Why U.S. Homeowners Should Not Hold The Market Portfolio

1. Why U.S. Homeowners Should Not Hold The Market Portfolio Guoliang Feng Ph.D. Candidate Department of Economics The George Washington University April 10th, 2013

2. Research Question how should consumption constrained households allocate wealth to housing and risk assets wealth house stock

3. Introduction 1. Problem and Motivation 2. Literature Review 3. Theory and Model of Homeower’s Problem 4. Empirical Tests and Data 5. Simulation 6. Conclusions and Implications

4. 1. Problem: Failure to own equities • Previous research focuses on portfolio problems of the unconstrained households • Consumption constrained households behave very differently • They consume far more housing than they would hold in diversified portfolios • They hold a single house as their only risk asset along with risk free assets • As wealth increases, they pay down mortgage rather than owning other risk assets

5. 1. Problem: Low participation rate • Empirical evidence from research

6. 1. Problem: Low equity holding Source: SCF chart book 2010

7. 1. Problem: Low equity holding Source: SCF 2010. stock share and riskless asset shares are their ratios in financial assets (without housing wealth). Renters are excluded.

8. 1. Problem: behavior vs theory • What households should do • Equity should be a significant share of the risk assets in a well diversified household portfolio • What households actually do • Households appear to be taking substantial unique risk in holding housing as a large single risk asset along with government guaranteed (often riskless) assets • Motivation: stockholding puzzle • Divergence between standard theoretical prediction and empirical evidence • The existing literature contributes little to explaining this puzzle

9. 1. Problem: contribution of this paper • Estimating housing return for 38 cities • Explain the low participation rates of equity market • Explain the weak representation of S&P500 as stock market • Introduce the diversification gains from holding individual stocks

10. 2. Literature : Positive analysis

11. 2. Literature : Normative analysis

12. 2.Literature : this paper builds on previous research • Make use of Correlation between housing and stock returns • Flavin and Yamashita (2002): use 4 cities’ housing return and S&P 500 to find no correlation • Pelizzon and Weber (2008) etc.: use market portfolios (not stocks) to calculate correlation • More accurate estimation of total housing returns • Method I: use HPI appreciation rate: Cocco (2005) • Method II: use returns of REITs: Yang et al (2012) • Method III: use returns of composite price index: Bucciol and Miniaci (2011) • Method IV: use constant CAP rate across MSAs: Flavin and Ymashita (2002 • My method: accurate estimate local housing return • Total housing returns=capitalization rate (CAP)+ appreciation rate

13. 3. Model • Variable definition • Mortgage schedule • Home equity return: Leveraged & Unleveraged • Model solving • Bench mark model (no leverage) • unconstrained households • Primary model (leverage) • consumption constrained households • Net Wealth=Housing Value*20% • proposition

14. 3.1 Model: variable definition 0.1

15. 3.2 Model: solve bench mark model Bench mark model: Unconstrained households’ maximization problem:

16. 3.2 Model: solve primary model Primary model: constrained households’ maximization problem

17. 3.3 Model: difference between two models Portfolio Returns primary model Bench mark model Portfolio Risk

18. 3.3 Model: propositions

19. 4. Empirical Tests and Data • asset and city definition • estimating home CAP rate • calculate home equity return • calculate variance-covariance matrix of asset returns

20. 4.1 asset definition • Household allocates wealth to financial assets and housing equity. • There are two models: choosing individual stocks or market portfolios. • Stocks: choose 10 representative stocks for 10 sectors • American Electric Power Co Inc. (AEP) • British Petroleum Plc. (BP) • DuPont Chemical (DD) • General Electric Co (GE) • International Business Machines (IBM) • Procter & Gamble Co (P&G) • Progressive Corp (PROG) • Universal Health Services Inc. (UHS) • Verizon Communications Inc. (VZ) • Wal-Mart Stores Inc. (WMT) • Market portfolios: only choose one of the 5 quasi mutual funds • market value-weighted portfolio (Vrate) • market equal-weighted portfolio (Erate) • S&P 500 Index (SP500) • 10-stock value-weighted portfolio (Vfund) • 10-stock equal-weighted portfolio (Efund))

21. 4.1 city definition • 38 cities

22. 4.2 estimating CAP rate

23. 4.2 Data • Data for computing total housing return • Mortgage interest rate: 30-year fixed mortgage rate, Freddie Mae • Annual property tax and cost rate: 2% • Data for CAP estimation: AHS • Data for Appreciation estimation: FHFA • Data for Stock and market portfolio: CRSP • Data for Inflation: BLS • Year: 1985-2009

24. 4.3 Data –Housing Return & Risk by City

25. 4.3 Data – return & risk of housing and other assets

26. 4.3 Data – return & risk of housing equity and other assets

27. 4.3 Data: Leveraged housing equity return fluctuation at Washington DC

28. 4.4 Data- negative correlation between housing and stock returns

29. 4.4 Data- negative correlation between housing and market portfolio returns

30. 4.4 Data: Covariance between fluctuation leveraged asset return: Washington DC

31. 4.4 Data: Covariance between fluctuation leveraged asset return: Houston

32. 4.4 Data: Covariance between fluctuation leveraged asset return: Detroit

33. 5. Simulation • Bench mark model Simulation • Case I: choose individual stocks and house • Case II: choose market portfolios and house • Primary Model Simulation • Case III: choose individual stocks and house • Case IV: choose market portfolios and house

34. 5. Simulation • Bench mark model Simulation • Case I: choose individual stocks and house • Case II: choose market portfolios and house • Primary Model Simulation • Case III: choose individual stocks and house • Case IV: choose market portfolios and house

35. 5.1 Bench mark model: case I (individual stocks)

36. 5. Simulation • Bench mark model Simulation • Case I: choose individual stocks and house • Case II: choose market portfolios and house • Primary Model Simulation • Case III: choose individual stocks and house • Case IV: choose market portfolios and house

37. 5.2 Bench mark model: case II (market portfolio)

38. Summary I • Households have different portfolios as they live in different cities • Low shares of housing in standard portfolio model can only be applied to the unconstrained households

39. 5. Simulation • Bench mark model Simulation • Case I: choose individual stocks and house • Case II: choose market portfolios and house • Primary Model Simulation • Case III: choose individual stocks and house • Case IV: choose market portfolios and house

40. 5.3 Primary model: case III (individual stocks)

41. 5.3 Primary model: case III (individual stocks)detail 1

42. 5.3 Primary model: case III (individual stocks)detail 2

43. 5. Simulation • Bench mark model Simulation • Case I: choose individual stocks and house • Case II: choose market portfolios and house • Primary Model Simulation • Case III: choose individual stocks and house • Case IV: choose market portfolios and house

44. 5.4 Primary model: case IV (market portfolio)

45. Summary II • Consumption constrained households have different optimal housing shares as city changes • Consumption constrained households hold much higher housing compared with those in fully diversification case • Negative correlation between housing return and stocks returns bring diversification benefit

46. 6. Conclusion • Households have different optimal portfolios as their cities change • Individual stocks can bring more diversification benefits than market portfolios do to household portfolios • Consumption constrained households face higher portfolio risk, hold higher housing than that for investment purpose alone

47. APPENDIX I: Portfolio performance in primary model: Washington DC

48. APPENDIX II: Portfolio performance in primary model: Houston

49. APPENDIX IIII: Portfolio performance in primary model: Detroit