectation of price growth would be weaker under uncertainty and increase in

risk. That means,

< 0

Therefore,

> 1

The second derivative of respect to ,22 =

22

Represent the risk attitude of individuals. A strictly positive value meaning strictly increasing

indicates risk aversion, while a strictly negative value meaning strictly decreasing indicates

risk-seeking. However, the sign of the second derivative is indeterminate so far.

For = , r would be equal to the risk free interest rate, as illustrated by the vertical intercept.Given risk premium > 0, the return curve must be contained in the region above the


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= line. The figure gives intuition in the situation of interest rate change. For instance, whenthe interest rate increase from 1to 2, the return line will shift to 2. As a result, a higher rate ofreturn would be demanded in order to compensate the extra cost of investment induced by higher

risk, hold other conditions constant.

Clearly, is not the only factor affectingE. A shift of return line to 2could be induced bypessimistic expectation. Then, a lower equilibrium would be resulted.Although the Portfolio asset theory reveals the relationship among property price, rate of return,

risk and expectation, one cannot extract a definite injective relationship of the variables. The

question can be posed as this way: Given a change of risk element , how randEwould beadjusted to give another equilibrium, while both of them are simultaneously affected by the risk

element.

The risk of investment also depends on theLTVratiog. If the banks offer a highergratio, it not

only means an easing credit policy is adopted, but also the banks are willing and capable of

bearing a larger proportion of risk from the investor. For instance, if the bank provides 100%

mortgage to the investor, the investor would be able to buy the property without any initial cash

out flow. Given property appreciation, the investor would extract the capital gain. Given

depreciation, the investor may default and buy the same attributes if the property price falls

below 0 . represents the accumulated equity in the property during the period t. A longerrepayment period gives lower rate of equity accumulation and higher chance of default. Thus, the

terms of mortgage and credit availability incorporate financial concerns as well as risk

consideration.


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b) Determination of Purchase Price

As usual, a property can be viewed as a capital which provides future cash flow as rent. In effect,

purchase of a property is equivalent of buying the right to enjoy such a series of income (net of

taxes and various expenses). In the perspective of aninvestor, the purchase price should not

exceed the present value of the aggregate future income. That means a non-negative investment

decision.

We denote property tax rate and market interest rate with Tand i.

We first consider a competitive property market, whereas discount rate will be equal to the

market interest rate. With normal discount model,

0 = 1 0

+

where the last term is the discounted value of future selling price.

As to estimate the rent, we assume

() = 0 whereis the expected growth rate of the property price.Similarly, we have

= 0


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Inserting the above two estimates into the discount model,

0 = 1 00

+ 0

= 1 0 1 +0

Making 0as the subject, gives

0 = 1 0 1

Note that,

0 > 00 < 0

The results matches our intuition and reality: an expectation of appreciation impose positive

effect on current purchase price while the increase of interest rate tends to suppress it. The

expected price growth can be affected by political uncertainty. A lower can be induced byhigh political risk.

In view of Mankiw and weil (1989), the property price can be represented implicitly in a

differential equation,

= ()

where R(h) is the rental price function andis the operation cost.The above relation can be viewed as an analog to our previous equation,


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= 1 +

In our equation, we allow adjustment subject to principle of optimization, in which the subjective

rate of time preference is composed of after-taxR/Hratio and future price expectation. Contrast

to the assumption of constant made by Mankiw and Weil, the operation cost show be afunction of expectation, affected by inflation, interest rate, tax and political concerns under

dynamic economic environment. It is evident that prices fluctuate and grow at a rate much faster

than interest rate.

c) Supply of Housing

Under the principle of optimization, developers should maximize their profits subject to a

production function with land structure inputs. Here we pose the profit function as equation (2),

max, = ,

Kis the structure inputs

Lis the land inputs

His the average property price per Qunit of quantity of housing

qandware rental rates of structures and land respectively.

As Qis a function of K andL, we impose Cobb-Douglas production function as an estimate,

, = Putting this estimate into equation (2), and take first derivative with respect to K and L, yields

equation (3),


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=

And equation (4),

=

Combining all conditions,

=

1

+1

= 1

+1

+

+

It is equation (5), where

= 11 Denote the profit rate as

= +

Also from (3) and (4),

+ = + Substituting the equation into , yields

= 1 + 1


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With the assumption of existence of short term profit, we have + < 1. The implicationbehind would be a decreasing rate of increase of quantity of housing supply with respect to

inputs.

In order to derive implication on relative land and structure costs, we let

= + =

+

= + =

+

be the ratio of land and structure cost to total cost respectively.

Equation (5) now can be rewritten as

= Note that the supply is positive correlated with the property price while negatively correlated

with input costs. From the optimization perspective, it matches the intuition that rising property

price tend to attract developer to increase supply, while increasing production costs suppress

production.

To derive more quantitative measurement from the above results, we can calculate the elasticity

of the three components as follow,

=

=1

= =

= =


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Where

=

=

Normally, 1 > > 0, thus we have

< 1

Equation (6) implies that the change of demand with respect to change of population depends on

first, the effect of economization of housing in respond to rent movement and second, rent

movement in respond to population growth. In other words, population growth tends to raise the

property price and economization on housing service simultaneously. Thus, there would be a

proportionally smaller increase in total demand than the increase in population.

To investigate into the owner-occupier demand, denote it by

= ( , ,)

Which is a function of ratio between rent and property price (R/H), mortgage rate (rm) and the

loan to value ratio (g). Individual makes choice between purchase and renting by comparing the

property price and rent as well as operation costs including interest cost. Ownership can be

substantially increased by increasing availability of housing finance. [J. Gyourko and J.K. Han

(1989)]


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Therefore, we may derive the following results,

> 0

< 0 > 0

M is the demand for housing services which is different from housing stock since the former is

referred to consumption element while the latter one is regarded as wealth. Thus for a giveng

and rm,Mexpresses the yield ratio but not the expected return rate as an endogenous variable of h.

Consequently, the expected return rate would affect the demand for housing stock rather than the

housing service. Conversely,R/Haffects the demand of housing stock as well as housing service.

It is because the expected return rate depends onR/H. WhenRapproaches 0, individuals will not

buy a house, thenM(0)=0.

By subtracting the owned dwelling from the total demand, we can obtainDR, the demand as

equation (7),

= ( )Note that

< 0


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Denote the supply of rental housing by A, then we have equation (8),

=;

> 0As the rent increases, we can expect more people will lease their premises. The supply consists

of existing and newly built premises. If there is no new supply of flats, then A(r) can be regarded

as a switch between owning and renting. Here we use the definition of notional supply as the

supply of premises depends on the property price. If there exists emigration, this reveals a pure

substitution of renting for owning.

With (7) and (8), we can derive the equilibrium position as equation (9),

= ( )The expected rate of return is a function of R/H as one of the endogenous variables, thus

r=r(R/H)

assuming constant parameters.

At the same time, the equilibrium r would in turn determine the R/H ratio as r tends to depend on

other competing assets. Given the existing economic parameters, the property yield R/H (which

determines the tenure choice) depends on the rate of return on the asset. However, given anR/H

ratio, one cannot go further to estimateRandHseparately.

To investigate the relationship betweenR/H, consider (9) again. For a given r there would be an

equilibriumR*satisfying


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=

People tend to economize housing with a rising real rental price, which then results in higherR/H

ratio andr. Generally speaking, the maximization of intertemporal utility function subject to a

wealth constraint determines the household consumption of housing service in its consumption

bundles.

If the actual ris low compared to other competing assets, the demand for housing would

decrease, vice versa. Investors would decrease the relative ratio of property in their asset

portfolio and switch from owner-occupation to renter-occupation. In consequence, the property

priceHtends to decrease whileRtends to increase.R/Hwould rise until the r(R/H)is again

equal to the competing assets in equilibrium.

Provided that there is no counteracting force on the market induced by income effect, there

seems to be absence of upper limit for property price. However, there exists a downward ratchet

effect for rentals. IfRis at a low level, a persistent excess demand for housing services may

result. It is because a lowRwould be associated with a relatively low property priceHfor

maintaining a competitive return rate. ForHis not enough to compensate the cost to the

developers, this will result in a decrease of supply of new premises. IfRfalls below a certain

critical point, then the demand of housing cannot be satisfied by the supply of housing and there

will be no motivation for new construction as the transfer earning^ on the other is higher. Thus,

there exists no equilibrium.

B. Cash Flow Model


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As the previous chapter use the demand supply model to derive the equilibrium, I am now using

another microeconomic approach to derive the equilibrium. Here I consider the choice between

renting and buying, from the perspective of investors.

Assume that is no friction, in equilibrium, the rental cost/benefit should the same as the

cost/benefit of owning a house. Simply putting,

= Rtis the market rent, is the estimated property price and is the cost of ownership expressedin terms of cost per monetary unit of house value. For simplicity, the rental-relevant terms are

put in the term, as the equivalent cost/benefit with respect to owning. For example, we putcapital gain on the right hand side is equivalent to the opportunity cost to renting a house.

The next step involves choosing elementsfor . The following show some significant (but notall) elements that should be included in .

a) Risk-free interest rate

The risk-free rate is representing the base line of the opportunity cost of the amount of money

used on the property. Note that it is not that total opportunity cost for the amount of money. The

total should include liquidity premium, immediate consumption, risk premium etc. However, I

try to incorporate these aspects to the other variables so to make the information extraction

accessible.

b) Property tax rate

Rates are taxes levied on real estate property, is one of Hong Kong's indirect tax, the revenue

becomes part of the general revenue .Rating is based on the rateable value of the property is


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multiplied by a percentage levied on the rental value of the property is assumed that when the

designated valuation reference date of vacant rental reasonable estimate can be made of the

annual rent is calculated. In fiscal year 2013-2014 , the percentage was 5% , based on the date of

valuation , compared with October 1, 2012 .

c) Mortgage interest rate

Different banks offer different mortgage plans. Examples include prime rate-, HIBOR+. The

prime rate, discount and premium rates vary from bank to bank. For the sake of simplicity, we

choose the most common and influential rate, the HSBC prime rate at a reference to all the plans.

d) Maintenance cost

Maintenance costs is a board base of costs supporting daily operation of the building, including

repairing, security, cleaning, shared facilities, and other service fee.

e) Expected capital gains

We assume that (i) buyers form their capital gains expectation according to past observation as

well as their local knowledge about future price dynamic and (ii) the relative risk of owning

versus renting can vary slowly over time.

f) Risk premium

The risk premium should, among others, depend on the degrees of price and rent fluctuation and

the ability of homeowners and renters to hedge risks, which may not be constant over time and

fluctuate more in a crisis.


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IV. Estimation of Property Price-A Macroeconomic Approach

Generally speaking, the degree of information asymmetry in macroeconomic information tends

to be smaller than that of microeconomic information. It is because the accessibility of

information intermediates, or simply media, is higher in case of macroeconomic factors. For

example, public media and newspaper spread information about general economy faster than

brokerage firms or landlord to spread price and rent information. Thus, one could expect the

price movement is more likely to follow macroeconomic data rather than microeconomic factors.

Note that the price inducted by such information is not necessarily representing the true value of

a property. Relative to the cash flow argument which estimates equilibrium in exact terms, the

actual price imposes illusion induced by information asymmetry, transaction cost, friction,

degree of speculation and various social-economic factors.

In the previous chapter, we always consider an equation in exact form. For demand supply

approach, we equate demand and supply in absolute term. In the rent-buying approach, we

consider the equality between rent and cost of purchase in also absolute term. Here, in the

macroeconomic approach, we consider regression, which is an approximation form of equation. I

employ various macroeconomic factors as follows:

a) Gross Domestic Product

GDP is a measure of productivity and economic activity in a city. Like most of the other

countries, Hong Kong's GDP has a positive correlation with housing price. This is easy to

understanding as most of the literatures suggest an obvious intuition, "GDP growth indicates

people wealth and prosperity, thus drives up housing price". Strictly speaking, saying GDP leads

housing price may be logical to countries that housing contribute a relatively small proportion as


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GDP. However in Hong Kong, property price is a very heavy component in every business. I

will therefore relax the assumption to GDP and housing interact each other. To certain extent, It

may be a situation that property price leads GDP. If this is the case, From the regression

perspective, although the model still work as long as there are relationship, but the reason-result

relationship behind would be reversed (the property price is independent variable while the GDP

is dependent one). From a time series perspective, it is important to note any time lag between

these two variables. Clearly, there are dynamics ignored by most of the literature that have to be

explored in this paper.

b) Inflation

Inflation is important in such a way that it effect nominal price movement as well as interest

policy. Usually, the government will impose a series of money supply tightening policies in the

circumstances of substantial inflation. Such operations include raising interest rate. Some people

may also regard real estate as an investment tool to hedge inflation. There would be a possible

case that property price follow inflation movement in real term.

c) Interest rate

Certainly interest rate is a vital influential parameter in any finance area. Putting it into the

property price model, it reveal, affordability, asset distribution, money supply, investment

atmosphere.

d) Mortgage rate

There exists a lot of different mortgage plan in the market, vary by banks, investor preference

and property value. For most of the mortgage plans, the term is expressed as prime rate plus or


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minus a certain rate or HIBOR plus a certain rate. The mortgage rate is the cost of capital from

the perspective of investors. A low mortgage rate encourage real estate activities, vice versa.

From the perspective of banks, the provided mortgage rate indicates the general risk level of the

market. A high mortgage rate may inject a message of high risk into the market, thus further

suppress the price.

e) Unemployment rate

Unemployment affects the property price both directly and indirectly. First, unemployment

directly influence the general income level of the public. The affordability towards different asset

classes will deteriorate in case of high unemployment. Unemployment rate also reflect general

market atmosphere and investment incentive. Thus, unemployment rate can also be used as an

indirect indicator of the real estate market.

f) Liquidity and money supply

Liquidity affects the interest rate and the willingness of bank lending. Here I use money supply

to estimate the general liquidity of the specific economy. Informally speaking, the amount would

be proportional to the ability and tendency of investment going to the real estate market. The

higher the liquidity, the higher the property price.

g) Land supply

Land supply refers to the government land selling. Note that it is not the actual supply of the

property. Increasing land supply sends message of potential price fall in the future to the market.

With a certain time lag, the land supply is realized and become realistic. By observing the time

series between property price and auction performance, a 5-quarter lag may be reasonable, which


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represents the maximization timing for the effect of price expectation and realized output.

h) Change of Transaction number

The transaction number reflect the activity of the real estate market. It indicate the investment

atmosphere/emotion and the investors confidence.Generally, a price growth should be

associated to an increase in transaction number. Note that unlike other asset like stock with low

friction and transaction cost, property price drop is usually associated with a low transaction

number. Apart from the high transaction cost, possible reasons include durability of property, a

different prospect utility curve and belief of long-term growth of property price.

i) Change of actual price (momentum)

This is related to the investors expectation of price movement.I assume the trade behavior is

similar to momentum trading. After the observation of persistent price growth in property price,

investors tend to purchase more in order to earn the capital gain afterwards.

We use the following abbreviation for linear model,

= Where MACRO are relevant statistically significant factors identified in the empirical tests.


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V. Event study and Error Analysis

In the section of macroeconomic factors, we discuss several reasons of property price movement.

However, I did not include political measurements into the model. It is because some of the

policy elements do not change frequently over time. If they are added to the linear regression, the

result may be distorted. On the other hand, they are so important that they lead to substantial

price movement.A way out is to insert the political elements into the model of the change of

price, not the price itself, and investigate the period around change of policy (event-study).

In the section of empirical testing, we select effective explainers from the macroeconomic model

as fundamental drivers of the property price. After the estimated price is generated

In Hong Kong, the common ways of political measures affecting the property market include,

a) LTV ratio-a market barrier

To maintain stable and safe credit situation in the property sector, a traditional tool actively

employed is the LTV ratio (Wong et al, 2011). For instance, a rise in the required LTV increases

the amount of credit available to borrowers with a given level of assets for a down payment,

speeding up mortgage lending and property purchases. LTV brings message to the public about

the mass market segment risk level. However, as more assets are accumulated, the effect may

erode.

b) Stamp Duty

The government has imposed several stamp duty measures and stamp duty usually suppress

demand and lower the price in short term. It effectively increases the cost of transaction and was

supposed to reduce the incentive to do flipping. The stamp duty tax in Hong Kong includes,


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i) Normal Stamp duty

ii) ad valorem stamp duty (AVD)

iii) Special Stamp Duty (SSD)

iv) Buyers Stamp duty (BSD)

c) Land Supply

Land supply refer to the auction performance. Compared to choosing apartment supply, land

supply drives property supply and is more influential in a way that it sends out fiscal message

from the government that affecting the price expectation and is more concentrated in effect

because completion of property spread over years. It is already included in the macro model as it

is a varying quantity.

Note that the first two measure, LTV and Stamp duty are not frequently adjusted, it is reasonable

in practice to adopt event study and consider period around the implementation of policy. We

will investigate the transaction volume and price movement in the empirical session.

Formally speaking, we are employing the co-integration estimation methodology. Unlike the

frequently used linear regression, a co-integration estimation methodology is a two-stage

regression reveals not only correlation between variables, but also the time series autocorrelation

and stochastic drift. First, the long run co-integrating relationship among the variables will be

estimated. We are now using the regression result from the empirical test on the macro line. Next,

an error correction equation would be used to estimate the short run dynamic relationship. It is a

regression model with the change in price as dependent variable and change of fundamental

factors as independent variables. One of the special independent variable is the residual from the


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first equation. It is representing the deviation of actual price from our model macro price. As

mentioned that LTV and stamp duty are stationary policy variables, we can include them in our

second equation. The model is significant and explains the fundamental effects. The price

generated by the model is close to reality.

To show the short term price dynamics, the corresponding error correction model is represented

as,

= + 1 + 1 + 2

where1= is the error term, representing the deviation between actual price andequilibrium price. Note that here we added the two stationary variables LTV and SDT. The most

important estimate is , which reveals the efficiency in the sense that it is the speed ofadjustment to the long run equilibrium.


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VI. Volatility Measure

As the fundamental economic factors explain the price movement in absolute term, we have to

find a way to explain the volatility of the price movement. We use the fundamental model to

estimate the mean price of each time interval, then we extract the residual from it. It is necessary

because if we just look at the price itself, the volatility composes also the macroeconomic factors.

For example, in a rapidly blooming city, the volatility tends to be high because of rising price.

However in this part, we want to isolate those predicted factors and consider only the noise

component (the error). The residual is an estimator for the error in the true model. Then, we

calculate the volatility of it. Note that our hypothesis is that the volatility varies with time, due to

other time-changing factors. So, we divide the residual sample into numbers of group according

to their time. Say, we group every 12month residual together, and calculate the corresponding

volatility. Then, I try to regress them against various social-economic factors. Here, we show the

factors that may be relevant to the volatility of the error.

a) Wealth distribution

The market barrier of the real estate market is rather high (as determined by price), only

individual with certain wealth level (or credit, which is associated with wealth also) can enter the

market. Not just about the number of market participant, but wealth distribution also related to

liquidity, credit level and investment incentive. Thus, the wealth distribution can be a relative

measure of sensitivity of investors towards macroeconomic changes and price movement.

Assume the market barrier with respect to wealth is not set in the middle but somewhere lie

around more wealth group.That means people left to the barrier can actively participate in the

real estate market. In an economy with moderately even wealth distribution, we expect the


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volatility should be relatively low. Assume the total wealth of the whole city is a constant, when

there is a more average wealth distribution, the purchasing power of each individual would be

associated with small deviation. Then, the tail of distribution is thinner. While in the case of

uneven distribution, we may expect more market activities are induced by a larger group of

participators (a thicker tail). Note that the income distribution is different from general wealth

level. When general wealth level increase, property price also increases, so the market barrier is

shifting simultaneously with the wealth distribution. This effect would be accounted by the

macroeconomic regression. Again the income distribution concern the volatility of the residual

after removing the effect of other economic factors.

b) Intermediate-Brokerage firm

Brokers play an important role in information transfer and market making. It facilitates trade and

push transaction (increase sensitivity). Due to their commission salary, their existence tends to

make the trade willingness become negatively skewed (imagine a probability distribution

describing the willingness of trade). So, when number of brokers should be proportional to the

volatility. Also, the number of brokers reflects the participation of the whole economy into the

property market.

c) Number of Transaction per asset number

Number of transaction together with number/commission of housing agents/intermediate reflect

market efficiency and friction. Friction tends to decrease when market is blooming. First, more

people will engage in the real estate brokerage business as commission in absolute term is higher.

Second, transfer process become shorter and more frequent as the portion of speculation become

larger. In the stage of recession, friction increase and due to preference theory people tend to


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retain the existing investment position. Combining two effects, one may expect the property

price follow an error term which is consist of a wiener process with a lower bound. Number of

transaction tends to be high when price movement change rapidly (internal/underlying value hit a

certain level). In order words, Number of transaction drives volatility. However, low number of

transaction may imply high volatility in the near future and usually it is associated with price

drop. As underlying value moves in a continuous manner, while prices are recorded once

transaction is made in a discrete manner, we may expect price jump within small time interval.

This effect is more substantial in high friction market, which is in the case of real estate,

especially in the state of recession.

d) Vacancy rate

Some vacancies are intentional and aim at speculation. Even for natural vacancy, the rate should

be proportional to the volatility as the transaction cost and speed is higher for both case. When

investors observe some price change, it would be easier for them to do the trade with a vacant

apartment than an occupied apartment.

e) Absolute value of Previous Price Change

Assume momentum exists, a large change of actual price should be responsible for the increase

in volatility in the later periods.

f) Volatility of Stock Market & investment environment

As a way to quantify the investment behavior and risk-attitude over an economy, I use the stock

market as a proxy. I choose quantities include volatility of market index, amount of short-selling,

total margin account value. It is a way to access the likelihood of general investors to participate

into speculation and price tracking.


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VII. Empirical Testing-Using Hong Kong as an Example

Normally, if we calculate price-to-rent ratio across different property classes, they should give

similar results. However, it may not be a case in Hong Kong. A rising trend of price-to-rent ratio

has been observed since 2003. Although similar trend is also observed in the overall markets in

other cities in Mainland China, the abnormally high ratio is concentrated in the high-end and

larger residential units in Hong Kong. That is, the ratio rises much more significantly and rapidly

in the market of large and high-end property. In 2005, the price-to-rent ration of large premises

(Class C-E) exceed the record high while there is only average increase for the smaller, mass-

market units (Class A-B).

As before, we measure the affordability as price to income ratio. Housing affordability worsened

since 2004, especially in the high-end market. Although the ratio is very high, the mass market

segment is still more affordable compared to the peak in 1990s. Around the end of 2007, the

prices relative to the average household disposable income elevated rapidly, and it seems to be

more significant in the luxury segment (Classes D-E). Under the enormous amount of

quantitative easing, the hot money tends to drive up the price while the income growth is not

significant. The spike of price-to-income ratio is cultivated in the circumstance of extraordinarily

low real interest rates. Up till now, the price-to-income ratio in Hong Kong is among the highest

compared to other Chinese cities.

Since 2003, the increase in supply in the mass market segment become lower. At the same time,

however, the vacancy rate tends to increase in the luxury market. In fact, land developers

concentrate in the construction of larger and more profitable units (Class D-E) instead of smaller


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flats since around 2008. With the robust growth of China economy and relaxed constraints

towards investment from China, prices react vigorously to the shortage and strong demand.

The high end market seems to be standing at a special position in the whole property market.

Compared to other segments, the luxury classes record more noticeable price growth relative to

average income and rent metrics. This increases the risk of housing bubble in the high-end large

units.

A. Determination of Market Equilibrium

In the chapter of Microeconomic model, I can rephrase our model into two directions; equating

demand and supply, and equating rent and annual owning cost. Fundamentally, they share the

same concept of market equilibrium and competition between rental market and purchasing

market. For the sake of simplicity and information accessibility, I choose the latter to calculate

the micro equilibrium.

Under the assumption of no arbitrage and frictionless equilibrium, the following condition holds,

= whereRtis rent, is benchmark house price and is the cost of ownership ratio relative to thehouse value. From the session of cash flow model, we evaluate as,

= + + +

For the risk free rate, , we use the five-year yield of Exchange Fund Notes. The property tax(named rate in Hong Kong) are approximately 0.08% of the property value. In fact, it is 5% (for

the whole modelling period) of the rateable value of the property which is an estimation by the


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government. For mortgage rate, I use HSBC prime rate-2%, which is the general mortgage rate

indicator of the city. For maintenance and depreciation, it is estimated to be 2.5% (by Harding,

Rosenthal, and Sirmans, 2007). For expectation, we use a constant growth of geometric mean of

historical return. For risk premium, it is assumed to be a product of market geometric mean

return and . is calculated with respect to Hang Seng Index.

The result is originally in monetary term and then rescaled to index for comparison. Again, the

equilibrium price reflect true value of the property while the true price engages macro

information that may not aligned with the true value. From the graph, it is observed that during

recession, from 1998 to 2003 and just after financial crisis for example, the macro information

bring down the price and underestimated the implicit true value of property. During booming

time, around 1996-97 and the recovery after financial crisis (liquidity rose rapidly due to

0.0

50.0

100.0

150.0

200.0

250.0

300.0

1 2


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quantitative easing) for example, it is recorded that the actual price generally exceed the implicit

equilibrium.

The above graphs for US and UK market are generated by approximate data of rent and relevant

variables. Both show the similar phenomenon as Hong Kong market.

90

95

100

105

110

115

120

125

130

Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09

US Market

Actual Price Benchmark

90

100

110

120

130

140

150

Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09

UK Market

Actual Price Benchmark


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B. Regression on Macroeconomic Factors

A linear regression is used to include all the relevant variables mentioned in the previous section.

The model used is expressed as,

= 0 + 1 + 2 + 3 + 45 + +6 + 71 + 8 Below is the summary for the variables.

Variables Symbols Measure Source

GDP per

Capita

Gross Domestic Product percapita

Census and Statistics

Department (Censtatd)

Prime Rate HSBC prime rate/best lendingrate

Hong Kong Monetary

Authority (HKMA)

Liquidity Money supply (M3) Hong Kong MonetaryAuthority (HKMA)

Land Supply 5 Government auction result (5-quarter lag)

Land Registry of Hong Kong

Unemployment

rate

Unemployed population overwork force


Department (Censtatd)

1-lag Price

change

1 Percentage of price change overthe last quarter

Rating and Valuation

Department (RVD)

Risk-free rate Exchange Fund Notes Yield (5- Hong Kong Monetary


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year) Authority (HKMA)

Standardized coefficients:

Source Value

Standard

error t Pr> |t|

Lower bound

(95%)

Upper bound

(95%)

GDP per Capita0.278 0.223 1.245 0.219 -0.170 0.725

Prime Rate -

0.455 0.150 -3.030 0.004 -0.756 -0.154

Liquidity0.660 0.271 2.434 0.018 0.116 1.204

Land Supply0.301 0.116 2.590 0.012 0.068 0.535

Unemployment rate -

0.611 0.122 -4.998 < 0.0001 -0.856 -0.366

1-lag Price change0.133 0.072 1.856 0.069 -0.011 0.277

Risk-free rate0.741 0.235 3.158 0.003 0.270 1.211

Statistic

GDP per

Capita

Prime

Rate

Liquidit

y

Land

Supply

Unemployment

rate

1-lag price

change

Risk-free

rate

Toleran

ce 0.057 0.125 0.038 0.208 0.189 0.550 0.051


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VIF 17.640 7.987 26.067 4.799 5.288 1.818 19.492

Adjusted R2=0.825

Analysis of variance:

Source DF Sum of squares Mean squares F Pr> F

Model 8 90040.758 11255.095 37.512 < 0.0001

Error 54 16202.311 300.043

Corrected Total 62 106243.069


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C. Volatility Measure

There are two propositions from our argument:

1. There is a positive relationship between volatility and deviation (DEV) between micro

equilibrium and actual.

2. Volatility depends on social economic factors.

For the first proposition, we extract the absolute value of DEV and compare it to the volatility of

the error term from the macro model. To calculate the volatility, I use the standard deviation of

residuals of 4 quarters from the macro model to generate a series of volatility measure. The result

show some lag effect. I adjust the standard deviation to be 2-quarter lagged behind the DEV. The

following graph show the result.

For the whole period between 1999Q1 and 2013Q1, the correlation between them is 0.3315.

However if I calculate the correlation between 1999Q1 and 2009Q3, the correlation becomes

0.600. The samples seem to exhibit a good positive relationship.

0

10

20

30

40

50

60

r- -

Jl- r- -

Jl- r- -

Jl- r- -

Jl- r- -

Jl- r- -

Jl- r- -

Jl- r-

DEV vs 2-quarter lagged volatility

DEV 2-quarter lagged SD


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Our second proposition is the volatility depends on social-economic factors. I first investigate the

correlation matrix between those data. Note that the data are expressed in a 5-year base.

Proximity matrix (Pearson correlation coefficient):

SD GINI Brokerage Transaction/ass Vacancy stock volatility

SD 1.000 0.573 0.592 0.432 -0.251 0.600

GINI 0.573 1.000 0.540 0.326 -0.147 0.578

Brokerage 0.592 0.540 1.000 0.276 -0.276 0.289

Transaction/ass 0.432 0.326 0.276 1.000 -0.255 0.152

Vacancy -0.251 -0.147 -0.276 -0.255 1.000 -0.251

stock volatility 0.600 0.578 0.289 0.152 -0.251 1.000

The sample show some degree of dependence between variables. A regression model can be

constructed as follow,

Volatility of residual = Lm(GINI, BROK, ASPA, VACA,HSIV)

Where Lm stands for linear model, the summary of variables are as follow,

Variables Symbols Measure Source

Wealth distribution GINI Gini Index Census and Statistics

Department

(Censtatd)

Brokerage/Intermediate BROK Number of individuals engaged

in real estate brokerage or


Department


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agency (Censtatd)

Transaction per Asset

numbers

ASPA Number of agreement of sale

and purchase divided by total

property number


Department (RVD)

Vacancy VACA Vacancy rate is calculated by

dividing vacant property by total

property


Department (RVD)

Market Volatility HSIV Average volatility of Hang Seng

Index over 5-year period

Hang SengIndexes

Company Limited

The data are limited to 5-year period because the Gini Index can only be obtained by Census

each five years. The numerical model cannot be established because of the small number of

samples.


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VIII. Risk Model-Criteria for identifying substantial risk

A. Price misalignment

By considering various economic factors and asset price relationships, we can derive a

benchmark price with respect to the current economic fundamentals. Then, we can compare it

with the real property price and identify the degree of deviation from the benchmark.

Consider again the demand analysis: In equilibrium, the cost of owning a house should be equal

to the cost of renting a similar one, provided well-functioning rental and credit markets. If there

exist deviation between the two costs, the induced arbitrage will then affect rent level and

individual investment distribution, until a new equilibrium is reached. Essentially, it is the micro

model in the previous chapters.

Under the assumption of no arbitrage and frictionless equilibrium, the following condition holds,

= where is rent, is benchmark house price and is the cost of ownership ratio relative to thehouse value, which is measured as,

= + + + However, the assumption of low-cost arbitrage between owning and renting cannot stand in the

property market. There are significant costs including financial service fee, commissions and

moving cost. These transaction cost allow persistence of deviation between benchmark and

actual price. We then have to set criteria on the persistency and unstable deviation.


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This measurement can act as a foreseeing indicator of possible housing bubble, as the underlying

metric is calculated with a set of fundamental factors. Although we allow house price behavior

which is inconsistent with our benchmark, it should be noted that it is a sufficient but not

necessary condition for misalignment from fundamentals. One possible case is when both rent

and price increase at the same time, there is still chance of sharp decline during market deflation.

B. Deviation/volatility (DEV/VOL)-a bottleneck hypothesis

After calculating the deviation by finding the difference between , estimated equilibrium, andP, the actual price, we divide the result by the volatility. It should give us the potential/tendency

of price movement towards equilibrium. That is, a high DEV/VOL means a strong tendency

towards equilibrium while a low deviation allow persistent deviation until it hit a high level.

Although empirically such a drop after hitting a high DEV/VOL will bring the price back to

around equilibrium in a short period of time, note that a high DEV/VOL is not necessarily

related to bubble burst. For example, for a market with low volatility, the DEV/VOL will easily

get to a high level, so the deviation would be eliminated faster. For market with high volatility,

Deviation can rise to a high level without hitting a High DEV/VOL. When DEV/VOL is high

enough, then the price tends to drop back to equilibrium price. Such a sharp drop can be regarded

as bubble burst. The definition of HIGH and LOW varies with different city and time

interval. This can only be a hypothesis so far, as there is not enough samples of generally-

recognized bubble burst in history. However, it seems to be a reasonable measure.


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IX. Conclusion

This paper provides a systematic way to analysis the property market, in both microeconomic

and macroeconomic way. It is shown that price movements are generally induced by

macroeconomic factors. At the same time, microeconomic factors usually build a price floor and

price ceiling in growing and shrinking economy respectively. The deviation between them

maybe due to information asymmetry and market inefficiency. It is observed that investors tend

to utilize macroeconomic information to make pricing decision. It may be because of the high

accessibility and low information barrier for macroeconomic information, investors tend to adopt

the macro pricing model. On the other hand, there may exist certain barrier and distortion for

microeconomic factors, investor tend to have less utilization on micro model. A high transaction

cost and time consuming procedure may also prevent the price from going to the micro

equilibrium. Though, information asymmetry and market inefficiency are difficult to be

quantified and thus cannot be used to drive any constructive conclusion. This paper in another

way, however, try to relate such deviation with the volatility of the price after accounting for

predictable macro-driven movements. Simply putting, as the micro line provides boundary for

the macro line in different economic states, the larger the fluctuation around the macro line allow

a larger DEV. The paper empirically shows that in Hong Kong the volatility of the macro error

term has positive effect on the DEV. After knowing the importance of the volatility, I used

social-economic factors including wealth distribution, prosperity of brokerage business and

speculation tendency, to estimate the volatility. Due to a small data size, so far we can conclude

that there exists some positive relation between them but no concrete model has been drawn.

Using this relation, a new risk measure is proposed as DEV divided by volatility, compared to


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the existing one that use the DEV in absolute term. The measure exhibits rationality using the

positive correlation between volatility and DEV.

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An Analysis on Property Price Fluctuation YEUNG Yan Ho 260591446

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