### The Equity Premium Puzzle: Pitfalls in Estimating the Coefficient of Relative Risk Aversion

"... Abstract Standard consumption-based models typically fail in pricing asset returns. In a famous seminal paper, ..."

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Abstract Standard consumption-based models typically fail in pricing asset returns. In a famous seminal paper,

### How Taxes and Required Returns Drove Commercial Real Estate Valuations over the Past Four Decades How Taxes and Required Returns Drove Commercial Real Estate Valuations over the Past Four Decades *

"... Abstract We document the evolution of U.S. tax law regarding commercial real estate (CRE) since 1975, noting changes in income and capital gains tax rates and tax depreciation methods. The most prominent changes were the 1981 and 1986 Tax Acts, but numerous significant changes occurred in the last ..."

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Abstract We document the evolution of U.S. tax law regarding commercial real estate (CRE) since 1975, noting changes in income and capital gains tax rates and tax depreciation methods. The most prominent changes were the 1981 and 1986 Tax Acts, but numerous significant changes occurred in the last dozen years. We then compute the present value of tax depreciation per dollar of acquisition price and an effective tax rate for CRE. We explain the quarterly variation in CRE capitalization rates using an error correction framework and find that the long run estimates are statistically significant in the way theory would suggest. Moreover, the required financial asset return and the tax depreciation variable temporally predict ("cause") capitalization rates in the long run, but not vice versa.

### New Goods and Asset Prices

, 2008

"... I propose an extension to the consumption capital asset pricing model to incorporate the introduction of new goods over time and states of nature. In the model, consumers have a love of variety, and consumption consists of different components—product groups and brands. Expected growth in product gr ..."

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I propose an extension to the consumption capital asset pricing model to incorporate the introduction of new goods over time and states of nature. In the model, consumers have a love of variety, and consumption consists of different components—product groups and brands. Expected growth in product groups increases expected future marginal utility, raising the incentive to save—thereby reducing the risk-free rate of interest. Meanwhile, variations in brand and quality growth over the business cycle make marginal utility more volatile and countercyclical—thereby raising the expected equity premium.

### * Barclays Global Investors and Columbia Business School, respectively. We thank I0B0E0S

"... The returns earned by U.S. equities since 1926 exceed estimates derived from theory, from other periods and markets, and from surveys of institutional investors. Rather than examine historic experience, we estimate the equity premium from the discount rate that equates market valuations with prevail ..."

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The returns earned by U.S. equities since 1926 exceed estimates derived from theory, from other periods and markets, and from surveys of institutional investors. Rather than examine historic experience, we estimate the equity premium from the discount rate that equates market valuations with prevailing expectations of future flows. The accounting flows we project are isomorphic to projected dividends but use more available information and narrow the range of reasonable growth rates. For each year between 1985 and 1998, we find that the equity premium is around three percent ~or less! in the United States and five other markets. THE EQUITY RISK PREMIUM LIES at the core of financial economics. Representing the excess of the expected return on the stock market over the risk-free rate, the equity premium is unobservable and has been estimated using different approaches and samples. The estimates most commonly cited in the academic literature are from Ibbotson Associates ’ annual reviews of the performance of various portfolios of U.S. stocks and bonds since 1926. Those

### defined-contribution pension plans

, 2008

"... Inter-temporal optimization and deterministic lifestyle asset allocation strategies for defined-contribution pension plans are investigated and compared both analytically and numerically. The pension plan is assumed to invest in two types of asset, risk free assets and equities, or bonds and equitie ..."

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Inter-temporal optimization and deterministic lifestyle asset allocation strategies for defined-contribution pension plans are investigated and compared both analytically and numerically. The pension plan is assumed to invest in two types of asset, risk free assets and equities, or bonds and equities, and the plan members‟ terminal utility a power function of pension wealth at retirement with their final wages as numeraire. The optimal asset allocation strategy using two assets is derived analytically for fully hedgeable wage incomes and compared numerically with that for non-hedgeable wage income and deterministic lifestyle strategy. The deterministic lifestyle strategy is shown to be replicable by a static allocation strategy with same expected returns and lower variances. The inter-temporal optimization strategy outperforms the lifestyle strategy in numerical simulations both when there is no further pension contribution or non-hedgeable wage risk and when the wage income is not fully hedgeable. When there are further pension contributions, the optimal proportion invested in the more risky asset is higher than that when future pension contributions are transformed into augmented wealth by short-selling a replicating portfolio to be paid by future pension contributions. With usual assumptions on market parameters, the optimal pension portfolio composition is independent of the value of non-hedgeble wage risk and the value of pension contribution rate.

### replacement ratio

, 2008

"... This paper considers the optimal asset allocation problem for defined-contribution pension plan members whose terminal utility is a function of replacement ratio, i.e. the pension-to-final wage ratio. When three asset types are available for investment, the optimal portfolio composition, which is ho ..."

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This paper considers the optimal asset allocation problem for defined-contribution pension plan members whose terminal utility is a function of replacement ratio, i.e. the pension-to-final wage ratio. When three asset types are available for investment, the optimal portfolio composition, which is horizon dependent, includes investment in both riskless and risky assets. The investment in risky assets has three components to hedge wage risk, to speculate on risk premiums and to hedge for financial market risk respectively. When the terminal utility is a power function, closed form solution is derived for the cases where there is no further contribution from wage incomes or there is no nonhedgeable wage risk. The horizon dependence of optimal pension portfolio is deterministic under assumptions of constant equity risk premium, constant interest rate volatility and constant stock return volatility. The short-sale of wage replicating portfolio also contributes to the horizon dependence of pension plan financial wealth (the sum of pension portfolio and the short-sold wage replicating portfolio), and the effect is stochastic due to the stochastic interest rate and stock return. Therefore, the optimal asset allocation strategy in terms of financial wealth is “stochastic lifestyling”. For the cases where wage incomes cannot be hedged due to non-hedgeable wage risk, optimal asset proportions can be solved numerically by Monte Carlo simulation. The proportions invested in stocks and especially bonds are higher in early stages than those when wage replicating portfolio is used, hence more short-sale of cash assets. The optimal asset allocation derived by numerical simulation is also horizon dependent.

### strategies in defined contribution pension plans

, 2008

"... The threshold and constant proportion portfolio insurance (CPPI) strategies are considered for their application in managing defined-contribution (DC) pension plans. The pension plans invest in two types of asset, riskless asset and stocks, or bonds and stocks. When the objective of pension plan is ..."

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The threshold and constant proportion portfolio insurance (CPPI) strategies are considered for their application in managing defined-contribution (DC) pension plans. The pension plans invest in two types of asset, riskless asset and stocks, or bonds and stocks. When the objective of pension plan is to maximize expected terminal utility that is a function of terminal pension wealth with final wages as numeraire, both threshold and CPPI strategies are suboptimal to the portfolio from inter-temporal optimization. When the objective of pension plan is to minimize expected terminal disutility defined as squared difference between actual wealth and target wealth, the threshold and CPPI strategies are inferior to a corresponding static-to-riskless hybrid strategy. When the objective of pension plans is to maximize expected terminal utility that is a function of terminal wealth over a guaranteed minimum, the threshold and CPPI strategies are inferior to a minimum terminal wealth insurance (MTWI) strategy. Since the threshold strategy is not optimal in minimizing expected terminal disutility and the CPPI strategy not optimal in maximizing utility over a guaranteed minimum, for which they appear to be designed respectively, they are generally suboptimal in managing DC pension plans.

### Costs

, 2005

"... www.elsevier.com/locate/econbase 401(k) matching contributions in company stock: ..."

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www.elsevier.com/locate/econbase 401(k) matching contributions in company stock:

### 4 We are grateful for their helpful comments to Kazunori Araki, Jeremy Edwards, Günter Franke,

, 2006

"... the editors and referees for their extremely valuable suggestions on both the contents and exposition of the paper. 5 The genesis of this paper is as follows. Huang (2000a, 2000b) had first obtained most of the results in this paper. Working independently, Hara and Kuzmics established similar result ..."

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the editors and referees for their extremely valuable suggestions on both the contents and exposition of the paper. 5 The genesis of this paper is as follows. Huang (2000a, 2000b) had first obtained most of the results in this paper. Working independently, Hara and Kuzmics established similar results in a series of manuscripts since December 2001. These outputs are now merged into this paper. Its exposition We study the representative consumer’s risk attitude and efficient risk-sharing rules in a singleperiod, single-good economy in which consumers have homogeneous probabilistic beliefs but heterogeneous risk attitudes. We prove that if all consumers have convex absolute risk tolerance, so must the representative consumer. We also identify a relationship between the curvature of an individual consumer’s individual risk sharing rule and his absolute cautiousness, the first derivative of absolute risk-tolerance. Furthermore, we discuss some consequences of these results and refinements of these results for the class of HARA utility functions.