An overview of the real estate market the Fisher-DiPasquale-Wheaton model 13 January 2011 1 Real Estate Market What is real estate? How big is the real estate sector? How does the market for the use of real estate differ from the market for real estate assets? In this lecture, our objectives are 1. to define real estate 2. to describe how the real estate sector operates within the economy 3. to distinguish between the market for real estate use (where space is rented or purchased for occupancy) and the market for real estate assets (where buildings and units are bought and sold as investment). The most common definition of real estate is the economy s stock of buildings, the land on which they are built, and all vacant land. These buildings are used either by firms, government, nonprofit organizations, and so on, as workplaces, or by households as places of residence. When defined this way, the value of all real estates easily makes up the largest single component of wealth of the citizens of the country. The yearly value of new buildings put in place represents an annual investment in the economy s stock of real estate capital. In Hong Kong and in many other places, the dollar value of these new buildings also has been the largest single category of the economy s investment for many years. In Hong Kong, since 1980 and up until 1995, investment in new buildings accounted for roughly 24% of GDP and 61% of all investment on average. During the 1990s, the real estate and construction share of the total stock market capitalization was Reading: chapter 1. Urban Economics and Real Estate Markets by D. DiPasquale and W. Wheaton, 1
estimated at 45%. Furthermore, over 35% of bank lending is to the real estate and construction sector. These numbers have gone down quite a bit since the collapse of the real estate market in Hong Kong following the Asian financial crisis. Still, real estate remains a very important sector in the Hong Kong economy. And it was precisely the collapse in property values in 1997-98 and the further decline in the few years thereafter that was thought to be a major cause for the recession and the fiscal problem facing the government until the recovery in 2004. During the peak of the real estate bubble in the 1990s, over 33% of government revenues came from real estate and construction related items. During the early 2000s, however, with the decline in the real estate market, the revenue the government was able to extract from the sector was for all practical purposes minimal, and was commonly attributed as the main culprit of the fiscal problem facing the government then. It is important to note that land is not counted as part of investment or GDP since it is not a produced commodity. On the other hand, land is certainly an asset, and so the value of land beneath buildings should be counted as part of the stock of the economy s real estate and the wealth of the citizens. The distinction between real estate as space and real estate as an asset is most clear when buildings are not occupied by their owners. The needs for tenants and the type and the quality of buildings available determine the rent for space in the market for property use. At the same time, buildings may be bought, sold, or exchanged between investors. These transactions occur in the capital market and determine the asset price of space. In this lecture, we present a simple analytic framework which illustrates the connection between the market for real estate space (the property market) and the market for real estate assets (the asset and the capital market). As we will argue later, this same approach can be used for owner-occupied real estate, where the user of space is also the investor in the asset. The approach of separating the real estate market into two separate markets helps to clarify how different forces influence this important sector. If, for example, there is a sudden increase in demand by foreign investors to purchase Hong Kong office buildings, the impact on rents is very different than if firms suddenly decide that they wish to rent more office space for their use. A reduction in mortgage rates has just the opposite effect on house prices from that caused by a reduction in short-term rates for construction financing. Distinguishing between property and capital markets provides a clearer understanding of how such forces operate in the real estate sector as a whole. 2
2 Flow/Stock The rainfall in an hour is a flow, whereas the amount of water in the reservoir is a stock. How much you earn in a month is a flow, whereas how much money you have in the bank is a stock. How many classes you take this semester is a flow, whereas how many credits you have earned is a stock. A stock is the quantity of the object at a point in time, whileaflow is how much that quantity has changed per unit of time. The entirety of buildings in existence at the beginning of the year is the stock of buildings. The new construction completed during the year, which is commonly known as gross real estate investment, constitutes the flow of new buildings. The net flow of buildings during the year is the gross flow of buildings completed minus building depreciation the part of the building stock lost due to physical depreciation. At the end of the year then, the stock of building is the beginning of the year stock plus the net flow during the year. The relationship may be written as S t+1 = S t δs t + C t, where S t+1 and S t denote, respectively, the stock of building at the end of year t and the stock of building at the beginning of year t, δ the rate of physical depreciation, and C t new construction completed during the year. In the above, we assume that physical depreciation is always a constant fraction of the existing stock, a common assumption in economic analysis. 3 The markets for real estate assets and real estate use The four quadrants of figure 1 present our first analysis of the real estate market. The analysis is due to Jeffrey Fisher, Denise DiPasquale, and William Wheaton (the FDW model). Assume for the moment that all real estate in the economy is owned by investors who lease out space for rental income. 3.1 The property market The northeast quadrant depicts the rental market for property. We plot the quantity of real estate (in sq.ft. or whatever physical unit) on the x-axis and rent (per sq. ft., over one-period of time) on the y-axis. There is a downward sloping demand curve for space, given the state of the economy, denoted as D (r, Economy). 3
Figure 1: The FDW model 4
Movement along the curve depicts how much space would be demanded, as measured on the x-axis, given a particular rent, as measured on the y-axis. If the economy changes, then the entire curve shifts. For instance, an upward shift occurs with a population increase or an increase in income from which more space is demanded for the same rent. On the other hand, economic decline causes a downward shift of D (r, Economy), with the reverse implications. In equilibrium the demand for space, D (r, Economy), is equal to the stock of space, S. Thus rent, r, must be determined so that D (r, Economy) =S. The stock of space at a given point in time is more or less fixed, as determined by the history of investment. The equilibrium condition mainly serves to pin down the level of rent with a given stock of real estate. With this rent for the use of space, we then move to the asset market in the northwest quadrant. 3.2 The asset market: valuation Suppose the asset depreciates at the rate δ; that is, a fraction δ of the asset is lost in each time period due to wear and tear. Then, beginning with 1 unit of theassetinperiod1,1 δ units will survive to period 2, (1 δ) 2 will survive to period 3, etc. Say one unit of the asset generates a rental income equal to r in each period. If we begin with one unit of the asset in period 1, the stream of income generated by it is given by period 1 2 3 4... rental income r r (1 δ) r (1 δ) 2 r (1 δ) 3... Let i equal to the (risk adjusted) interest rate. Then the sum of the present values of rental income generated by the asset is P = r + r 1 δ 1+i = r + rγ + rγ 2 + rγ 3 +... (1 δ)2 δ)3 + r 2 + r(1 (1 + i) (1 + i) 3 +... where γ = 1 δ. Dividing both sides of the equation by γ, 1+i P = r γ γ + r + rγ + rγ2 +... P γ = r γ + P P = r + P γ P = r 1 γ. Next use the definition of γ, P = r 1 1 δ 1+i = r 1+i 1+δ 1+i 5 = r i+δ 1+i = 1+i i + δ r ' r i + δ
The above says that the present value of rental incomes generated by one unit of real estate is equal to the rent per unit of space divided by the sum of the interest rate and the rate of depreciation. The sum i + δ may be referred to as the capitalization rate for real estate, governing how a per period rent is capitalized into an asset price. The northwest quadrant of figure 1 represents the first part of the asset market. The x-axis depicts asset price and the y-axis rental income. The ray emanating from the origin, which has a slope equal to i + δ, the capitalization rate for real estate assets, governs how rental income on the y-axis should be translated into real estate asset values on the x-axis. The capitalization rate is nothing but the ratio of rent-to-price, i + δ = r P, which is the yield that investors demand in order to hold real estate assets. Why? Say asset price P > r ; that is, the capitalized rental income of real i+δ estate falls below the asset price. In this case, an investor who currently holds real estate assets in her portfolio can increase her wealth by disinvesting in these assets. By selling a unit of real estate asset, she will receive a payment equal to P that exceeds what she may earn in rental income over time by holding the real estate. The demand for real estate assets then drops to 0, exceeding the fixed supply of real estate asset at the given point in time. Conversely if P< r, the demand for real estate asset will rise to infinity, surely exceeding i+δ the fixed supply, as investors can pay a price P for an asset which will generate a stream of rental income that is greater than the cost of investment. For the real estate market to be in equilibrium, we must then have P = r i + δ. Thus, points on the ray in the northwest quadrant are all combinations of (P, r) that ensure the equality of demand and supply in the real estate asset market. Now given the equilibrium rental on the y-axis determined in northeast quadrant, the P = r ray in the northwest quadrant then yields the equilibrium i+δ real estate asset price on the x-axis. To see how the equilibrium asset price affects property development, we turn to the market for property development in the southwest quadrant. 3.3 The asset market: construction The stock of real estate asset changes over time because of new construction and because of physical depreciation. 6
Figure 2: Zero profit in property development How many new buildings would property developers like to build in each period of time? Say property development is perfectly competitive with free entry, meaning that any firms are free to enter and exit the industry. If one unit of real estate asset commands a price P that exceeds the cost (including the normal profit required) to construct a new unit, there is excess profit tobe made. Entry will take place until all such excess profits are wiped out. When the property development industry in equilibrium, we must have P = f (C), where f (C) denotes the unit cost to build one unit of real estate and C the units of real estate constructed in the given period; i.e., gross investment in real estate. We shall assume that construction exhibits decreasing returns to scale, meaning that the unit cost rises with the volume of construction. Why? Construction bottlenecks, scarce land and skilled labor, and other impediments to development may all be reasons for the unit construction cost to go up with the volume of development attempted. Under the decreasing returns assumption, the function f (C) is positively sloped. See figure 2. In the southwest quadrant of figure 1, we depict the equilibrium condition in the property development industry. The x-axis measures real estate asset price, whereas the y-axis measures new construction (in sq.ft.). For given volumes of new construction measured on the y-axis, the ray f (C) maps the real estate asset price that ensures the property development industry is in equilibrium. 7
We may next trace out the effect of the equilibrium asset price determined in the asset market depicted in the northwest quadrant on the volume of new construction by drawing a line starting at the equilibrium asset price on the x-axis to the f (C) ray and then to the y-axis. 3.4 Property market: stock adjustment The FDW analysis is a static analysis, meaning that it applies to a situation where quantities, rents, and prices are unchanging over time once they all settle down to equilibrium. This presumption makes sense. Remember that the analysis begins with assuming some demand curve for real estate space that is unchanging over time. If demand is unchanging over time, it is only reasonable that eventually, rents, prices, and the quantities of real estate should all be unchanging over time too once equilibrium in the various markets is reached. If the equilibrium quantity of real estate space to be rented is unchanging over time, the stock of real estate space/asset too should stay unchanging from one period to the next, as the two are one and the same. Recall the stock-flow relationship between the stock of real estate space/asset, depreciation, and new construction: S t+1 = S t δs t + C t, Rewrite the relationship as S t+1 S t = δs t + C t. The left hand side is the change in the stock of real estate in period t. Ifthere is no change in the stock of real estate during the period, 0= δs t + C t C t = δs t. This relationship says that once we have reached the point where the stock is unchanging over time, new construction in each period is just equal to the real estate lost due to physical depreciation. In this case, new construction just suffices to replace the depreciated stock. In economics, we say that the industry is in a steady state when this relationship holds. It is useful write the relationship as S = C δ, which relates new construction, C, to the stock of real estate, S, that is consistent with new construction just sufficient to replace the depreciated stock so as to leave the stock unchanging over time. In the southeast quadrant of figure 1, we measure on the x-axis the stock of real estate, S, andonthey-axisnew construction, C. TherayS = C depicts the relationship between S and C that δ ensures that new construction just suffices to replace the depreciated stock. 8
Then we may draw a line starting from the level of equilibrium construction determined in the market for property development in the southwest quadrant to the ray S = C, and then to the x-axis to yield the steady-state stock of real δ estate consistent with the equilibrium volume of construction. If this stock is just equal to the stock of real estate we assume to be in existence when we begin the analysis of the rental market in northeast quadrant, the market for real estate use (the property market), the market for real estate investment (the asset market), and the market for new construction (the property development market) are all in equilibrium. 3.5 Summing up The analysis assumes as given a demand curve for real estate use, a capitalization rate for rental income, i+δ, a function for the unit cost for new construction, f (C), and a rate of physical depreciation. Then the analysis determines the equilibrium stock of real estate, S, the equilibrium rental, r, the equilibrium asset price P, and the equilibrium volume of new construction C. Equilibrium is obtained at a stock in the northeast quadrant that eventually results in the same stock in the southeast quadrant. That is, when we have a rectangle that is just tangent to the demand curve in the northeast quadrant, with the three other corners of the rectangle cutting the respective rays in the three other quadrants. 3.6 Owner occupied real estate How does all of this work in the case of real estate that is mainly occupied by its owners? Think of a household purchasing a flat for P,paysD as down payment and takes out a mortgage of M; i.e., D + M = P. The interest payment is i M per period of time. The opportunity cost of the equity tied up in the flat, i.e., the forgone interest income is i D per time period. All together the amount is i M + i D = i P In each period of time, the flat depreciates at the rate of δ as it ages. That is, if the flat is worth P this period, the flat will only worth (1 δ) P next period. This is like the household having spent P (1 δ) P = δ P to purchase housing service in the period. The total cost of acquiring housing service for the period is therefore r I = i P + δ P =(i + δ) P. 9
Figure 3: Imputed rent and Price in Owner Occupied Housing We call this the imputed rent for owner-occupied housing. The household does not pay rent in name, but the cost of housing per period of time (out of pocket expense plus the implicit cost) is in effect a rent if rent is defined as the cost to purchase housing service per time period. If the household chooses to rent, the cost is an actual out-of-pocket expense paid to the landlord. If the household chooses to own, the cost is the sum of mortgage interest payment and the implicit costs of forgone interest income and depreciation. There should be the same amount whether the household rents or owns. Otherwise, there exist arbitrage opportunities; either all households want to rent or to own. The last conclusion hinges on the assumption of a perfect capital market. In the imperfect capital market of the real world, the costs to rent and to own could be different. Whatever, the equality of the market rental and the imputed rent of owner-occupied housing would be a close enough approximation to reality. And we should adopt this presumption in the analysis to follow. 3.6.1 FDW model with owner-occupied housing The four quadrants of the model still hold, but asset prices and rents are determined by the same market participants - the owner occupants. In the 1st quadrant, the demand for flats depends on population income the annual costs of owning a home the imputed rent 10
Figure 4: An increase in real estate demand A population increase shifts the demand curve out. With a greater demand and a fixed stock of housing units, the annual payment to occupy a flat must rise to choke off the excess demand. The northwest quadrant translates this payment into a higher actual price that households are willing to pay for the flat. Lower interest rates imply that with the same annual payment (imputed rent), households can afford and be willing to pay a higher purchase (asset) price. With owner-occupied real estate, decisions by the user-owner determine both (imputed) rent and price. These decisions are influenced by the same economic and capital market conditions that influence rental properties. Effectively owner occupiers have the same investment motives as the owners of rental property. Once the purchased price is determined, then new housing development and eventually a new equilibrium stock of space follow in the other quadrants. The same analysis can be applied to the case of corporate-owned and -occupied industrial or office space. The demand for this space is determined by the annual cost of owning it (imputed rent) as well as the number and size of firms in the market. In equilibrium, the annual cost of owning (imputed rent) equates demand with the fixed stock of office or industrial space. The cost of capital for the corporation (capitalization rate) converts this annual cost into the asset price that corporations are willing to pay for the space. 11
Figure 5: A decline in interest rate 12