Question

State of Economy Probability of State of Economy Rate of Return if State Occurs

Stock A Stock B Stock C
Boom .56 .13 .21 .39
Bust .44 .15 .05 −.06

Answer 1

To calculate the expected profit of a stock investment, we apply the expected value formula using the probabilities and outcomes for the stock's performance. In the scenario provided, using the given probabilities and values, the expected profit after one year is calculated to be $150.

Step-by-step explanation:

Expected Profit Calculation

To find the expected profit after one year for an investment in stock, we use the concept of expected value from probability theory. Given the probabilities and outcomes for the investment, the expected profit E(P) is calculated as:

E(P) = (Probability of Loss * Amount if Loss Occurs) + (Probability of No Profit or Loss * Amount if No Profit or Loss Occurs) + (Probability of Gain * Amount if Gain Occurs).

In the provided scenario:

Probability of the stock being worthless (loss of $1,000) = 35% or 0.35,

Probability of no profit or loss = 60% or 0.60,

Probability of the stock increasing in value (gain of $10,000) = 5% or 0.05.

We calculate the expected profit as:

E(P) = (0.35 * -$1,000) + (0.60 * $0) + (0.05 * $10,000)
= -$350 + $0 + $500
= $150.

Thus, the expected profit after one year is $150.