1351 Words6 Pages

Value-at-Risk (VaR)
Final VaR (10,99%) for August 3, 2017
After assessing the three models, it has been established that the share’s market risk should be computed using the normal distribution with a variance estimated by the Exponentially Weighted Moving Average (EWMA). Based on this model the VaR (10, 99%) for August 3, 2017 is 10.25127%. Therefore, employing this model allows us to be 99% sure the investment in BHP shares will not fall by more than 10.25127% over the next 10 trading days (August 3, 2017 to August 16, 2017). In dollar terms, this means over the next 10 days we can be 99% sure we will not lose more than $2,639.70 of our $25,750 investment. However, it should be noted that this 10 day VaR estimate is only a forecast of*…show more content…*

A high value of lambda places more weight on past observations and produces estimates of daily volatility that respond relatively slowly to new information. To calculate the one day VaR, the square root was taken of the daily variances calculated by the EWMA formula. With a given probability over a pre-set horizon, VaR is a measure of the maximum potential loss of a portfolio of instruments. Specifically: Where: = the probability of a loss greater than the VaR = the time horizon = the mean (estimated from the data using ‘=average()’ = the standard deviation (estimated using the square root of the last day’s variance from the EWMA formula) = the z-score that corresponds to 1- probability (using excel function =normsinv(prob.)) 2.3263 is the approximate z-score that corresponds to the 99% confidence level. The mean was estimated using the average return of the last 1,255 days and the standard deviation was derived from the EWMA formula. Employing the above equation, the VaR (1,99%) is -0.032649. To compute the 10 day VaR, the one day VaR needed to be time scaled. As variance scales linearly with time, the average return was multiplied by the time horizon denoted by h (10 days), and the standard deviation was multiplied by the square root of h. This resulted in the following formula: Evaluation of Models Back testing was used to establish which model should be selected to estimate the market risk for holding 1,000 BHP shares. This

A high value of lambda places more weight on past observations and produces estimates of daily volatility that respond relatively slowly to new information. To calculate the one day VaR, the square root was taken of the daily variances calculated by the EWMA formula. With a given probability over a pre-set horizon, VaR is a measure of the maximum potential loss of a portfolio of instruments. Specifically: Where: = the probability of a loss greater than the VaR = the time horizon = the mean (estimated from the data using ‘=average()’ = the standard deviation (estimated using the square root of the last day’s variance from the EWMA formula) = the z-score that corresponds to 1- probability (using excel function =normsinv(prob.)) 2.3263 is the approximate z-score that corresponds to the 99% confidence level. The mean was estimated using the average return of the last 1,255 days and the standard deviation was derived from the EWMA formula. Employing the above equation, the VaR (1,99%) is -0.032649. To compute the 10 day VaR, the one day VaR needed to be time scaled. As variance scales linearly with time, the average return was multiplied by the time horizon denoted by h (10 days), and the standard deviation was multiplied by the square root of h. This resulted in the following formula: Evaluation of Models Back testing was used to establish which model should be selected to estimate the market risk for holding 1,000 BHP shares. This

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