Value at Risk (VaR)

Financial commercialises started to use the shelter at jeopardize extensively since 1990s. But the sums of Value at gamble (var) were active in incompatible names since as early as 1920s (Holton 2003). It is the cadence of the trounce expected loss at a given arrogance direct under radiation diagram foodstuff figures over a specific meter interval. It buttocks also be expressed as the lowest confidence level of the potential losses that screw occur within a given portfolio during a specified judgment of conviction block. Value at Risk only presents the worst-case scenario (Harper n. d. ).The two major parameters to be chosen for risk bar atomic number 18 the time period of time and the confidence level. The time period support vary from a few hours to a few years. For example it tail assembly be stated that when a portfolio manager has a insouciant VaR at $1 peerless million million at 1%, it direction that thither is only 1 chance in light speed to incu r a daily loss of more than $1 million under normal grocery store conditions. The commonly apply modes to pronounce Value at Risk atomic number 18 Variance Covariance Method, historic operation and Monte Carlo Simulation (Benninga & dog 1998). Variance Covariance MethodThis model was made popular by J. P. Morgan in early 1990s. This approach is ground on the assumption that the underlying grocery store factors have a multivariate normal distribution. This assumption helps in find the distribution of specialise-to- grocery store portfolio lettuce and losses. After finding the distribution of workable portfolio pelfs and losses, the meter mathematical properties of practice distribution washstand be use to determine the loss that will be pertained or exceeded x percent of the time which is called Value at Risk (Linsmeier & Pearson 1996).The sideline example discharge be taken to discuss the theory. A U. S. company entered a FX frontward nail down in the past. The difference between genuine project and date of delivery is 91 twenty-four hourss. The contract requires the company to deliver $15 million in 91 days and in ex variety it will bring forth 10 million. The facts taken into consideration are the spot ex form judge expressed in dollars per stupefy (S), 3 month pound refer mark (rGBP) and 3 month dollar interest rate (rUSD). The current mark to securities industry values in dollars is opined fannyd on the following formulaUSD mark to food trade value= S x GBP 10million USD 15 million 1+ rGBP (91/360) 1+ rUSD (91/360) Here the holding period is one day and the probability is 5%. The distribution of possible kale and loss on this portfolio has the mean of zero as the expected reassign in portfolio value over a short holding period is almost always close to zero. A standard property of the Normal distribution is that if a probability of 5% is used in ending of the Value at Risk then it will be equal to 1. 65 times th e standard bending of win overs in the portfolio value. measuring stick divergency is the measure of the spread or dispersion of the distribution and computing the value of the standard recreation of changes in the portfolio value is the main factor in this system (Linsmeier & Pearson 1996). Value at Risk = 1. 65 x standard deviation of change in portfolio value The first abuse in measurement of VaR done this method is to determine the staple fibre grocery factors and alike(p) foodstuff place positions through Risk Mapping. In this case the raw material market factors are spot exchange rate and 3-month dollar and pound interest rates.The associated standardized positions are spot pounds, dollar dominated 3 month zero coupon bond and a 3 month zero-coupon bond exposed only to changes in the pound interest rate. The adjoining step is to estimate the parameters of distribution assuming that the percentage changes in the basic market factors have a multivariate Normal dist ribution with means of zero and thus capturing the variability of market factors by standard deviation and co-movement by the correlation coefficients.The triplet step is to compute standard deviations and correlations of the changes in the values of standardized positions using the covariance matrix of changes in the basic market factors. The final step is to calculate the value of variance and standard deviation of the portfolio using standard mathematical results about the distributions of sums of Normal random variables. Standard deviation is the square root of variance. In our case its value is $ 52500 approximately. directly as the probability was taken as 5%, the formula comes to Value at Risk = 1. 65 x standard deviation of change in portfolio value = 1. 65 x $ 52,500 = $ 86,625The benefit of this model is that it uses abridge and maintainable data set often available from market and third parties and calculation is quite speedy using algebraic formulae. The drawback of t his method is that it sucks the change of the portfolio value to be linearly helpless on all the changes in the values of assets and also that the asset returns normal distributed (Jorion 2006). Historical Performance Historical Performance method is the simplest and most transparent method that takes into account relatively lesser number of assumptions about the statistical distribution of underlying market factors (Linsmeier & Pearson 1996).The method works by using historical changes in market rates and prices to estimate potential future loss or value with the portfolio and thereby calculating the Value at Risk. This can be illustrated based on the above example. Here we assume the holding period as 1 day, probability of 5% and computation to be based on 100 preceding business days from the current date. The current day will be the 100th day. The method involves five steps. The first step is to position the basic market factors and to determine the formula to express mark t o market value.In our case the basic market factors are 3 month dollar interest rate, 3 month pound interest rate and spot exchange rate. The formula for mark to market value is derived as USD mark to market value= S x GBP 10million USD 15 million 1+ rGBP (91/360) 1+ rUSD (91/360) Next the values of the identified basic market factors for previous 100 days are to be obtained. Daily change in these rates will be able to set the base for constructions of vatic values of market factors useful in the calculation of divinatory profit and loss.The daily Value at Risk number is a measure of the portfolio loss caused by such changes over a one day holding period. The next and most important step is to open the current portfolio to the changes experienced in the previous 100 days to calculate daily supposed(p) profits and losses. In this step 100 sets of hypothetical values for market factors are calculated based on daily historical percentage changes in the market factors combined with current market factors. These hypothetical values are then used to compute 100 hypothetical mark to market portfolio values.Subtraction of current day mark to market portfolio value from distributively of the 100 hypothetical values gives 100 hypothetical daily profits and losses. Ordering mark to market profits and losses from the largest profit to the largest lost is the next step. Finally the loss, which equals or exceeds 5% of the time is selected. In the present example of 100 days calculation the fifth worst loss will be the value at risk. This method relies completely on the historical data. Thus it may non be able to predict most accurately if the period chosen is not a typical one and is posing any special market condition (Jorion 2006).Monte Carlo Simulation This method is quite similar to the Historical Performance Method. The major difference is that this method uses statistical distribution to capture the possible changes in the market factors instead of observing historical changes in market factors to calculate hypothetical profit and loss. The method involves five steps to estimate Value at Risk. The same example of single forward contract can be considered in this respect. The first step here is to identify the basic market factors and to determine the formula to express mark to market value similar to the Historical Performance Method.The next step is to assume a specific distribution for changes in the basic market factors and to estimate the parameters of that distribution. For the present example the percentage change in the basic market factors having multivariate Normal distribution is assumed and estimates of standard deviation and correlates are used as in this case the parameters like means, standard deviations and correlations can be interpreted naturally and their estimation is easier. However, it can be tell that Monte Carlo Simulation allows risk managers to choose the distribution according to their requirements.But this f lexibility also runs a risk of a bad choice that may not be fit for the particular case (Jorion, 2006). Pseudo-random generator is used in the following step to generate more than 1000 or sometimes 10000 hypothetical values of changes in market factors. These are then used to calculate hypothetical mark to market portfolio values. effective mark to market portfolio value on the current date is subtracted from each of the hypothetical values to get the hypothetical daily profits and losses.The following step is to order the mark to market profits and losses from the largest profit to the largest loss and the Value at Risk is selected as the loss which equals or exceeds 5% of time. While comparing the different aspects of these three methods it can be said that Historical Performance is the simplest method for estimating Value at Risk. It is suitable for estimation for any kind of options of the portfolio. It is easy to compute and give and can be explained without much effort.The drawbacks of the method are that it can be jerry-built if the data used is not typical and represents a specific condition quite similar to Monte Carlo Simulation and Variance-Covariance methods. It is too much dependent on historical data. It is not possible to analyze alternative assumptions through this method. Monte Carlo Simulation and Variance-Covariance methods on the other hand can slowly analyze alternative assumptions. Variance-Covariance method though can not determine distribution of market factors other than normal. Both of these methods are easy to implement but tougher to explain.Variance-Covariance method is easy in computation but can not capture the risks of portfolio with options when the holding period is long. Monte Carlo Simulation on the other hand is not easy to compute but it can surely capture the risks regardless of any options (Linsmeier & Pearson 1996). Thus it can be said that all of the three methods have their own benefits and drawbacks and it is c ompletely at the discretion of the risk manager to choose a method prehend to the portfolio based on the factors to be considered and the holding time.