Dissertation valuation companies

Dissertation valuation companies

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Dissertation About VaR Calculations | WOW Essays

We use cookies to enhance our website for you. Proceed if you agree to this policy or learn more about it. Type of paper: Dissertation. Topic: Virtual RealityVirtualizationInformationTimeObservationStock MarketInvestmentdissertation valuation companies, History. VaR calculations are becoming increasing important for all the investors, bankers, and regulators. There are several ways to calculate VaR; the historical method, the Variance — Covariance Method, and Monte Carlo method.

In this analysis, we will use the returns of stocks from Dow Jones Industrial Average for the last 40 years in order to make a comparison between different VaR calculation methods.

We will try to determine how that observation time, normality of the data, time frame, and variation of the data influence different ways of calculating VaR. Historical simulation is one of the popular methods used in the calculation of VaR. The data used in this case consists of monthly prices of 4 stocks: American Express, Boeing, Du Pont, and the Walt Disney, dissertation valuation companies. Dissertation valuation companies historical calculation will be done using the data from the last one year 12 observations to the last 40 years observations.

Then it will be seen how the VaR values change as the observation periods change from 12 to As can be seen from the above graphs that the VaR calculations continue to increase when the data is used for up to 10 years.

After 10 years, all dissertation valuation companies four companies show relatively less variations in VaR. There may be a few possible reasons for the same. The one year returns have only 12 observations in it. Therefore, due to the lack of data, there is a loss of tail. This is the primary reason for Boeing also other companies to have got minimum VaR value in the first and second year.

Therefore, when the number of observations goes fairly up more than 10 years or observationsthe normality of the distribution still holds good. As the above graphs show that all the four stocks have exhibited a decline around the th observation. This may have happened owing to some financial distress, market corrections, depression or recession. Before that, companies witnessed some volatility, but they were not as major as what happened during That is why as more and more data are used for the VaR calculation beyond the yearthe VaR values do not display high levels of volatility, dissertation valuation companies.

One of the major problems with historical simulation method is that it is highly dependent on the outliers. Also, if the historical data based VaR calculation is done using equal weights, dissertation valuation companies, then for a large data set, the data of older volatility and returns may not reflect the current market situation correctly.

In the data set used for this VaR calculation, it can be observed that the market returns and variations are relatively low during the first 20 years, whereas the market volatility has increased highly in the last 10 years.

This problem can be partially overcome using the following parameters wisely:. Too big an dissertation valuation companies period will create old data affecting the present result, dissertation valuation companies. Two small a data set may not represent the asset fully and may only capture the present volatility.

For the long term investors, a time frame of a year or month based observation is important, dissertation valuation companies, whereas for the daily investors, it is important to consider historical returns on a daily basis. In order to understand the strengths and weaknesses of the Variance - Covariance Method, two portfolios of data have been chosen. Portfolio B consists of American Express, 3M, dissertation valuation companies, and United Technologies.

The null hypothesis was that the returns of those portfolios follow normal distribution. Therefore, it can be concluded that the returns of portfolio B are not normally distributed. As normality is a big assumption in the Variance — Covariance Method and it has been seen in the previous sections that the number of observations below 10 years may not satisfy the normality assumption. Therefore, a minimum observation period of 10 years will be used for calculating the VaR in this method, dissertation valuation companies.

First, the return of the portfolio for the st month will be predicted by using dissertation valuation companies historical data from June to May 10 years data. Once the calculation will be complete, the next time interval will be considered by using the data of the returns for the next months from July to June The same procedure will be repeated for calculating the VaR for the nd month.

This procedure will be repeated for more time intervals, and the corresponding VaR will be calculated for each time interval. Using the 10 year observation period and data sets, we have constructed the above Dissertation valuation companies values. This way the whole graph for portfolio A red line and portfolio B black line is constructed. It is also dissertation valuation companies from the above graph that there is less volatility in the prediction of VaR for portfolio A.

This is primarily because 1 Portfolio A has normal distribution of returns that have already been discussed above, and 2 the three stocks in portfolio A behave in a more predictable manner without huge market corrections.

Portfolio B, on the other hand, dissertation valuation companies, is already established as a non-normal distribution. The Variance — Covariance Method used to calculate VaR for non-normal distribution gives erratic values.

Portfolio B has a thick-tailed distribution that causes huge variations in the VaR calculation. Because of the presence of outliers, these VaR values are also getting pronounced. The black line in the above graph shows that any variation in portfolio B is magnified in the VaR calculation.

For example, all the stocks in portfolio B have shown relatively stable growth with less volatility till However, bank stocks get huge market corrections when the market goes through any recession. In portfolio B, American Express is the financial stock that got market dissertation valuation companies during the bubble burst of and again for heavily corrected during subprime crisis.

These two huge corrections of American Express stock have pushed the VaR values up. Since we have used data sets 10 yearsany data set, used for VaR calculations, with the data of or included gave high VaR values. In the real world, it is almost impossible to find a portfolio that is normally distributed. Generally, any portfolio that contains callable bonds, options, and banking stocks is usually non-normal in nature.

In such cases, the above method used provides a good approximation of VaR, but Monte Carlo simulation dissertation valuation companies a better result. In Monte Carlo method, dissertation valuation companies will be using Pfizer Inc. as the stock for analysis. The data set of the time period of June to June will be used.

As Monte Carlo method is extremely computation-intensive process, we have only used a single stock for the calculation. We will use the same procedure by dividing the dataset as done in the previous section. This means that in each interval, the simulation will be running and predicting price point N times for each of those price paths.

As N increases, it is expected that the price path will become smoother because the dissertation valuation companies will be random and therefore, normally distributed, dissertation valuation companies. Based on the past historical data, dissertation valuation companies, Monte Carlo simulation tries to construct the future hypothetical market conditions. The number of possible hypothetical scenarios is infinite.

Therefore, the higher the value of N, dissertation valuation companies, Monte Carlo simulation will be able to generate more future possible dissertation valuation companies. That is why it can be seen from the above graph that as N increases, more random future scenarios are generated, and the VaR values become smoother. The dissertation valuation companies benefit of Monte Carlo simulation is that it has no underlying assumption like the Variance - Covariance Method.

Non-linear portfolios are best suited for calculating VaR using MC. Contrary to common dissertation valuation companies that Monte Carlo simulation provides best VaR result, we dissertation valuation companies see from the above figure that Monte Carlo simulation has provided worst VaR figures.

This is primarily because we have used only 24 historical data points based on which we are trying to predict possible future dissertation valuation companies. As this is a small data set, using a small number of scenario dissertation valuation companies will magnify the outlier effect, which has probably happened with the Monte Carlo method.

Between the Variance — Covariance and the historical method, dissertation valuation companies, the historical method gave better result because as the above graph shows that the data set is non-normal, there is negative skewness in the data set used for the calculation of VaR.

Therefore, in this type of scenario where the data set is small and non-normal, and we do not have huge computational ability, the historical method is the most suited one.

We have also compared the three methods using the data set of 40 years observations. In that case also, the historical method outperformed the Variance — Covariance Method. Again, it can be seen from the above graph that this has happened because the data set is still not strictly normal. The cumulative distribution function estimates can be done from non-parametric and semi-parametric method, dissertation valuation companies.

For small dataset, linear cumulative distribution functions are used with values and weights like the one used in the above section in which there are 24 observations. It is easier to construct a linear non-parametric CDF for the dataset. From the stairstep empirical CDF, it is easier to determine statistical parameters like mean, probability, and VaR.

As the number of data increases, CDF becomes more continuous, and it can approximated as a cumulative density functions. CDF is a step-wise function, whereas the kernel estimation makes the function smooth and non-parametric. Kernel density is a continuous non-parametric density dissertation valuation companies, which is difficult to calculate than linear CDF, but is more accurate for large data sets.

Kernel estimation can be used for VaR calculations, and it provides a huge advantage over the historical method and the Variance — Covariance Method as it is non-parametric in nature, dissertation valuation companies.

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