عدم نقدینگی، هزینه های معامله، و دوره برگزاری مطلوب برای دارایی واقعی: تئوری و کاربرد

Choosing the optimal holding period is an important part of real estate investment decisions, because “when to sell” affects “whether to buy”. This paper presents a theoretical model for such decision making. Our model indicates that the optimal holding period is affected by both systematic and non-systematic factors—market conditions (illiquidity and transaction cost) and property performance (return and return volatility). Other things being equal, higher illiquidity and transaction costs lead to longer holding periods, while higher return volatility implies shorter holding periods. Our empirical application suggests that the optimal holding period based on our model is quite consistent with previous empirical findings. In addition, we find that when illiquidity risk is incorporated the true real estate risk is significantly higher than the conventional risk estimate. Therefore, the current practice of real estate valuation, which is naively borrowed from finance theory, substantially underestimates real estate risk.

The real estate investment decision is not just “to buy, or not to buy”. It is as much “when to sell”. In fact, the two decisions are inherently interdependent, since the timing of the sale, which provides the single largest cash flow, critically affects the expected overall return of the investment. In the current practice, however, the issue of holding period for a real estate investment is basically a matter of arbitrary assumption. For example, a typical Discounted Cash Flow (DCF) analysis for commercial property valuation usually assumes a holding period of 10 years. A limited partnership may agree on the duration of the business to be a certain number of years. A private real estate equity fund may plan its mandatory liquidation date (extendable under certain condition) based on what is conventional in the industry. Whether such expected (ex ante) holding periods are economically or financially optimal is usually considered less important than and separate from deciding how much to pay for an asset (the valuation decision). Most investors understand that holding period affects investment performance. For instance, we know that real estate must be held long enough to mitigate illiquidity risk and high transaction costs. But how long must a property be held to achieve optimal performance? Is longer better, or is there an optimal holding period, at which time the expected (ex ante) risk-adjusted return is the highest? This is an important question because, to the extent that a property’s expected optimal performance determines the maximum valuation an investor should place on the property, finding the property’s ex ante optimal holding period is inseparable from the asset valuation decision. Classical finance theories argue that in an efficient market where asset returns over time are assumed to be independent and identically distributed (i.i.d.), holding period has no effect on an asset’s periodic (e.g. annualized) expected return and volatility. In other words, there is no optimal holding period for financial assets. Although the issue of i.i.d. remains debatable in the finance field, it is clear that the real estate market is not efficient and property returns are thus not i.i.d.1 The non-i.i.d. feature implies that real estate performance is holding period dependent. That is, the expected return and risk of holding a property for 1 year is different from the average annual return and risk of holding the property for multiple years. The purpose of this paper is to find out how ex ante holding periods affect the expected performance of a property, and to develop a theoretical framework that provides a formal analysis on an optimal holding period. Our analysis begins with a simple setting: a rational investor who has a mean–variance preference attempts to determine the appropriate price he is willing to bid on a property without overpaying for it. Since his valuation is determined by his expected performance of the investment, and the performance is holding period dependent, he first needs to determine the ex ante optimal holding period of the property before he can properly estimate the asset’s expected ex ante return and risk. His decision is determined by several competing effects: on one hand, due to high transaction cost and the difficulty involved in trading properties in general, he needs to hold the property long enough to achieve the desired investment return. On the other hand, holding the property for too long makes the future asset price (as well as income) much more uncertain; that is, it increases the risk of his investment. His objective, therefore, is to find the optimal holding time at which the expected risk-adjusted return is maximized. In order to solve this problem, he must first address two issues: (1) how does holding period affect real estate return and risk? (2) What is the proper measure for the risk-adjusted return? Presumably, such measure must integrate the effect of holding period, the uncertainty of future price, illiquidity risk, and transaction costs. The remainder of the paper is structured as follows. The next section provides a brief review of previous literature on the issue of real estate holding period. Section 3 presents an analysis that empirically examines the relationship between real estate performance and holding period. The findings of Section 3, in conjunction with recent developments in the literature, provide the foundation of our model in Section 4. Section 5 provides an empirical application of the model. Section 6 concludes.

If one accepts the fact that the real estate market is inefficient and property returns are not independent and identically distributed over time, then real estate investment performance cannot be properly measured without specifying the holding period. The expected optimal performance of a property corresponds to its ex ante optimal holding period. The decision of “how much to pay”, therefore, is affected by “when to sell”. Based on the premises that a rational investor has a mean–variance preference, this paper develops a closed-form formula of ex ante optimal holding period that maximizes the ex ante risk-adjusted return of a real estate investment. When applying our formula to empirical data, the range of optimal holding period estimated by the model is reasonably consistent with previous empirical findings. In addition, we find that, when illiquidity risk and non-i.i.d. nature of real estate returns are incorporated, the true real estate risk is about 2.5 times the conventional estimate from the NCREIF index, and is significantly higher than those reported by Giliberto (2003). It becomes clear that the current practice of real estate valuation, which ignores the non-i.i.d. nature of real estate returns and illiquidity risk, substantially underestimates the true risk of real estate investment. Knowledge of optimal holding period might potentially be useful in some common investment decisions. For example, it can provide a justification for setting the appropriate holding period of a target property in a standard DCF analysis. Second, such knowledge may provide a financial or economic justification for investors deciding on the appropriate liquidation date of a partnership or private equity fund. Third, as market conditions change, regular revision of the ex ante optimal holding period after acquisition helps investors to re-assess the pre-agreed liquidation date or to make appropriate sell versus hold decisions.