What is Value at Risk $($VaR$)$ and how has its calculation methodology evolved?

Question $5$Answer

a$.$

VaR is a risk measure that estimates the maximum potential loss on an investment over a given time period at a certain confidence level. Early VaR models used simple variance$-$covariance matrices, while modern approaches apply Monte Carlo simulations.

b$.$

VaR measures the liquidity risk of a trading portfolio by estimating the time required to exit all positions without disrupting the market. Traditional VaR models assumed normal distribution, while current models capture fat$-$tailed distributions.

c$.$

VaR quantifies the expected return of an investment strategy by analyzing historical returns data. It was first developed using basic statistical methods but now incorporates advanced machine learning algorithms.

d$.$

VaR is a technique to optimize a portfolio's risk$-$adjusted returns by minimizing volatility. Initially it relied on subjective risk preferences, but later adopted an analytical mean$-$variance optimization framework.