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# Asset Mgmt Factor Investing P2.T8 Stochastic Discount Factor is multiplied?

#### Fittyfive9

##### New Member
On page 9 of the notes for Ang's investment management - factoring investing, it says the stochastic discount factor is MULTIPLIED by the payoff to arrive at asset price, near the bottom of the page. Given that the STD, m, is = a + bf + bf...+bf and the CAPM discount is just = a + bf, why is the "CAPM discount" used to divide the payoff while the STD is used to multiply the payoff? Is this a typo?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Fittyfive9 it's not a typo: discount factors are multipliers. For example, if capm β = 1.2, Rf = 2.0% and equity premium is 5.0%, then E(r) = 2.0% + 1.2*5.0% = 8.0%, such that PV = FV/(1 + 8.0%) and df(1) = 1/1.08 = 0.9259. And this discount factor is a multiplier; ie., it multiplies by a future value and returns a present value. You mean "SDF" not "STD", yes?

See Ang below, where I copied Ang 4.2. It's harder than this, however, as this is NOT capm. Here is an illustrated example where I used some numbers to illustrate the (m): https://www.bionicturtle.com/forum/threads/p2-t8-701-multifactor-models-andrew-ang.10169/post-49871

FYI, our best writer is about to start the new draft of Ang, and then I will add what we've learned, so we will have a (much) improved note this semester. I hope that's helpful!