Power Utility Consumption Capm in Uk Stock Markets

Topics: Risk aversion, Standard deviation, Capital asset pricing model Pages: 15 (4138 words) Published: November 5, 2012
Pricing of Securities in Financial Markets
40141 – How well does the power utility consumption CAPM perform in UK Stock Returns?


1 Hansen and Jagannathan (1991) LOP Volatility Bounds

Volatility bounds were first derived by Shiller (1982) to help diagnose and test a particular set of asset pricing models. He found that to price a set of assets, the consumption model must have a high value for the risk aversion coefficient or have a high level of volatility. Hansen and Jagannathan (1991) expanded on Shiller’s paper to show the duality between mean-variance frontiers of asset portfolios and mean-variance frontier of stochastic discount factors. Law of one price volatility bounds are derived by calculating the minimum variance of a stochastic discount factor for a given value of E(m), subject to the law of one price restriction. The law of one price restriction states that E(mR) = 1, which means that the assets with identical payoffs must have the same price. For this constraint to hold, the pricing equation must be true.

Hansen and Jagannathan use an orthogonal decomposition to calculate the set of minimum variance discount factors that will price a set of assets. The equation m = x* + we* + n can be used to calculate discount factors that will price the assets subject to the LOP condition. Once x* and e* are calculated, the minimum variance discount factors that will price the assets can be found by changing the weights, w. Hansen and Jagannathan viewed the volatility bounds as a constraint imposed upon a set of discount factors that will price a set of assets. Therefore, when deriving the volatility bounds, we calculate the minimum variance stochastic discount factors that will price the set of assets. Discount factors that have a lower variance than these values will not price the assets correctly. Furthermore, Hansen and Jagannathan showed that to price a set of assets, we require discount factors with a high volatility and a mean close to 1.

After deriving these bounds, we can use this constraint to test candidate asset pricing models. Models that produce a discount factor with a lower volatility than any discount factor on the LOP volatility can be rejected as they do not produce sufficient volatility. Hansen and Jagannathan find evidence that using LOP volatility bounds, we can reject a number of models such as the consumption model with a power function analysed in papers such as Dunn and Singleton (1986).

2 Methodology

To test whether the power utility CCAPM prices the UK Treasury Bill (Rf) and value weighted market index returns, we first calculate the LOP volatility bounds. The volatility bound is derived by calculating the minimum variance discount factors that correctly price the two assets for given values of E (m). The standard deviations of the stochastic discount factors are then plotted on a graph to give the LOP volatility bound shown in figure one.

Figure 1 here

The CCAPM stochastic discount factors are then calculated for different levels of risk aversion. The mean and standard deviation of these discount factors are then plotted on the graph and compared to the LOP discount factor standard deviations.

Pricing errors can then be calculated and analysed to see whether the assets are priced correctly by the candidate model. To accept the CCAPM model in pricing the assets, we expect the stochastic discount factors variance to be greater than the variance of the LOP volatility bounds. It is also expected that pricing errors and average pricing errors (RMSE) will be close to zero. These results will be analysed more closely in the later questions.

3 Power Utility CCAPM vs LOP Volatility Bounds

In order for the power utility CCAPM to satisfy the Law of One Price volatility bound test at any level of risk aversion, the standard deviation of the CCAPM stochastic discount factor at that level of risk aversion must be above the Law of One Price standard...

References: Bansal, R. and A. Yaron, 2004, Risks for the long run: A potential resolution of asset pricing puzzles, Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08.
Burnside, C., 1994, Hansen-Jagannathan Bounds as Classical Tests of Asset-Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 57-79
Cecchetti, S
Cochrane, J.H. and L. P. Hansen, 1992, Asset Pricing Explorations for Macroeconomics, NBER Chapters, in: NBER Macroeconomics Annual 1992, Volume 7, pages 115-182 National Bureau of Economic Research, Inc.
Dunn, K., and K. Singleton, 1986, Modelling the term structure of interest rates under Non-separable utility and durability of goods, Journal of Financial Economics, 17, 1986, 27-55.
Ferson, W. E., and A. F. Siegel, 2003, Stochastic Discount Factor Bounds with Conditioning Information, Review of Financial studies, 16, 567–595.
Gregory, A. W. and G. W Smith, 1992. Sampling variability in Hansen-Jagannathan bounds, Economics Letters, Elsevier, vol. 38(3), pages 263-267.
Hansen, L.P. and R. Jagannathan, 1991, Implications of Security Market Data for Models of Dynamic Economies, Journal of Political Economy, Vol. 99, No. 2 (Apr., 1991), pp. 225-262 
Hansen, L.P
Kan, R., and C. Robotti, 2007, The Exact Distribution of the Hansen-Jagannathan Bound. Working Paper, University of Toronto and Federal Reserve Bank of Atlanta.
Mehra, R., and E. C. Prescott, (1985), The equity premium: A puzzle, Journal of Monetary Economics 15, 145-161.
Roussanov, N., 2010, Composition of Wealth, Conditioning Information, and the Cross-Section of Stock Returns, NBER Working Papers 16073, National Bureau of Economic Research, Inc.
Shiller, R., 1982, Consumption, Asset Markets and Macroeconomic fluctuations, Carnegie–Rochester Conference Series on Public Policy, Vol. 17. North-Holland Publishing Co., 1982, pp. 203–238.
Shiller, R. J., 1989, Market Volatility, MIT Press, Massachusetts. Journal of Economic Behavior & Organization, Elsevier, vol. 16(3), pages 361-364.
Weil, P., 1989, The equity premium puzzle and the risk free rate puzzle, Journal of Monetary
Economics 24
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • CAPM Essay
  • Capm Essay
  • CAPM Essay
  • Capm Essay
  • The Power Consumption Essay
  • Capm Essay
  • Stock Market Essay
  • Literature Review on Bangladesh Stock Market Essay

Become a StudyMode Member

Sign Up - It's Free