real estate vs stock market: approaching the required rate of return through the treynor and black...
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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
R
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
p
ppAR
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 wAppraisal 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
R r SM
1AR
p2
SM2 1
2 2m M pS S AR
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
1
1
m
m
M
M
R rr
VR r
r
V
SM 1
ARp2
SM2 1
1 r SM
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)
minP
minmin
PB
w
(w =optimal % of RE in the enlarged portfolio)
Effects of Indivisibility
Investor (CML) who whishes
higher minimum budget (for the volatility required)
i minB B
i m
minmin
mi
i i
BB B
x
( )i i mx
Investor needs higher budged to have lower volatility than
the enlarged portfolio
Enlarged portfolio
M
CML
mi
imR
iMR
Is the lose for an investor with insufficient budget who wants lower volatility than the volatility of the enlarged portfolio
im iMR R
Effects of Indivisibility
Investors with insufficient budget
Remain in CML
lose
im iM mm M
iM
M im
R r R rR R S S
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 : ⇒ =0
Indivisibility vs securitization
Critical value : =0⇒
p Mcritical
M p
R r
R r
Necessary condition
for creating value: ,REITS M critical
R p −r⎡⎣
⎤⎦− RM −r βp
⎡⎣
⎤⎦0
Indivisibility minmin
PB
w
∂w∂AR
> 0 min 0B
AR
min demand of real estateAR w B AR
Effects of indivisibility
In a bubble
In a crisis
min demand of real estateAR w B AR
(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=0 t=1
Purchase of exchange options -CH0 Max {0, RA-RM)
Credit CH0 - CH0 (1+r)
0 Max {0, RA-RM) - CH0 (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
rCHRRb MA 10
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 bubblesSimulation (not with real data) : Option valued according to
Margrabe (1978)
0 1A M C rR HR
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%
A M AM
0,08916 0,05 9,36%
0,08964 0,05 9,41%
0,09061 0,05 9,51%
0CH 0 (1 )CH rr
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