1. Risk Premium Puzzle in Real Estate: Are real estate investors overly risk averse? James D. Shilling DePaul University Tien Foo Sing National University of Singapore The American Real Estate Society (ARES) Meeting, April 11-14, 2007

2. Risk Premium Puzzle in Real Estate: Are real estate investors overly risk averse? James D. Shilling DePaul University Tien Foo Sing National University of Singapore

3. Outline of Presentation Introduction Motivation of study Data sources and analysis Empirical methodology: –Generating conditional ex-ante returns using VAR framework –Testing of relationship between ex-post and ex-ante returns –Variance tests on the ex-post and ex-ante returns Empirical Results Conclusion

4. Risk premium puzzle Mehra and Prescott (1985) first raised the puzzle on stock market The long term excess return of stock of 6.9% from 1889-2000 was too large to be explained by economic model (Mehra 2003) Based on the standard asset pricing model estimation The risk aversion coefficient is more than 98, which is much higher than many empirical evidence has suggested (   10). If   10 and   0.99 are assumed, the risk premium should be around 1.4% < 6.18% (observed) (Mehra, 2003) This irregularity is dubbed the “Risk Premium Puzzle” by Mehra and Puzzle in stock market.

5. Long-term Excess Stock Returns in the US Market Input Parameters (1889-1978): Std deviation of Consumption Growth Rate0.036 Correlation (consumption x real estate)0.070 Standard deviation of S&P 500 Return0.165 Period Mean Real Return Relatively Riskless Security Risk Premium Sharpe Ratio Risk Aversion Computation: C) Stock Market Data: S&P 500 (source: Mehra & Prescott, 1985) 1889-19786.98%0.8%6.2%0.374148.270 1802-19987.0%2.9%4.1%0.24898.367 1889-20007.9%1.0%6.9%0.417165.544 1926-20008.7%0.7%8.0%0.484191.935 1947-20008.4%0.6%7.8%0.472187.137

6. Is there a real estate risk premium puzzle? Shilling (2003) raised the above question and challenged the real estate researchers to explain the large ex-ante premiums in real estate He found ex-ante risk premiums of 6 to 6.75%, which were excessive to be explained by the standard asset pricing models The large risk premiums were translated into risk aversion coefficients of more than 878 in real term! Why is there such a large risk premium in real estate? Are real estate investors overly risk averse? This puzzle has yet to receive as wide attention in real estate research community compared to the comparable study in equity risk premium puzzle!

7. Real estate investors are overly risk averse? Property TypeExcess ReturnSharpe Ratio Excess Return Sharpe Ratio Risk Aversion Computation: NominalRealNominalReal A) Korpacz Data Apartment0.5977.4580.0312.8002959.3991111.111 Industry0.5989.7140.0302.7423854.9171088.219 Office0.5976.1130.0342.7232425.8471080.746 Retail0.5958.3590.0292.2133317.189878.367 B) NCREIF Data Apartment0.0541.0520.0180.330417.336131.039 Industry0.0430.6020.0070.095239.03637.877 Office0.0230.231-0.013-0.13391.638-52.623 Retail0.0460.6380.0100.139253.21755.313

8. Further examination of the historical return data Ex-ante return series are rather flat Investors’ expectation is rather uniform Shilling (2003) found the results to be consistent with the “normal range” hypothesis (Malkei, 1964) No variation across different property type When compared with ex-post (NCREIF) returns, he found unexpected capital losses of 2.2% to 5.7% (1Q88 to 3Q02) The losses narrow to 1.2% to 4.3% over the full sample period (1Q88 to 3Q06) What drive the unexpected losses? –Increase in expected future real interest rate (rejected by evidence) –Increase in future excess returns (rejected by evidence) –Lower than expected cash flow growth (difference in ex-ante and ex- post rent growth)

9. Are investors overly risk averse? Historical return (nominal) expectation is flat

10. Ex-ante returns (in real terms)

11. Ex-ante vs Ex-post return (Retail)

12. Motivations of this study This paper seek to test the puzzle that the unexpected losses in real estate are too large to be explained by economic models. Study of long-term expectation of investors in real estate investments Puzzles: –Why are investors’ expected return uniform and flat? –Are the expected returns excessive given the risk-return characteristics of the markets? –Investors’ expected returns do not seem to vary much across sectors Story: investors’ expectations drive long-term investment decision in real estate, and they do not adjust the return to reflect short-term volatility in the market. Portfolio rebalancing is highly expensive for real estate investors. The long-term return expectations remain rather stable. Hypothesis: real estate investors expect higher risk premiums to compensate for market uncertainty in long term. Ex-ante return information is decoupled from the actual returns

13. Data Source & Analysis Korpacz real estate investor survey data first published by Korpacz, then by Pricewaterhouse Cooper after 1993Q3 are used as proxy for ex-ante variables Quarterly survey of institutional investors, and contain information on rent growth, capitalization rate (Overall cap rate, IRR and residual IRR), expense change National Council of Real Estate Investment Fiduciaries (NCREIF) data are used to represent ex-post returns Inflation rates – ex-ante (Livingston survey data by Philadelphia FED) and ex-post (computed from CPI) Commercial paper rate as a proxy of short-term interest rate Returns data are collected for four market sectors: Apartment (A), Industry (I), Office (O), Retail (R) Descriptive Statistics (Table 2) & PP-Unit Root tests (Table 3)

14. Dynamic Dividend Ratio Model by Campbell-Shiller (1989) Log-return equations: Where and Taking the log-return in multi-period forward, and setting Constant excess return, [E t h t =E t r t + c],

15. Generating conditional ex-ante returns using VAR For one period lagged VAR model, The VAR system can be written in matrix form Let vector e1 = [1 0 0]’ and e2 = [0 1 0]’ Restrictions on VAR systems: The discounting factor,  i = exp (h it -  it ) Estimating forward ex-ante returns: ApartmentIndustryOfficeRetail 0.92100.92070.91620.9251

16. Conditional ex-ante returns Mean: 15.96% Std dev: 8.54%

17. Predictability of Ex-post returns Do investors’ expected returns explain variation in ex-post return? If investors are risk averse, they would expect higher premiums to compensate for the investment risks If their expectations are aligned with market fundamental, we should expect the ex-ante returns to explain variations in ex-post returns To test the hypothesis, the following regression specifications are tested: The results summarized in Table 5

18. Variance Tests using GARCH-M The GARCH-M (1,1) proposed by Engle, Lilien and Robins (1987): Results are summarized in Table 6 Persistence in ex-post returns Hypothesis testing: H0:  = 0 If rejected, conditional variance in the ex-ante returns do contain incremental information on variance in ex-post returns

19. Conclusion Historical evidence suggest that real estate investors are risk averse There were unexpected losses in ex-post real estate returns Income changes drive the deviations between ex-ante and ex-post returns In the tests of the first and second moments of return relationships, ex-ante returns were found to have significant effects on ex-post returns in industry market. Investors in apartment, office and retail markets seem to have expectations that are not in line with market fundamental In other words, the expected risk premiums may not be realizable in the actual market The hypothesis that they are risk averse can not be rejected. Implications: higher expected returns do not commensurate with the fundamental of the market, and they may be priced out of the market The higher returns may reflect investors’ long term investment returns Thank you