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Article Excerpt
Recent analyses have suggested the irrationality of Australian and U.S. office property investors in that they have failed to raise capitalization rates sufficiently at rental cyclical peaks to account for the obvious mean reversion in real rents and thus have significantly overvalued properties. In this article, we present a model of capitalization rates and explain U.K. office and retail cap rates in an error correction framework. We demonstrate that our proxies for expected real rental growth do, in fact, forecast future real growth and that cap rates reflect rational expectations of mean reversion in future real cash flows. Moreover, property cap rates are linked to the equity capitalization rate (dividend/price ratio) and expected real dividend growth in the expected manner.
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A capitalization rate is the ratio of current cash flow to value or the inverse of the price-earnings (or rent) ratio. Thus, capitalization rates tell us how assets are priced. A low capitalization rate indicates that investors are willing to pay a relatively large amount per current dollar cash flow, while a high capitalization rate indicates the reverse.
Property capitalization rates should be linked to capital market capitalization rates because all rates should incorporate the real default-free rate and reflect common risk factors. Capitalization rates should also be linked to the expected rate of growth in real cash flows. The higher the expected real growth is, the more investors will be willing to pay for a current dollar of cash flow and thus the lower the cap rate will be. For property the cash flow is rent: for stocks the cash flow is dividends. Thus, the movement of real estate capitalization rates relative to stock market capitalization rates should be negatively related to expected real rental growth, but positively related to expected real dividend growth.
Real property cash flows per unit space have been shown to be mean or trend-reverting series in Australia (Hendershott 1996) and the United States (Wheaton and Torto 1994). Figure 1 shows that real office and retail rents are also mean (trend in the case of retail) reverting in the United Kingdom. This empirical regularity has logical underpinnings. Surging real rents on newly written leases owing, say, to rising demand for space, should be partially reversing when existing tenants face these higher rates at renewal. Moreover, higher real rents mean higher real property values and thus increased development. The additional space, too, will act to reverse the initial rise in real rents.
[FIGURE 1 OMITTED]
Hendershott (2000) and Sivitanides et al. (2001) argue that Australian and U.S. investors have not built the "obvious" mean reversion of real rents into their forecasts of real rental growth. As a result, investors have overvalued property at rental cyclical peaks (used too low cap rates) and undervalued them at cyclical troughs. That is, investors have behaved irrationally. Providing evidence on this aspect of the rationality of the U.K. property markets is the primary goal of the present article. (1)
This article estimates both a long-run equilibrium cap rate relationship and a short-run adjustment process toward equilibrium. The next section describes the link between property cap rates and stock market cap rates. The third section reviews the key literature, the fourth section presents an error correction model and the fifth section describes data sources and expectation proxies. Results for the U.K. office and retail markets are reported in the sixth and seventh sections. The final section highlights our major findings and presents additional interpretations and evidence.
Modeling the Capitalization Rate
We motivate our empirical estimation with a derivation based on the simple Gordon growth model. If net rents are expected to grow at a constant rate [G.sub.p], then [R.sub.p] is the (constant) required rate of return on property and rents adjust annually,
[K.sub.p] = [R.sub.p] - [g.sub.p] - [pi], (1)
where we have expressed the growth rate as the sum of expected general inflation [pi] and the expected growth in real rent on the property type [g.sub.p].
Based on a simplified Capital Asset Pricing Model we specify the required nominal return on property as the risk-free rate plus the property beta, w, times the difference between the market return (taken to be the required return on stocks [R.sub.s]) and the risk-free rate
[R.sub.p] = R[R.sub.b] + [pi] + w[[R.sub.s] - (R[R.sub.b] + [pi])], (2)
where the nominal risk-free rate is expressed as the real risk-free rate, R[R.sub.b], plus expected inflation. Assuming constant growth in real dividends and a constant required real equity return, the required nominal equity return can be expressed as the sum of the cap rate for corporate stocks (the dividend/price ratio) and the expected growth rate in dividends. Again, partitioning the growth rate into general inflation and real growth,
[R.sub.s] = [K.sub.s] + [g.sub.s] + [pi]. (3)
Substituting Equation (3) into Equation (2), the result into Equation (1), and canceling the inflation terms, we obtain
[K.sub.p] = w[K.sub.s] + w[g.sub.s] + (1 - w)R[R.sub.b] - [g.sub.p]. (4)
Of course, it is unlikely that real growth rates and future discount rates are expected to be constant forever at each point in time. Further, the United Kingdom has multiyear upward-only adjusting leases, not one-period up-or-down leases, and the market portfolio contains more than stocks. Thus, Equation (4) is an approximation that motivates our empirical estimation. The approximation suggests the following general relationship where the signs over the variables indicate the signs of partial derivatives with respect to the variables,
[K.sub.p] = [K.sub.p]([+.K.sub.s],[+.g.sub.s], R[+.R.sub.b], [-.g.sub.p],[+.w]). (5)
Unfortunately, only one of the five variables in this equation, the dividend/price ratio, is observed. Proxies for the others will be specified below. (2)
Literature
The early literature on modeling real estate cap rates emphasized a link to the bond market and estimated simple lag structures. For the United Kingdom, Hetherington (1988) modeled appraisal-based cap rates from Hillier Parker, and Key et al. (1994) modeled the U.K. all-property appraisal-based cap rate from the Investment Property Databank. Some early U.S. work recognized the links to the stock market as well. Both Evans (1990) and Ambrose and Nourse (1993) estimated the link between the S & P 500 and the ACLI market cap rates. Jud and Winkler (1995) and Viezer (1999) modeled market cap rates for property types from the National Real Estate Index, the former emphasizing links to both the bond and stock markets and the latter to the bond market only.
Sophisticated lag structures have been estimated only recently. Sivitanidou and Sivitanides (1999) use the National Real Estate Index (twice yearly from the end of 1985 to the end of 1995 for each of 17 MSAs) for office properties. They identify the discount rate and income growth expectations as the key components affecting cap rates. Both are affected by variables that could be time invariant or time variant. They consider two sets of variables: local office market effects and time-variant effects in the local office markets and the national capital market. A process of adjustment to equilibrium is specified.
The equilibrium cap rate [C.sup.e] is given by
[C.sub.jt.sup.e] = [a.sub.j][L.sub.j] + [b.sub.j]F(t),
where [L.sub.j] is a vector of metropolitan dummies (so that the estimated values of [a.sub.j] represent fixed local effects), F(t) represents time-variant effects, j denotes metropolitan areas and t is a time index.
The actual cap rate C is the equilibrium value plus error with autoregressive and random components,
[C.sub.jt] = [a.sub.j][L.sub.j] + [b.sub.j]F(t) + [[rho].sub.j][[epsilon].sub.jt-1] + [v.sub.jt],
where [[epsilon].sub.jt-1] = [C.sub.jt-1] - [C.sub.jt-1.sup.e], [rho] denotes the serial correlation coefficient and [v.sub.jt] is an independent random error term.
In the first set of estimations, the cap rates are modeled in panel with spatially varying intercepts, a deterministic time trend (F(t) = t/(1 + [t.sup.2])) with spatially variable coefficients and a spatially varying autoregressive error. The seemingly unrelated regressions (SUR) estimation procedure is used to deal with cross-sectionally correlated metropolitan-specific errors. The results show significant inter-market differences...
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