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Empirical Asset Pricing Theory

In other words, the paper will look at the negative covariance of SDF and excess returns. The paper will also outline the Fama-French factors. This will include entailing how these factors work, and the motives behind choosing or selecting of models. Finally, the paper will discuss how the technique used by Pastor and Stambaugh differ from the ones used by Fama-French factors. Stochastic Discount Factor Pricing Model SDF as a Factor Pricing Model According to Fama and French (25 - 30) this model helps in the formulating of n econometric analysis that is used in the pricing of assets. The methods included this model include the capital asset pricing model that was proposed by Sharpe in 1964 and other as well as the consumption based inter-temporal capital asset pricing models (CCAPM). Stochastic discount factor (SDF) uses both of the approaches that are used in asset pricing. This includes the absolute and the relative pricing of asset. The absolute pricing of asset involve the pricing of an asset relative to the sources that expose it to the macroeconomic risks. The relative pricing of asset entails pricing assets according to how other assets are priced. The pricing equation that is used to estimate the stochastic discount factor is normally assumed. The limitations that are imposed on the behavior relating to the stochastic model are assumed to be standard. Based on the pricing equation assumptions the model, the price of n asset which is denoted as ‘t’ is calculated through discounting the value of the assets in the period of paying off. The equation for determining the price of the asset is: Pt=ET (Mt+sXt+s). The assets pay off is represented by Xt+s while the discounting factor is represented by Mt+s. the part denoted as ET represents the expectation given the information that is available at a given time t. The discounting factor represents the stochastic variable (Renault and Hansen 3-15). The assets that can be priced using this model include a stock that pays a dividend of DT+1. This stock should also have a resale value and a pay off period. A treasury bill is also applicable if only it pays only one unit of goods or a good being consumed. This equates the payoff to 1. A bond whose coupon payment is constant and yet can be sold is applicable for pricing using this model. This model can also price bank deposits that pay the risk free return rate and equate the pay off period to 1+ rft. Finally the call option whose price is Pt and gives the holder of the option the right of purchasing any stock at the price exercised (Renault and Hansen 12-21). Assumptions Relating to the Form of SDF In the development of the stochastic estimator, there are four assumptions that are taken into considerations. The first assumption is that the pricing equation 2 always holds. This equation is equivalent to the law of one price. The assumption here is that all the securities that have the same pay off should bear the same price. There are no choices of the preference. The second assumption states that the stochastic discounting factor labels Mt to be greater than zero. The same applies even to mimicking portfolio. The implication here is that no arbitrage opportunities exist. The third assumption states that the risk free rate exists. The risk free rate is measurable relative to sigma-algebra. The conditioning set that is also used in the computation of the conditioning moments generates this algebra. The existence of this rate allows for payoff space that is
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