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Measuring and Modelling Variation in the Risk-Return Trade-off


  • Lettau, Martin
  • Ludvigson, Sydney


Are excess stock market returns predictable over time and, if so, at what horizons and with which economic indicators? Can stock return predictability be explained by changes in stock market volatility? How does the mean return per unit risk change over time? This chapter reviews what is known about the time-series evolution of the risk-return tradeoff for stock market investment, and presents some new empirical evidence using a proxy for the log consumption-aggregate wealth ratio as a predictor of both the mean and volatility of excess stock market returns. We characterize the risk-return tradeoff as the conditional expected excess return on a broad stock market index divided by its conditional standard deviation, a quantity commonly known as the Sharpe ratio. Our own investigation suggests that variation in the equity risk-premium is strongly negatively linked to variation in market volatility, at odds with leading asset pricing models. Since the conditional volatility and conditional mean move in opposite directions, the degree of countercyclicality in the Sharpe ratio that we document here is far more dramatic than that produced by existing equilibrium models of financial market behaviour, which completely miss the sheer magnitude of variation in the price of stock market risk.

Suggested Citation

  • Lettau, Martin & Ludvigson, Sydney, 2001. "Measuring and Modelling Variation in the Risk-Return Trade-off," CEPR Discussion Papers 3105, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:3105

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    References listed on IDEAS

    1. Lettau, Martin & Ludvigson, Sydney, 2002. "Time-varying risk premia and the cost of capital: An alternative implication of the Q theory of investment," Journal of Monetary Economics, Elsevier, vol. 49(1), pages 31-66, January.
    2. Cochrane, John H., 1991. "Volatility tests and efficient markets : A review essay," Journal of Monetary Economics, Elsevier, vol. 27(3), pages 463-485, June.
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    Cited by:

    1. Brandt, Michael W. & Kang, Qiang, 2004. "On the relationship between the conditional mean and volatility of stock returns: A latent VAR approach," Journal of Financial Economics, Elsevier, vol. 72(2), pages 217-257, May.
    2. Rangvid, Jesper, 2002. "Output and Expected Returns - a multicountry study," Working Papers 2002-8, Copenhagen Business School, Department of Finance.

    More about this item


    consumption; expected returns; sharpe ratio; volatility;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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