Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets

Wachter, Jessica A.

doi:10.2139/ssrn.291472

Cited by 196 publications

(296 citation statements)

References 25 publications

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“…As shown in Wachter (2002a), computing the solution to this case does not require solving a new partial differential equation. 10 As in the case of terminal wealth, the dynamic problem can be recast as static problem for an endogenous pricing kernel.…”

Section: Complete Nominal Markets: General Resultsmentioning

confidence: 99%

“…Based on this finding, a number of studies (e.g. Balduzzi and Lynch (1999), Barberis (2000), Brandt (1999), Brennan, Schwartz, and Lagnado (1997), Campbell and Viceira (1999), Liu (1999) and Wachter (2002a)) document gains from timing the stock market based on the price-dividend ratio, and from hedging time-variation in expected stock returns. One result of this literature is that when investors have relative risk aversion greater than one, hedging demands dictate that their allocation to stock should increase with the horizon.…”

Section: Introductionmentioning

confidence: 99%

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Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?

Sangvinatsos

Wachter

2003

SSRN Journal

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We consider the consumption and portfolio choice problem of a long-run investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a three-factor Gaussian model with a time-varying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for long-term bonds.

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Section: Complete Nominal Markets: General Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?

Sangvinatsos

Wachter

2003

SSRN Journal

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“…In particular, stochasticity of expected returns has been used in a number of papers: as a possible way to explain greater long-term allocations in stocks than in bonds [CV99,Wac02]; to study the risk-aversion of investors under greater uncertainty than a standard CAPM [BEW88]; to say something more about the equity premium puzzle [Bre98].…”

Section: History and Motivationmentioning

confidence: 99%

Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions

2014

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Abstract. We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns. The results are an extension of the partially-informed investment strategies obtained by the Black-Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.Key words. Filtering, control, Hamilton-Jacobi-Bellman equation, portfolio optimization, partial information, expert opinions. Subject classifications. 91G20, 60G35, 35Q93, 35C201. Introduction. It is well-known that optimal mean-variance portfolio weights are quite different from the weights used in real-life investment. As pointed out in [BL92], unconstrained optimization often results in large short positions among many asset classes, and constrained optimization results in zero weight in many assets and unreasonably large weights in assets with small capitalization. The model of Black and Litterman [BL91] is a practical solution to this problem, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.In continuous time or multi-period settings, a natural extension of the Black and Litterman model is to include a separate stochastic process for the level of expected returns. Due to the large amount of data required for accurate estimation of this new process, much of the existing literature considers it to be unobserved, hence making this an investment problem with only partial information. Several papers consider expected returns to be an unobserved Markov process and then use filtering methods (i.e. Kalman filter or Wonham filter) to track the hidden state. Indeed, investment with partial information is studied in [Bre98,Bre06,ESB10,BR05,FPS14,Pap13,Pha09,SH04]. The effect of this added stochasticity is that optimal investment strategies will change from those suggested by the standard Merton problem [Mer69], with the effects of riskaversion characteristics and the investment horizon playing a role in the solution [Bre98,Wac02].The analysis in [FGW12] combines filtering with so-called expert opinions, a concept which is similar to the Black-Litterman model's consideration of investors' views. The idea is the following: in a dynamic investment problem, the nature of...

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“…Koijen and van Nieuwerburgh (2011) survey this literature. The implications for stock-bond asset allocation has been explored by Kim and Omberg (1996), Campbell and Viceira (1999), Barberis (2000), and Wachter (2002) in stylized models disregarding housing and income. Since expected stock returns vary counter cyclically in these models, intertemporal hedging considerations lead to an increased demand for stocks, although the quantitative effects are typically found to be modest.…”

Section: Introductionmentioning

confidence: 99%

Predictors and Portfolios Over the Life Cycle

2016

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We show that the net corporate payout yield predicts both the stock market index and house prices and that the log home rent-price ratio predicts both house prices and labor income growth. We incorporate the predictability in a rich life-cycle model of household decisions involving consumption of both perishable goods and housing services, stochastic and unspanned labor income, stochastic house prices, home renting and owning, stock investments, and portfolio constraints. We find that households can significantly improve their welfare by optimally conditioning decisions on the predictors. For a modestly risk-averse agent with a 35-year working period and a 15-year retirement period, the present value of the higher average life-time consumption amounts to roughly $179,000 (assuming both an initial wealth and an initial annual income of $20,000), and the certainty equivalent gain is around 5.5% of total wealth (financial wealth plus human capital). Furthermore, every cohort of agents in our model would have benefited from applying predictor-conditional strategies along the realized time series over our 1960-2010 data period.Keywords: Return predictability, human capital, housing, investments, welfare JEL subject codes: G11, D91, D14 Predictors and Portfolios over the Life CycleAbstract: We show that the net corporate payout yield predicts both the stock market index and house prices and that the log home rent-price ratio predicts both house prices and labor income growth. We incorporate the predictability in a rich life-cycle model of household decisions involving consumption of both perishable goods and housing services, stochastic and unspanned labor income, stochastic house prices, home renting and owning, stock investments, and portfolio constraints. We find that households can significantly improve their welfare by optimally conditioning decisions on the predictors. For a modestly risk-averse agent with a 35-year working period and a 15-year retirement period, the present value of the higher average life-time consumption amounts to roughly $179,000 (assuming both an initial wealth and an initial annual income of $20,000), and the certainty equivalent gain is around 5.5% of total wealth (financial wealth plus human capital). Furthermore, every cohort of agents in our model would have benefited from applying predictor-conditional strategies along the realized time series over our 1960-2010 data period.

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Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets

Cited by 196 publications

References 25 publications

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?

Does the Failure of the Expectations Hypothesis Matter for Long-Term Investors?

Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions

Predictors and Portfolios Over the Life Cycle

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