What is a Stochastic Discount Factor?

The stochastic discount factor, often abbreviated as (SDF) is a concept in mathematical finance whereby the discounting of future cashflows,is by the stochastic factor,as opposed to the WACC of traditional DCF Valuation.

The following sequence is representative of the relationship between initial price inputs and payoff output values of and , respectively

 

implying

If the assets comprise a portfolio, then SDF rationalizes

The covariances standard identity presents

If a risk free asset, then  signifies Inserting this into the preceding  equation produces the following formula for the risk of any portfolio or asset with the return 





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