Market Risk Management - Assignment Example

Name: Course: Instructor: Date: MARKET RISK MANAGEMENT REPORT Table of Contents An Overview of Our Portfolio 2 Part A1: Calculation of the 95% daily portfolio VaR using the basic methodology of the historical simulation approach 2 Part A2: Calculation of the 95% daily portfolio VaR using the exponential weighting methodology of the historical simulation approach 3 Part B1: Calculate the 95% daily VaR for the portfolio using the model-building approach. Generate a VaR report for the portfolio based on the model-building approach, which should contain the following elements: 3 i)An analysis of the diversification effect (undiversified VaR and diversified VaR) 4 ii)Marginal VaR 5 iii)Component VaR 5 Part B2: The relationship between marginal VaR and incremental VaR 5 Part B3: On average, the relationship between component VaR and individual VaR for a particular position 6 Part B4: Marginal VaR in Part B1 are useful tools for risk management. Discuss how to change the portfolio positions to minimizing the portfolio VaR while keeping the portfolio fully invested. Generate a new VaR report based on the risk-minimizing positions. 6 Part C1: Implement backtesting procedures to evaluate the portfolio VaR determined in Part A1, Part A2 and Part B1, respectively with unconditional coverage 6 Part C2: Implement back testing procedures to evaluate the portfolio VaR determined in Part A1, Part A2 and Part B1, respectively with conditional coverage. 7 Part C3: Back testing is usually conducted on a short horizon, such as daily returns. Explain why. 7 Part D: Contrast and compare your findings in Part C1 and Part C2 and further comment on the performance of the market risk measurement approaches used in Part A1, Part A2 and Part B1. 8 An Overview of Our Portfolio Our portfolio as at 1 January 2015 was worth $20 million AUD consisting of investments in five stocks on domestic and international markets. Table 1 below provides details of the portfolio allocation, including trading symbols of five stocks and their holdings in Australian Dollar (AUD) as shown below: Stock (1) Stock (2) Stock (3) Stock (4) Stock (5) Stock Symbol AZJ.AX FXJ.AX AIG ARM.L SAN.PA Market [Australia] [Australia] [US] [UK] [France] (AUD millions) 3 2 8 5 2 Table 1: An illustration of our portfolio consisting of the investments in the five stocks We had to download historical exchange rates from the Reserve Bank of Australia from the website: http://www.rba.gov.au/statistics/historical-data.html#exchange-rates. The daily closing stock prices were downloaded from yahoo finance website: http://au.finance.yahoo.com/, and a sampling period of 3 years starting from 1 January 2012 all through to 31 December 2014. Part A1: Calculation of the 95% daily portfolio VaR using the basic methodology of the historical simulation approach On the basis of the historical simulation approach, in which the number of simulation carried out is representative of the number of day the simulation is carried out. This implies that for the first simulation, it is assumed that the changes in terms of percentage through all market variables are on the first day. For the second and third simulation trials, the assumptions are that the percentage changes in all market variables are on the second and third day respectively. This pattern continues with the subsequent number of simulation trials. Taking into account the ith trial, is assumed that in order to determine the value of the market variable the following day, the following equation ought to be used: After ranking the losses for the portfolio, it was found that the 95% daily portfolio VaR amounted to – AUD 24,365,668.57 (See the attached excel file). Part A2: Calculation of the 95% daily portfolio VaR using the exponential weighting methodology of the historical simulation approach In this task, different weights were observed differently. It was also assumed that the weights assigned to the observations experienced exponential decline with respect to time. For the Scenario, the weight was given as: What followed was the ranking of observations from the very worst to the very best. The weights were then added together in total up to the point when the anticipated percentile was achieved. It is from this process that the 95% daily portfolio VaR was found to be AUD - 25,598,809.71 (See the excel file attached). Part B1: Calculate the 95% daily VaR for the portfolio using the model-building approach. Generate a VaR report for the portfolio based on the model-building approach, which should contain the following elements: Just like the historical simulation approach, the Model Building Approach is also an efficient method for determining the daily VaR for a given portfolio. The assumption made herein is that there is normal distribution in the returns of the stock (See the attached excel file). i) An analysis of the diversification effect (undiversified VaR and diversified VaR) The formula that is quite synonymous with the calculation of variance for a portfolio and one that was heavily applied herein is given as follows: Thereafter, the portfolio VaR was eventually calculated using the formula given below: It was at this point, and using the above formulae, that the 95% daily portfolio VaR was then determined to be AUD -21,243,896.11 Taken in isolation, the VaR values for each of the five components were tabulated in the table below (See the attached excel file): From the table shown above, it can be seen that the Undiversified VaR is greater than the Diversified VaR. ii) Marginal VaR These values were tabulated as follows (See the attached excel file): iii) Component VaR Consider the tabulated information in the table below (See the attached excel file): Part B2: The relationship between marginal VaR and incremental VaR The marginal VaR and incremental VaR are related in such a way that the incremental VaR is the product of the value of individual stock in a portfolio and its corresponding marginal VaR. Part B3: On average, the relationship between component VaR and individual VaR for a particular position Component VaR and Individual VaR are related in such a way that the component VaR equals the product of individual VaR and the correlation between the component and portfolio. Part B4: Marginal VaR in Part B1 are useful tools for risk management. Discuss how to change the portfolio positions to minimizing the portfolio VaR while keeping the portfolio fully invested. Generate a new VaR report based on the risk-minimizing positions. See the attached excel file for more information on this as illustrated by the table shown below: Part C1: Implement backtesting procedures to evaluate the portfolio VaR determined in Part A1, Part A2 and Part B1, respectively with unconditional coverage From the manipulations in the attached excel file, the table shown below was prepared on the basis of unconditional coverage: Part C2: Implement back testing procedures to evaluate the portfolio VaR determined in Part A1, Part A2 and Part B1, respectively with conditional coverage. Part C3: Back testing is usually conducted on a short horizon, such as daily returns. Explain why. According to Christofferson (1998), the occurrence of the current day is largely dependent on the very immediate anticipation, usually a day, of the returns. For that reason, therefore, back testing only makes sense if performed on the basis of short term projections. Part D: Contrast and compare your findings in Part C1 and Part C2 and further comment on the performance of the market risk measurement approaches used in Part A1, Part A2 and Part B1. When we check the model, the number of observations falling outside VaR should be in line with the confidence level. So, we determined the number of exceptions corresponded to the number of losses exceeding the VaR value for the specific approach by comparing VaR with actual loss of the portfolio. As shown in the historical simulation method used originally, this method is simply re-organizes actual historical returns, putting them in order from worst to best. It then assumes that history will repeat itself, from a risk perspective. Using this approach we got the 95% daily portfolio VaR equal to – AUD 24,365,668.57 (See the attached excel file). In the basic historical simulation, we give an equal weight to all observations. In exponential weighting methodology of the historical simulation we give recent observations more weight because it is more relevant and important. Under this approach we got the 95% daily portfolio VaR equal to AUD - 25,598,809.71 (See the excel file attached). In pare B1 we calculate the undiversified VAR (individual VaR ) for all the stock , then we calculate the diversified VaR ( portfolio VaR), we got VAR for portfolio equal to AUD -21,243,896.11, which is less than the sum of individual VaR (AUD 651,884.01). On the other hand, Marginal VAR (value at risk) allows risk managers to study the effects of adding or subtracting positions from an investment portfolio. Since value at risk is affected by the correlation of investment positions, it is not enough to consider an individual investment's VAR level in isolation. Rather, it must be compared with the total portfolio to determine what contribution is makes to the portfolio's VAR amount. Back testing is one of the important tools to check whether a model is adequate (Model validation). Back testing is a formal statistical framework that consists of verifying that actual losses are in line with projected losses.In the back testing approach there are two test used in this case for calculation of VAR. First test is known as the proportion of failure or un-conditional coverage and second test is known as the conditional coverage ratio. Using the Kupiec (1995) test, the log-likelihood ratio for all approach is less than 3.84, therefore, we cannot reject the model under 95 % confidence level. However, unconditional coverage ignores the possibility that exceptions could “bunch” closely in time. So, the Christofferson (1998) test check if today’s occurrence of exception is independent of what happen the previous day. Using Christofferson (1998) test, LRcc for all the approach is larger than 5.99, therefore, we reject the model, so, it seems there is bunching. Marginal VaR consider as an important tool to minimize the portfolio risk, this is possible by cutting the positions with the greatest marginal VaR and adding the positions with the lowest marginal VaR. In our portfolio AC.PA stock has the greatest marginal VaR while BHP stock has the lowest VaR. Read More