Short answer questions. Points are listed for each question Explain how you woul

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Short answer questions. Points are listed for each question Explain how you would use Value at Risk (VAR) as a way to measure market risk. Also explain some of the limitations of the VAR measure. (5 points) 1. 2. In terms of measuring market risk, backtesting is a method for evaluating your Value at Risk (VAR) The graph below. plots the results of a backtest of a specific trading scenario. The dots are the Profit and loss (Pnl.) each day, and the lines are the VAR. Is this a good or bad backtest? Explain your answer. (5 points) 1000

Explanation / Answer

Value at risk is a statistical measure to determine market risk of a portfolio for a given confidence level over a time horizon. One method for VAR calculation is the historical method which sorts historical data from worst to best and puts data points in frequency buckets using a histogram. Then worst losses that one can expect can be deduced from this histogram for a given confidence level. Say, for a confidence level of 95% worst losses can be deduced from the left tail of the histogram. Obviously this method using historical data assumes that history will repeat itself.

There are two other methods to calculate VAR namely Variance-Covariance method and Monte-Carlo simulation.

Variance covariance method uses average returns and standard deviation to calculate VAR assuming that the returns are normally distributed. Monte-Carlo simulation, on the other hand, is not based on historical data but generates scenarios using samples from probability distribution.

Limitations of VAR:

VAR is not additive which means sum of VAR of the individual components of portfolio is not equal to VAR of portfolio.

For a confidence level of 95%, 5% of cases are not accounted for. So the magnitude of losses in 5% (10-15 trading days) of these cases could be enough to cause monumental damages

For VAR calculations, one needs to calculate the mean returns , standard deviation as well as correlations between individual assets. For large portfolios with diversity in positions, this calculation becomes tedious.

Sometimes normal distribution is erroneously assumed for returns with non-normal skewness and excess kurtosis.

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