A discussion by: Vicente Cu ñ at Univ. Pompeu Fabra

1. Efficient portfolios when housing needs change over the life cycle.Loriana PelizzonGuglielmo Weber A discussion by: Vicente Cuñat Univ. Pompeu Fabra

2. Approach • Test whether household portfolios are efficient in a mean-variance setup, conditional on housing position • Housing position includes ownership and discounted future needs as a liability • Depending on net position home ownership is a net asset or a hedge against rent needs • Empirical negative correlation between housing and financial excess returns Efficient Portfolios…- Discussion by Vicente Cuñat

3. Approach • Households have some housing needs • Treat house ownership as a position in rents • Housing is a relatively illiquid asset, agents are unlikely to adjust it very often • While the discounted future rent needs of a household may vary continuously, the adjustment of housing wealth is likely to be infrequent • The gradual evolution of human capital also may make the optimal portfolio drift Efficient Portfolios…- Discussion by Vicente Cuñat

4. Approach • As housing needs change over the life cycle of a household, housing positions are likely to be imperfect hedges of housing rent, households may be underhoused or overhoused • Financial portfolios may be used to (imperfectly) hedge against unhedged housing risk Efficient Portfolios…- Discussion by Vicente Cuñat

5. Approach • The optimal position in financial assets would crucially depend on whether the household overhedge or underhedge in housing wealth • Financial assets help diversify both positive and negative positions, however, due to negative correlation higher optimal weight in risky assets for overhoused households • Financial portfolios that may seem inefficient by themselves may prove efficient as they serve as a hedge for housing wealth (and vice versa) Efficient Portfolios…- Discussion by Vicente Cuñat

6. Empirical Results • Households that are underhoused seem to be the ones that are closer to the efficient portfolio. I.e. a portfolio with a relatively low amount of stocks • Households that are overhoused are the ones with least efficient portfolios. They are the ones that hold more stock, but well below what they should Efficient Portfolios…- Discussion by Vicente Cuñat

7. Discounted Future Rent Needs These are annual equivalent of the future discounted rent needs of a representative household This is the profile, but there is a risk that the whole thing goes up or down, plus an expected growth rate If housing transactions were frictionless, these would be the desired housing sizes purely for hedging motives. Efficient Portfolios…- Discussion by Vicente Cuñat

8. Discounted Future Rent Needs Note that the housing consumption needs are surely a less smooth version of this profile. However the paper assumes a frictionless rental market. A way to see it is that you buy one home that hedges your housing needs and rent it to someone else, then rent your own house (and continuously adjust). Plus you may want to invest in housing Efficient Portfolios…- Discussion by Vicente Cuñat

9. Discounted Future Rent Needs Note that it is a very flat profile!! By buying a 700 (?) home the household is nearly hedged for life Buying a house of 680 and trading it up for another one of 710 gives a better hedge, but surely not worth it given transaction costs. Why are not all agents buying a 700 home? Efficient Portfolios…- Discussion by Vicente Cuñat

10. Home ownership leads to additional borrowing capacity • Buying a home is typically a highly leveraged operation, at least the first one • Households have rarely access to unsecured loans at low rates • It is only when they own a home that they can borrow at (close to) risk-less rates • Mortgage loans have relatively low risk and it is highly correlated with the performance of the individual portfolio so if anything the residual risk provides a hedge Efficient Portfolios…- Discussion by Vicente Cuñat

11. An Example E(R) Suppose that a young household with a sum of wealth of euro 50k. It faces borrowing constraints Point h represents investment in housing. The household has naturally a large negative position in h several times larger than its net financial wealth How can we represent this? h Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

12. An Example How can we represent this? It is like short selling several times their total wealth in housing and putting the proceeds in the risk free asset h E(R) Rf σ Effective position in h H Efficient Portfolios…- Discussion by Vicente Cuñat

13. An Example E(R) Putting all their wealth in housing is not feasible, as there are no houses of 50k. The unconstrained “market” portfolio is even less feasible (i.e. You need to find a house worth say 5k). Furthermore, this would be inefficient as it does not take into account the big negative h Not feasible h Not feasible Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

14. An Example E(R) One possibility is to invest in a combination of the market portfolio that excludes housing and the risk free asset This will provide some hedge but is unlikely to be the most efficient option The household is massively underhoused, it would still have a large negative position in h. Not feasible h Feasible Not feasible p Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

15. An Example E(R) H The household can instead buy a 250k home and borrow 200k, this is a standard mortgage deal and borrowing constraints should not operate. Graphically this is an investment in housing with a 5x leverage factor. By buying, the household is taking the symmetric position to the negative liability of rents h p Rm Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

16. An Example E(R) H Note that only a segment around H is feasible and not the whole line. This is determined by the minimum house size and the maximum mortgage that a bank would give to this household h p Rm Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

17. An Example Where do they end up? It basically depends on the size of the house that they bought Wherever they are they will start sliding down gradually, as their discounted expected rents rise (also total wealth will change leverage and rescale things) E(R) h overhoused Rf σ Rougly hedged Effective position in h Still underhoused H Efficient Portfolios…- Discussion by Vicente Cuñat

18. An Example That is H moves and pulls from the effective position of the household At the beginning H gets further down and to the right, at some point it starts returning E(R) h overhoused Rf σ Rougly hedged Effective position in h Still underhoused h Efficient Portfolios…- Discussion by Vicente Cuñat

19. E(R) An Example If the household can borrow a large multiple of its wealth as a mortgage, the right thing to do is to buy a 700 home, slide down and then up h Rf σ Effective position in h h Efficient Portfolios…- Discussion by Vicente Cuñat

20. E(R) An Example If the household has a limited mortgage capacity it would maximize it. Is it better to get a smaller house and diversify through financial assets? If the mortgage multiple is large, Probably not. Although the test may qualify the household as inefficient for not doing so h Rf σ Effective position in h h Efficient Portfolios…- Discussion by Vicente Cuñat

21. The asset side E(R) H Let´s concentrate on household that has just bought a house at full leverage and starts saving money h p Rm Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

22. The asset side E(R) H As time passes the household starts saving money they can pay back part of their mortgage and reduce their exposure to housing. h p Rm Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

23. The asset side E(R) H However, for high levels of leverage, it may be more efficient to keep as much as possible borrowed and invest in the stock market. (depends on where the market lies with respect to h) But it crucially depends on which side of the “mirror” we are!!! h p Rm Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

24. The asset side E(R) H But it crucially depends on which side of the “mirror” we are!!! On the asset side, stocks give diversification advantages with a negative correlation, on the liability side with a positive one! h p Rm Rf σ Efficient Portfolios…- Discussion by Vicente Cuñat

25. First and second order effects Still all of these considerations seem to be of a second order when compared with the decision on how big the house should be, and how much leverage to get Just get your housing decision right!! E(R) h Rf σ Effective position in h h Efficient Portfolios…- Discussion by Vicente Cuñat

26. Indivisibility Plus Access to Borrowing • The access to additional funds associated with buying a house is likely to play a role • Large discontinuities in feasible housing portfolios due to indivisibility, illiquidity and leverage • Some combinations of housing wealth are effectively unfeasible • home owners and the ones that do not borrow at all may behave very differently Efficient Portfolios…- Discussion by Vicente Cuñat

27. Housing wealth is illiquid in a particular way • Round trip costs of buying a home and selling it back 7% to 15%. • Equivalent costs for a mutual fund 1% to 4% • Hedge funds 2% to very high costs 20% or higher • Effectively higher adjustment costs, that would justify lower updating, but not many orders of magnitude higher Efficient Portfolios…- Discussion by Vicente Cuñat

28. Housing wealth is illiquid in a particular way • However, one key characteristic is the indivisibility of housing wealth • One can sell partially a mutual fund, but a house is hard to sell partially • Selling a large house to buy a smaller one would have a transaction cost on the whole value of the house • This is similar to illiquidity, but not exactly the same. For example multiple home owners should behave very differently to single home owners Efficient Portfolios…- Discussion by Vicente Cuñat

29. Some other comments • The period chosen to compute housing returns may matter a lot. • The Present Value of Rent is calculated as if it was the effective need for rents. • However this is a constrained optimum due to illiquidities. True needs are probably sharper • The representative agent is also likely to smooth things • With high discount rates should also give a “sharper” profile, (clarify discounted PVH) Efficient Portfolios…- Discussion by Vicente Cuñat

30. Summing up • Nice paper! Complex but simple message • Approaches a complicated problem through a very natural way (portfolio theory + short term fixed housing + gradually changing housing needs) • Good mix between theoretical background and empirical implementation • Results are convincing and improve on pre-existing literature Efficient Portfolios…- Discussion by Vicente Cuñat

31. Summing up: Issues side • Housing wealth is treated as too fixed, a complementary paper on housing decision is needed • Mortgages and access to finance are likely to play a large role and the approach in the paper is not rich enough to capture this • More of a life cycle approach, follow portfolios before and after trading up (down) Efficient Portfolios…- Discussion by Vicente Cuñat