Competing Selling Strategies in the Housing Market

Abstract

Due to the heterogeneous nature of real estate assets, housing market is characterized by a sequential search and seller’s optimal strategies. This paper provides a side-by-side performance comparison of the two competing stopping rules (i.e, the reservation rule and the number rule) in the housing market. It demonstrates that the selling strategies by these two stopping rules are not mutually exclusive, and the optimal choice of the two strategies varies over market conditions. Our analyses reveal clear evidence that no strategy consistently outperforms the other under all market conditions. Therefore, a single selling strategy is likely to result in suboptimal selling outcomes, and the widely-used reservation rule in academic research is likely to result in biased findings. Furthermore, we identify the explicit impact of several supply and demand factors on the optimal trading outcome and provide rich insights into optimal selling strategies in the housing market.

Appendices

Appendix: I

Given that $\eta =(\overline {p}-R^{*})/(\overline {p}-\underline {p})$ in Eq. 6, we can obtain,

$$ 1-\eta=\frac{R^{*}-\underline{p}}{\overline{p}-\underline{p}} $$

(30)

In addition, we have,

$$ \mu_{M}\equiv E[{P}^{bid}]=\frac{\underline{p}+\overline{p}}{2} $$

(31)

$$ {\sigma^{2}_{M}}\equiv {Var}[{P}^{bid}]=\frac{(\overline{p}-\underline{p})^{2}}{12} $$

(32)

Since we have,

$$ \frac{\overline{p}+R^{*}}{2}=\frac{\overline{p}+\underline{p}}{2}+\sqrt{3}\left( \frac{R^{*}-\underline{p}}{\overline{p}-\underline{p}}\right)\sqrt{\frac{(\overline{p}-\underline{p})^{2}}{12}} $$

(33)

and,

$$ \sqrt{\frac{(\overline{p}-R^{*})^{2}}{12}}=\frac{\overline{p}-R^{*}}{\overline{p}-\underline{p}}\sqrt{{\frac{(\overline{p}-\underline{p})^{2}}{12}}} $$

(34)

From Eqs. 6, 8, 9, 30, 31 and 32, we can therefore rewrite Eqs. 33 and 34 as Eqs. 10 and 11.

Appendix: II

Since we have

$$ R^{*}=\frac{R^{*}+\overline{p}}{2}-\sqrt{3}{\times}{\frac{\overline{p}-R^{*}}{\overline{p}-\underline{p}}}{\times}{\frac{\overline{p}-\underline{p}}{2{\sqrt{3}}}} $$

(35)

From Eqs. 6, 8, and 32, we can have,

$$ R^{*}=E[P^{bid}|P^{bid}\ge{R^{*}}]-\sqrt{3}{\eta^{*}}{\sigma_{M}} $$

(36)

From Eq. 10, we can further have,

$$ R^{*}=\mu_{M}+\sqrt{3}(1-2{\eta^{*}}){\sigma_{M}} $$

(37)

Appendix: III

Since we have,

$$ x-E[P_{T_{n}}(\theta)]=(x-\underline{p})-\frac{\theta{n}(\overline{p}-\underline{p})}{\theta{n}+1} $$

(38)

Substituting Eq. 38 into Eq. 23 and simplifying it will result in Eq. 24. This derivation is consistent with Eq. 6 to 9 in Cheng et al. (2008).