The expected return of a security given multiple states of the economy _____.

Group of answer choices

b. is computed as the geometric average of the returns for each state

d. is unaffected by its return in any economic state

c. will vary as the probability of each state varies

a. is computed as the arithmetic average of the returns for each state

The correct answer is:

**c. will vary as the probability of each state varies**

### Explanation:
The expected return of a security depends on the returns in each state of the economy and the probabilities associated with each state. It is calculated as a **weighted average** of the possible returns, where each return is weighted by the probability of the corresponding economic state.

The formula for the expected return is:
\[
E(R) = \sum_{i=1}^{n} p_i \cdot R_i
\]
Where:
- \(p_i\) = Probability of the economy being in state \(i\)
- \(R_i\) = Return in state \(i\)
- \(n\) = Total number of states

This shows that the expected return will vary if the probabilities \(p_i\) change.

### Would you like a deeper explanation or have any other questions? Here are 5 related questions you might explore:

1. How do you compute the weighted average return for a set of possible states?
2. What is the difference between arithmetic and geometric averages in finance?
3. How does risk affect the expected return of a security?
4. How do changes in economic conditions impact the expected return?
5. What are some examples of different states of the economy and how they influence returns?

**Tip:** The arithmetic average is often used to compute the average of historical returns, but for calculating expected return, the weighted average is more appropriate because it considers probabilities.

The expected return of a security given multiple states of the economy _____.

Group of answer choices:

b. is computed as the geometric average of the returns for each state

d. is unaffected by its return in any economic state

c. will vary as the probability of each state varies

a. is computed as the arithmetic average of the returns for each state

Explore how the expected return of a security varies as the probability of different economic states changes. This problem covers key financial concepts, including expected return, weighted averages, and the impact of state probabilities on returns. Suitable for undergraduate students in finance or economics.

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