Consider the Following Multi-Index Model $R _ { \mathrm { it } } = R _ { F t } + \beta _ { i 1 } I _ { 1 t } + \beta _ { i 2 } I _ { 2 t } + \ldots + \beta _ { i j } I _ { j t } + e _ { i t }$

question 40

Essay

Consider the following multi-index model: $R _ { \mathrm { it } } = R _ { F t } + \beta _ { i 1 } I _ { 1 t } + \beta _ { i 2 } I _ { 2 t } + \ldots + \beta _ { i j } I _ { j t } + e _ { i t }$ where: $R _ { it }$ is the return on asset i in period t $R _ { F t }$ is the risk-free rate in period $$t$$ $\beta _ { i j }$ is the sensitivity of asset $i$ to factor $j$ is the value of factor $j$ in period $t$ $e _ { i t }$ is a random error term for asset $i$ in period $t$
a. Assuming the APT holds, what is the expression for the expected return of asset i?
b. How can the APT be used in decision making?
c. Outline, in list form, the assumptions underlying the APT.

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Definitions:

Reinforcer

In operant conditioning, any event that strengthens the behavior it follows.

Conditioned Stimulus

An initially neutral stimulus that, upon association with an unconditioned stimulus, elicits a conditioned response.

Unconditioned Stimulus

A trigger that inherently and effortlessly evokes a reaction without the need for previous learning.

Skinner Box

An experimental apparatus designed by B.F. Skinner for studying behavioral conditioning in animals, typically using rewards and punishments.