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.

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.

RISK PREFERENCES

Risk-Averse Behavior

Risk-Neutral Behavior

Risk-Loving Behavior

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%

Risk Estimates

Variance (2)

= (oi-E(R))2pi

Standard Deviation ()

= square root of the variance Coefficient of Variation ()

= standard deviation/expected return

RISK MANAGEMENT

Three primary tools may be employed by investors to minimize their expose to risk:avoid risky projectsuse insurance and hedgingdiversification

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.

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%

Covariance and Correlation

• Covariance between asset A and B (COVAB):

COVAB = E[(A-A)(B-B)]

• Correlation coefficient (AB):

AB = COVAB/AB

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.

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

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%

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%

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.

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.

ACCOUNTING FOR RISK

Asset Pricing Model to Estimate RiskSensitivity Analysis