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
Name: University: Course: Tutor: Date: Empirical Asset Pricing Theory Introduction Empirical pricing theories relating to the assets are used as benchmarks for valuation of an asset. Stochastic discount factor method of pricing is itself a criterion through which assets are valued…
There is a famous saying that one should not place all the eggs in one basket. The concept of portfolio also came from this saying which means that one should not make all the investment in one asset or security and should diversify the investment by investing in a group of assets so that the loss from one security can be compensated by the gain of the other security.
One of the limitations of the model is that the investors are solely interested in the return of the investment and the rate at which the investment gives return whereas it is not the case. Investors invest in the securities so as to earn profit which shall be either in the case of interest that the security gives upon the investment or by means of capital gain that when the price of the security gets high then the investor sells the investment and earn a capital gain.
The CAPM model therefore relies on the ability to measure market volatility as a whole. With several possible investments available in the market, the model assumes that one can accurately assess the volatility of each of these investments. This is impossible.
Whilst some of these data may be due to data-snooping from the analytical work of armchair researchers attempting to discern some meaning to what could just be a simple collection of facts, much of the empirical data such as beta, stock volatility, co-variances, etc.
The idea of investing in the financial market is to purchase the asset while the price is low, and to sell when the price appreciates.
The seeming arbitrary movement of prices of assets, such as stocks, has
The risk free rate is the government bond ideally, that has a fix ten years. The Beta is the true measure of the risk that is in the stock that one has invested on.
With the risk in it, measure the volatility of the investment. It is in this
To start with, we will understand the concept of an efficient portfolio as described below.
Most investors, according to mean-variance analysis and asset pricing model, tend to invest in a more efficient portfolio
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