Market Risk Analysis

## Description

When we examined historical market returns, we saw the broad stock market had a risk premium of 7.5% and a standard deviation of 15% annualized. The objective of this exercise is characterize the risk of investing the broad market. Attached is a template for your answers.

## Questions

For all questions, assume the market return is Normally distributed with an expected return of 7.5% and standard deviation of 15% annualized.

- What is the probability of having a year in which the return on your investment is less than -5%?
- What is the probability of having a year in which the return on your investment is greater than -5%?
- What is the probability of having a year in which the return on your investment is less than 5%?
- What is the probability of having a year in which the return on your investment is between -5% and 5%?
- There is a 10% probability of having a return less than x. What is x?
- There is a 10% probability of having a return greater than x. What is x?
- There is a 10% probability of having a return within ±x of 7.5%. What is x?
- There is a 10% probability of having a return between x and 5%. What is x?
- 95% of returns fall between LB and UB. What is LB and UB?
- 5% of years will have a loss worse than x. What is x?
- You invest $100 in the market. What is your investment's expected value in one year from now?
- In one year from now, your investment value will fall within [LB,UB] with a probability of 95%. What are LB and UB?
- What is the 5% VaR (Value at Risk)?