Question

The 1 percent value at risk (VAR) of an investment is defined as the value v such that there is a 1% chance that the investment will lose more than v. Let X be a random variable representing the profit from the investment. The VAR of this investment is the value of v such that P(−X>v)=0.01. If X∼N(μ,σ²), approximate the VAR for this investment.

Answer 1

To approximate the VAR for an investment with a normal distribution, we need to calculate the z-score corresponding to the desired probability. The VAR can be calculated using the formula VAR = mean - z * standard deviation.

Step-by-step explanation:

To approximate the VAR for an investment with a normal distribution, we need to calculate the z-score corresponding to the desired probability. In this case, the probability is 0.01, so the z-score is -2.33 (obtained from a standard normal distribution table). The VAR can be calculated using the formula VAR = mean - z * standard deviation. Given that X follows a normal distribution with mean μ and variance σ², the VAR is v = μ - z * σ.

Let's say the profit from the investment is modeled by a normal distribution X ~ N(μ, σ²). In order to find the VAR, we need to know the values of μ and σ. Once we have these values, we can plug them into the formula to calculate the VAR. The VAR represents the value below which there is a 1% chance of the investment losing more.