1. Dynamic portfolio and mortgage choice for homeowners 0 Otto van Hemert, Frank de Jong Joost Driessen January 23th, 2006

2. Dynamic portfolio and mortgage choice for homeowners 1 Research Agenda For many investors, house is largest asset, and mortgage largest liability Research questions –How does optimal financial portfolio depend on housing tenure and size? –What mortgage type to finance your house? –How to hedge house price/future housing cost risk? –When to own, when to rent?

3. Dynamic portfolio and mortgage choice for homeowners 2 Main findings this paper Unconstrained investor: closed-form solution –Mean-variance tangency portfolio –Portfolio hedging real interest rate (/inflation) risk –Portfolio hedging house price risk –Leverage financial positions to get desired risk exposure total (financial + housing) wealth –Weights depend on effective housing wealth Constrained investor with mortgage choice –ARM alleviates short-sale constraint on cash –FRM alleviates short-sale constraint on 20y bond –Risk-tolerant homeowner chooses ARM –Risk-averse homeowner chooses FRM (or hybrid)

4. Dynamic portfolio and mortgage choice for homeowners 3 Two complementing papers Dynamic portfolio and mortgage choice for homeowners –Utility from terminal wealth –Capitalised labor income –No tenure choice –Fixed house size Implicit closed-form solution unrestricted case enhancing intuition restricted case Interpretation: retired or wealthy investor Life-cycle housing and portfolio choice with bond markets –Full-fledged life-cycle model –Stochastic labor income –Choice renting/owning –House size choice Brute force solution with aid supercomputer Builds on intuition acquired in other paper

5. Dynamic portfolio and mortgage choice for homeowners 4 Related literature Brennan-Xia (2002,JF), Campbell-Viceira (2001,AER) –Portfolio choice with bonds. No house, no labor income. Flavin-Yamashita (2002,AER) –Static mean-variance setting. Little role for bonds, no advice on mortgage choice Cocco (2005,RFS), Yao-Zhang (2005,RFS) –Life-cycle model with house. Only cash and stocks as financial assets. No mortgage choice. Campbell-Cocco (2003,QJE) –Mortgage choice in life-cycle setup. No housing or portfolio choice. No persistent real interest rate shocks.

6. Dynamic portfolio and mortgage choice for homeowners 5 Investor’s objective At the investor solves: where utility is given by: with

7. Dynamic portfolio and mortgage choice for homeowners 6 Housing ratio We define We interpret financial wealth as including capitalised labor income and maintenance costs We typically think of housing to total wealth ratio in order of magnitude of 0.2 to 0.4

8. Dynamic portfolio and mortgage choice for homeowners 7 Price dynamics Stocks: Real riskless rate: Expected inflation rate: House price: Price level: Model extends Brennan and Xia (2002,JF) with house price process Market imp. rent: corr. for housing services

9. Dynamic portfolio and mortgage choice for homeowners 8 Th. II: cf sol. when no constraints [..] is blend of the two Brennan-Xia portfolios. 1) mean-variance tangency portfolio 2) portfolio hedging real interest rate (/inflation) risk originates from 3) portfolio hedging house price risk is leverage factor to obtain desired exposure for total portfolio Investor acts as if house is worth only because –Adjustment for PV(market imputed rent until T) –Take into account unhedgeable idiosyncratic house risk

10. Dynamic portfolio and mortgage choice for homeowners 9  (h,t) for  =3

11. Dynamic portfolio and mortgage choice for homeowners 10 Calibration asset price parameters Step 1: estimate term structure model –1973Q1-2003Q4 data on nominal interest rates and inflation –Kalman filter technique Step 2: determine correlations –residuals step 1 –1983Q1-2003Q4 data on stock and house prices

12. Dynamic portfolio and mortgage choice for homeowners 11 Implication bond price dynamics Nominal bond price dynamics: Half life shocks: 1.1 years Half life shocks: 12.6 years years 20-year bond has slightly larger exposure to shocks and much larger exposure to shocks $1 in 5-year bond, -$4.37/12.15 in 20-year bond real interest rate hedge without exp. inflation exposure

13. Dynamic portfolio and mortgage choice for homeowners 12 Unconstrained portfolio choice (  =3) Leverage & effective wealth effect clearly visible –In stock allocation; in allocation to different bonds 5y bond allocation positive for it has relative large negative exposure to real interest rate risk –Hedge against real int. rate risk; exploit risk premium

14. Dynamic portfolio and mortgage choice for homeowners 13 Constrained portfolio choice (  =3) Leverage & effective wealth effect clearly visible –In stock allocation; in duration of bond portfolio 20-year bond has slightly larger exposure to shocks and much larger exposure to shocks

15. Dynamic portfolio and mortgage choice for homeowners 14 Constrained Portfolio choice (T=20,  =3)

16. Dynamic portfolio and mortgage choice for homeowners 15 Mortgage choice Mortgage modeled as negative position in bond –Valued at market price –Costless rebalancing size and type Up to market value of the house Adjustable-rate mortgage (ARM): -cash Fixed-rate mortgage (FRM): -20y bond Hybrid mortgage (hybrid): -cash and -20y bond

17. Dynamic portfolio and mortgage choice for homeowners 16 Portfolio choice with a mortgage (  =3) Desire to leverage risk exposure Cash constraint binding ARM utility enhancing

18. Dynamic portfolio and mortgage choice for homeowners 17 Portfolio choice with a mortgage (  =7) 5y bond to hedge real interest rate 20y bond constraint binding FRM utility enhancing Hybrid mortgage even better!!!

19. Dynamic portfolio and mortgage choice for homeowners 18 Main findings Unconstrained investor: closed-form solution –Mean-variance tangency portfolio –Portfolio hedging real interest rate (/inflation) risk –Portfolio hedging house price risk –Leverage financial positions to get desired risk exposure total (financial + housing) wealth –Weights depend on effective housing wealth Constrained investor –ARM alleviates short-sale constraint on cash –FRM alleviates short-sale constraint on 20y bond –Risk-tolerant homeowner chooses ARM –Risk-averse homeowner chooses FRM (or hybrid)