Question

1. If a Normal distribution is assumed for the possible future outcomes, the Value at Risk (VaR) is fairly straightforward and simple to calculate if the mean and standard deviation are known.
   1. True
   2. False

2. A fairly accurate estimate of the Value at Risk (VaR) can be determined by using the generally accepted assumption that daily returns of the stock market as measured by the S&P 500 Index are consistent with a Normal distribution.
   1. True
   2. False

3. The Value at Risk (VaR) tells us nothing about the possible losses worse than the VaR amount.
   1. True
   2. False

4. Three approaches commonly used to calculate Value at Risk (VaR) and Expected Shortfall (ES) are (1) A parametric approach in which a specific distribution is assumed, (2) A non-parametric approach which uses historical data with an assumption that the future will be similar to what has happened in the past, and (3) A Monte Carlo simulation which develops multiple trials to produce a distribution of potential future outcomes.
   1. True
   2. False
5. A non-parametric historical simulation approach for calculating Value at Risk (VaR) can be implemented by sorting historical data for a given period and using the Percentile function in Excel to determine the VaR.
   1. True
   2. False
7. The Exponentially Weighted Moving Average (EWMA) removes autocorrelation by assigning equal weights to historical variances.
   1. True
   2. False
9. A successful GARCH method of modelling variance over time will remove autocorrelation in the squared returns of a data series.
   1. True
   2. False

Answer 1

a. The statement is true.

b. The daily returns of the S&P 500 do not follow a normal distribution due to extreme fluctuations at different points. So this statement is not true.

c. VAR gives us the maximum loss over a given time period and given confidence level. It cannot tell us about losses worse than VAR. This statement is true.

d. This statement is true. Parametric method includes the variance/covariance method, historical method is the non parametric method and the third one is monte carlo simulation method.

e. This statement is not true. After sorting the data quantile function is used.

f. This statement is false. The EWMA uses lambda, which is called the smoothing parameter. Lambda must be less than one and instead of equal weights, each squared return is weighted by a multiplier.

g. This statement is true. The introduction of a moving average component in the GAARCH model allows the model to both model the conditional change in variance over time as well as changes in the time-dependent variance. Examples include conditional increases and decreases in variance.