Q2 Essays - Financial Risk, Actuarial Science, Mathematical Finance

Q2 Essays - Financial Risk, Actuarial Science, Mathematical Finance Q2 On account of the widespread use of financial knowledge, risk management has become increasingly crucial. One of the most important risk measures is Value at Risk which is defined by Linsmeier and Pearson (1996) as Using a probability of x percent and holding period of t days, an entitys value at risk is the loss that expected to be exceeded with a probability of only x percent during the next t-day period. In addition, there are numerous method to calculate VaR and the three most commonly used VaR approaches are the variance-covariance method, the historical stimulation method, and the Monte Carlo method. In order to evaluate the VaR, back testing should be involved as it provides the users about the accuracy of the models. Costello, Asem and Garder (2008) also states that back testing ensures that the models are properly formed. Besides, Stambaugh (1996) mentions that each model has pros and cons and they should be viewed as alternatives which may be suitable in different circumstances. Back testing method can be unconditional and conditional approach. Unconditional approach counts the number of exceptions and compare them with confidence level. On the other side, conditional approach test whether the exceptions are independent of each other. According to our back testing, results reveal that in three models accuracy in both conditional and unconditional are rejected for all confidence levels. However, it shows that 95% confidence level performs better than 90% confidence level in all model consistently. Within the back testing, we also found that the number of exception is either too small or too big for the given confidence level therefore this causes back testing may reject a correct model. As a result, choosing a lower VaR confidence level or increasing the number of data observations will be a solution to improve the current framework (Philippe. J, 2007). On the other hand, Corkalo (2011) say that VaR is not the best model for risk management because small firms will find that sensitivity analysis is easier to implement and other non-financial firms use alternative measure at risk. Firstly, all of the VaR approaches take assumptions that the return distribution is based on the historical data directly but history can be a wrong predictor. Besides, the observed time period is also an important factor. For an example, we have observed 9 years historical data of those five assets obtained in our portfolio, however, we dont know whether there is any unusual volatility in that period. Hence, the VaR we calculated is not strong in a changing economic environment. When we calculating VaR of a portfolio, we not only need to measure the return and volatility of individual assets but also the correlation between all assets included in the portfolio. Generally, with growing numbers of assets, the precision rate of VaR will be influenced. The VaR is determined by the past changes in the market factors and their variability in the portfolio. In other words, more variable market factors with greater sensitivities will result in greater VaR. Besides, the VaR is also determined by co movement of both two exchange rates in our case. Due to the high covariance of two exchange rates in our case which is 0.66, we construct the portfolio by taking two positions in order to reduce the risk being taken. Thus, the extension to which changes in the value of long position in USD/GBP are offset by the changes in the value of short position in YEN/GBP. According to our calculation, the highest VaR is not excessed three hundred thousand within three models with both 90% and 95% confidence levels and our portfolio average value is 9.35million after taking the account of VaR. However, we remain two million cash from the pension fund. In conclusion, we are likely to hold too much capital that could be invested in the portfolio to gain th e better return instead of holding it with non-interest. Q4 Difference Models from the VaR Literature The following methods will show how it is possible to get a VaR figure when there are different variables that play a factor in the portfolio. Conditional VaR using the Historical Method Conditional Value at Risk (CVaR) is the expected loss, meaning that it computes the average loss if, under any circumstance