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RISK AND REAL ESTATE INVESTMENT
LEARNING OBJECTIVESCalculate and interpret the basic measures of
risk for individual assets and portfolios of assets.Identify the problems with, and limitations of,
traditional sources of real estate risk and return data.
Incorporate information regarding project riskiness into the investment decision-making process.
Describe sensitivity analysis.
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RISK
The Concept of Variability
The expected rate of return = E(R).
E(R) = Sum of (oi x pi ),
where oi is the value of the ith observation and pi is it’s probability.
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RISK PREFERENCES
Risk-Averse Behavior
Risk-Neutral Behavior
Risk-Loving Behavior
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MEASURING PROJECT- SPECIFIC RISK
State of the Economy Probability Return
Deep recession 0.05 3.0%
Mild recession 0.20 5.5%
Average economy 0.50 7.0%
Mild boom 0.20 8.5%
Strong boom 0.05 11.0%
Expected return 7.0%
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Risk Estimates
Variance (2)
= (oi-E(R))2pi
Standard Deviation ()
= square root of the variance Coefficient of Variation ()
= standard deviation/expected return
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RISK MANAGEMENT
Three primary tools may be employed by investors to minimize their expose to risk:avoid risky projectsuse insurance and hedgingdiversification
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PORTFOLIO RISK
Diversifiable Risk: (unsystematic risk) can be eliminated by holding assets that are less than perfectly correlated.
Nondiversifiable Risk: (systematic, or market risk) is the risk remaining in a fully-diversified portfolio.
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Diversification and Risk
Year
Stock
Shopping Center
Eq.-Wt. Portfolio
1995 14% -10% 2.0%
1996 -10% 8% -1.0%
1997 23% 12% 17.5%
1998 -5% 17% 6.0%
1999 8% -5% 1.5%
2000 12% 15% 13.5%
Mean 7.00% 6.17% 6.58%
Std. Dev. 12.36% 11.13% 7.37%
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Covariance and Correlation
• Covariance between asset A and B (COVAB):
COVAB = E[(A-A)(B-B)]
• Correlation coefficient (AB):
AB = COVAB/AB
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OPTIMAL PORTFOLIO DECISIONS
Investors base their investment decisions on its contribution to the portfolio’s risk and return.
Efficient investments increase the portfolio’s expected return without adding risk.
Efficient investments decrease the portfolio’s risk for a given expected return.
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Expected Risk and Returns of a Portfolio
• Expected Portfolio Return:
E(Rp) = (wA)E(RA) + (wB) E(RB)
• Standard Deviation of Portfolio Returns
p = (w2A2
A + w2B2
B + 2wA wB AB )1/2
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OPTIMAL PORTFOLIO ALLOCATIONS
Stock
Proportion
Real Estate Proportion
Portfolio
Return
Portfolio Standard Deviation
0.00 1.00 6.17% 11.11%
0.20 0.80 6.33% 8.71%
0.40 0.60 6.50% 7.40%
0.50 0.50 6.58% 7.37%
0.60 0.40 6.67% 7.78%
0.80 0.20 6.83% 9.66%
1.00 0.00 7.00% 12.36%
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HISTORICAL RETURNS & RISK
1979 to 1999
Asset Average Std. Dev.
NPI 8.7% 7.7%
NAREIT 14.5% 15.6%
S&P 500 18.6% 12.8%
Russell 2000 16.6% 17.8%
Bonds 10.9% 13.7%
Portfolio 13.8% 9.2%
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HISTORICAL CORRELATIONS (1979-99)
Asset NPI NAREIT Stocks Russell 2000 Bonds NPI 1.000 0.091 -0.014 -0.023 -0.333 NAREIT 1.000 0.395 0.735 0.214 S&P 500 1.000 0.677 0.405 Russell 2000 1.000 0.180 Bonds 1.000
Correlation coefficients are estimate using annual returns.
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ACCOUNTING FOR RISK
The investor’s required rate of return is (E(Rj)).
E(Rj) = Rf + RPj
where Rf is the risk free rate and RPj is a
premium for bearing risk.
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ACCOUNTING FOR RISK
Asset Pricing Model to Estimate RiskSensitivity Analysis