Real Estate vs Stock Market: approaching the required rate of return through the Treynor and Black model Joan Montllor-Serrats (Universitat Autònoma de Barcelona) Anna-Maria Panosa-Gubau (Universitat de Girona)

Summary of the paper Study of the properties of real estate combined with financial assets in an optimal portfolio –Application of Treynor and Black Model Effects of the indivisibility –Relationship with value and bubbles Analysis of bubbles based on exchange options

RealEstate is outside the financial market Combining Real Estate with the Market Index of financial assets Real Estate will be included in a portfolio if provides an alpha that compensates this drawbacks Incentives to combine: -Low correlation with financial assets -Way to create value Drawbacks: -Low liquidity - high transaction costs

Combining Real Estate with the Market Index of financial assets Treynor and Black Model (1973) portfolio combining : - portfolio of undervalued assets - market index This work: enlarged portfolio portfolio combining : real estate assets + market index Central difference undervalued assets short run real estate long run (stable portfolio)

Combining Real Estate with the Market Index of financial assets Enlarged portfolio M RE

The optimal percentage of real estate in the enlarged portfolio (w) depends on: -The expected market index risk premium -The total risk of the market index -The beta of real estate -The alpha of real estate -The specific risk of real estate Real Estate in the enlarged portfolio

Introducing the appraisal ratio or information ratio Real Estate in the portfolio

Introducing the appraisal ratio The optimal percentage (w) depends on: -A variable that only depends on real estate  its appraisal ratio -A variable that only depends on financial assets  the Sharpe ratio of its market index -Two variables that depend on real estate and financial assets at the same time  The coefficient beta of real estate  The ratio between the specific risk of real estate and the specific risk of market index Real Estate in the portfolio

Studying the sensitivity variables Sensitivity of w Appraisal ratio of RE positive Sharpe Ratio of market index negative Standard deviations ratio negative Beta of real estate positive

The Sharpe ratio of the enlarged portfolio from Bodie, Kane and Marcus (2002) : On this basis : Real Estate in the portfolio Increase in the expected risk premium for the volatility assumed by the investor: The increase in the risk premium depends on a sole variable connected with real estate: its appraisal ratio

Real Estate in the portfolio From the value of a portfolio at one year horizon increase in value: The increase in value depends on the same variables as the increase in the risk premium, encapsulated on the appraisal ratio

Importance of this analysis for the agents: They have to pay attention to the Appraisal ratio (alpha and the specific risk of the real estate) not only to the risk premium. Real Estate in the portfolio

Effects of Indivisibility Indivisibility (real assets) minimum budget in Real Estate Minimum investor’s budget (total) (w =optimal % of RE in the enlarged portfolio)

Effects of Indivisibility Investor (CML) who whishes higher minimum budget (for the volatility required) Investor needs higher budged to have lower volatility than the enlarged portfolio

Enlarged portfolio M CML Is the lose for an investor with insufficient budget who wants lower volatility than the volatility of the enlarged portfolio

Effects of Indivisibility Investors with insufficient budget Remain in CML lose

Indivisibility vs securitization Substituting real estate assets by REITs consequences : - Avoid the problem of indivisibility (recoup value) -Increase correlation with market index (lessen value) Critical value :

Indivisibility vs securitization Critical value : Necessary condition for creating value:

Indivisibility  Effects of indivisibility In a bubble In a crisis (Bubble: overvaluation of a kind of assets) Securitization: a way of reducing indivisibility effect

Detecting Bubbles Overvaluation  obtain a positive anomalous return (positive Jensen alpha) not justified by facts or change of expectations ( the challenge is to evaluate the weight of the change of expectations) Proposal: an indicator of overvaluation through exchange options

Detecting bubbles Strategy : Option to exchange the market index for real estate i.e. exchange a final value of 1 € invested in market index for the final value of 1 € invested in real estate t=0t=1 Purchase of exchange options-CH 0 Max {0, R A -R M ) CreditCH 0 - CH 0 (1+r) 0Max {0, R A -R M ) - CH 0 (1+r)

Detecting bubbles In this strategy : -The risk premium is embedded in the initial value of the exchange option -The exchange option is valued according to Margrabe (1978) This analysis -Is based on the reliability of option valuation: -is independent of risk attitudes -enables a direct comparison between the two rates of return under consideration An extra return (b>0) at the end of the period ( not due to a change of expectations or unexpected facts) can indicate a bubble

Detecting bubbles Simulation (not with real data) : Option valued according to Margrabe (1978) Example: Option to exchange A (we receive real estate) for M (we deliver market index). Free interest rate: 5%. Cost of carry (maintenance costs: 2%) at the end of the period, an extra return has been obtained if 10,00%20,00%25,00% 5,00%20,00%10,00% 5,00%20,00%5,00% 0,089160,059,36% 0,089640,059,41% 0,090610,059,51%

Conclusions (central ideas) - The expected rate of return of RE has to compensate for lack of liquidity and higher transactions costs (compensatory alpha) -Investor can create an enlarged portfolio – apply T&B model – combining Real Estate and Market index -The appraisal ratio is regarded as the driver through wich real estate creates value -Indivisibility requires a higher budged for a lower volatility (to maintain an optimal position) -Indivisibility contributes to boost bubbles and to make crisis deeper -Proposal of an indicator for detecting bubbles through exchange options

Thank you for your attention -