Hedging housing price risks: some empirical evidence from the US

Abstract

We analyze household hedging costs and market liquidity of exchange traded options on a set of well-developed U.S. home price indexes allowing homeowners to hedge the downside risk of housing prices. We estimate empirically the impact of hedging costs on market liquidity of housing derivatives using prices from Case–Shiller Home Price Index (CSI) futures options and Barone-Adesi and Whaley [Efficient analytic approximation of American option values. J. Finance, 1987, 42, 301–320] simulations. We find that hedging costs significantly affect household savings resulting from hedging. We propose a new cost-based illiquidity measure for housing derivatives and link it with traditional contract-based liquidity measures in thinly traded derivatives markets. We document a negative relation between savings from hedging and our cost-based illiquidity measure. We further perform a series of robustness checks. Overall we suggest that the liquidity of exchange traded housing derivatives could benefit U.S. homeowners.

Keywords:

• Derivative market liquidity
• Household finance
• House price hedging
• Real estate derivatives
• Case–Shiller home price index

JEL Classification:

• D14
• G11
• G21
• H31

Acknowledgments

We thank Ke Tang (Editor), Yen-Cheng Chang, Tong Chen (ICFOD discussant), Yao-Min Chiang, Joao Cocco, Lauren Cohen, Eamonn D'Arcy, Marc Francke, Scott Fung, Robin Goodchild, Martin Hoesli, Eran Hoffman, Yuichiro Kawaguchi, Kuan-Cheng Ko (TFA discussant), Chung-Ming Kuan, John Kuong, Qingfu Liu, Daisuke Nagazato, Steffen Sebastian, Robert Shiller, James Shilling, Ke Tang, Walter Torous, Stefan Trück, Jun Uno, Yanzhi Wang, Rafal Wojakowski and seminar participants of The 7th International Conference on Futures and Other Derivatives (Fudan), The Econometric Society North Amercian Meetings 2018 (Davis), Econometric Society Meeting 2018 (Fudan), TFA 2018 (Taipei), Real Estate Derivative Summit 2017 (Zürich), FMA 2017 (Boston), The Econometric Society Meeting 2017 (Hong Kong), AsRES 2017 (Taichung), ERES 2016 (Regensburg), AREUEA 2015 (Washington DC), National Central University, National Chengchi University, National Taiwan University and Waseda University for their valuable comments. Special thanks to the late Sir James Mirrlees for his support throughout the project. We thank the AsRES for the best paper award. We also thank John Mannebach and Jireh Ray of the CME Group for their explanation of their real estate product data. Cheung gratefully acknowledges the Designated Research Grant (no. BAR800081301) of Waseda Business School, Waseda University. All errors are ours.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In 2015, there are no transactions of any housing index options listed in the Chicago Mercantile Exchange (CME) and only 93 futures were traded (see CME Exchange ADV Monthly Report, December 2015).

2 In January 2016, the average open interest of CME real estate futures is around 40, compared to 22 thousand weather-related futures, 7 million equity futures and 27 million energy futures (see CME Exchange ADV Monthly Report, January 2016).

3 Exogenous shocks occur from changes in either interest rates or wages. We consider homeowners whose homes would have been foreclosed due to income shocks. We estimate empirically the hedging benefits with unique sets of put option data.

4 We focus on options rather than futures contracts because increases in housing-prices would lead to potentially large losses for a homeowner if she has long futures positions. Furthermore, Shiller et al. (2014) analyze continuous workout mortgages which contain futures-like features. However, this CME option data covers only the period from 2006 to 2008.

5 We compute a 12-month rolling volatility of the S&P/Case–Shiller U.S. Composite index. While house prices were known to be volatile between 2006 and 2008, a similar level of volatility is observed during 2002–2005 and 2011–2014. We believe that our findings during 2006–2008 is not specific to only that period and could be generalized to other periods, as hedging cost also matters in other periods.

6 In our estimation, the monthly mortgage repayment for an average U.S. homeowner is USD 1361.04. This is based on our simulated average initial house price of USD $326080$ and a $20\mathrm{\%}$ down payment for a 30-year adjustable-rate mortgage.

7 Equivalently, one standard deviation decrease in our cost-based illiquidity measure will increase the number of contracts with trading by $5.9\mathrm{\%}=\frac{6.45\times 0.0227}{2.49}$ over its mean.

8 We use the S$\mathrm{\&}$P Case–Shiller Home Price Index and the Case–Shiller Index interchangeably throughout this paper.

9 Björk and Clapham (2002) perform some pricing of real estate index linked swaps. Englund et al. (2002) analyze hedging potential when trading housing indexes, while Hinkelman and Swidler (2008) investigate the impact of futures trading on house-price risk. Buttimer et al. (1997) develop a two-state model for pricing securities, dependent upon a real estate index and an interest rate. Banks et al. (2015) and Damianov and Escobari (2019) consider the problems of hedging housing price increases through buying property. In our framework, we consider house owners who already possess a house and want to buy a put option in order to hedge against declining house prices.

10 The S&P/CS New York City Home Price and the S&P/ CS Chicago Home Price Index are not for the MSAs. They represent customized metro areas that measure single-family home values in select counties with significant populations that commonly commute to New York or Chicago for employment purposes. (http://us.spindices.com/documents/methodologies/methodology-sp-cs-home-price-indices.pdf?force_download=true)

11 http://stats.bls.gov/bls/blswage.htm

12 Both markets are illiquid. In unreported results we find that during the 2006 to 2008 sample only less than $1\mathrm{\%}$ of days with trades.

13 Details of option availability, wages and treasury bond yield could be found in the appendix.

14 http://www.cmegroup.com/rulebook/CME/IV/400/419/419.pdf

15 Debt-to-income ratio is the monthly repayment divided by the monthly wage of a household when they apply for a mortgage. The ratio will not affect our results.

16 $O_c-O_b$ is ${\xi }_{H_T}$ in equation (A9(A9) $\begin{array}{rl}{P}_{s_{t+i}^{\xi }}& ={\mathbf{1}}_{W_{t+i}<M_{p_{t+i}}\left(r\right)}(H_{p_{t+i}}-H_{p_t}-I_{t+i}-{\xi }_{H_T})>0,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\\ i& =0,1,2,\dots ,n\mathrm{a}\mathrm{n}\mathrm{d}t=0,1,2,\dots ,n.\end{array}$(A9) ). Then profits described by equation (A7(A7) $\begin{array}{rl}{F}_{s_{t+i}}& ={\mathbf{1}}_{H_{p_{t+i}}>(H_{p_t}+I_{t+i})\wedge W_{t+i}<M_{p_{t+i}}\left(r\right)}(H_{p_{t+i}}-H_{p_t}-I_{t+i})>0,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\\ i& =0,1,2,\dots ,n\mathrm{a}\mathrm{n}\mathrm{d}t=0,1,2,\dots ,n,\end{array}$(A7) ), and equation (A9(A9) $\begin{array}{rl}{P}_{s_{t+i}^{\xi }}& ={\mathbf{1}}_{W_{t+i}<M_{p_{t+i}}\left(r\right)}(H_{p_{t+i}}-H_{p_t}-I_{t+i}-{\xi }_{H_T})>0,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\\ i& =0,1,2,\dots ,n\mathrm{a}\mathrm{n}\mathrm{d}t=0,1,2,\dots ,n.\end{array}$(A9) ) can be calculated by equation (6(6) $\begin{array}{r}Profits=H_{p_{t+i}}-H_{p_t}-\sum _{t=1}^m{I}_t-O_c+O_b,\end{array}$(6) ).

17 Similar to Dolls et al. (2012), we use 5$\mathrm{\%}$ as the income shock threshold. As the mean of the quarterly wages in the U.S. and other 9 locations is around USD 1,065, we generate normally distributed random errors with zero means such that income shocks would be less than or equal to USD 200 with a 99$\mathrm{\%}$ probability. As a robustness check, we also generate other sizes of income shocks, such as less than or equal USD 100 with a 99$\mathrm{\%}$ probability.

18 There is no assumption about the relationship between future price and spot price, but it still work if we assume the cost of carry relationship between the spot price and the future price, and the spot follows $\frac{\mathrm{d}S}{S}=\alpha \mathrm{d}t+\sigma \mathrm{d}z,$ where α is the expected relative spot price change, σ is the instantaneous standard deviation, and z is a Wiener process.

19 While some of these transaction prices are observable, we cannot perfectly match the agent in our model in each day with the transactions that take place in these cities.

20 There are two reasons for negative savings. The first is that households need to pay a liquidity premium, which increases the option costs. The second is that the Case–Shiller index's trend matters.

21 Similar to the expectation of the stock market, we assume that the household formulates their expectation based on a six-month historical index. The bubble expectations index level seems to be related to the change in a financial market over the prior six months (see Shiller 2000 for more evidences in stock markets). We also use a 5-year historical housing index to estimate the option benefits ex-ante and results are similar. They are available upon request.

Additional information

Funding

Cheung gratefully acknowledges the Japan Society for the Promotion of Science (JSPS) [Grant number 19K01744], research grants from Waseda Business School and Waseda University.