Using the z-scores table for the standard Normal distribution In finance, the acronym VaR stands for "value at risk". JP Morgan introduced value at risk in the 1980s as a way to answer a common question asked by investors: "How much money might I lose?" For example, if a portfolio of stocks has an annual 5%-VaR of $0.6 million, this means that there is a 5% probability that the value of the portfolio will drop by more than $0.6 million over the next year.

Suppose that you are managing a client's $10 million portfolio. You can assume that the annual return of the portfolio follows a Normal Distribution with a mean return of 10% and a standard deviation 20%. a. What is the probability that the portfolio returns will be between -30% and +50%?

b. What it the annual 5%-VaR for this portfolio?

c. Suppose that you will receive a bonus of $50,000 if the portfolio return in the next year exceeds 15%. What is the probability that you will receive the bonus?