Power Utility Consumption Capm in Uk Stock Markets
Pricing of Securities in Financial Markets
40141 – How well does the power utility consumption CAPM perform in UK Stock Returns?
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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
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
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