Returns to an Asset - Assignment Example

Returns to an Asset Introduction Returns is a significant terms in finance. Returns are the measure to determine the alternating in the value of the assets over a fixed period of time. The returns could be daily, monthly, yearly, etc. However, there can be different between the expected value of the assets and the real value of the assets. On the other hand, the statistical properties of returns may determine the efficiency of the financial assets. Having knowledge of the statistical properties also makes it easier to evaluate the efficiency of the financial assets. The financial assets are then modelled for better knowledge of the returns. Background to the Data Sample There are many concepts that are adopted in the finance to make the concept of finance management more clear. Some of the concepts are considered to the appropriate for other branches and some are altered to suite the financial setup. Interest is considered as one of the fundamental concepts incorporated in finance and related organizations. Interest is termed as the fixed profit over an investment in a particular time frame. Mostly, it is calculated in terms of percentage, like if a person invests £100 and the rate of interest is 5% in a year, the organization that deposited the amount will have to pay £105 in a year (Wang, Lecture 1, n.d.,). Sometimes the rate of interest is divided into monthly basis like if the interest rate of 5% is divided into monthly instalments, the person that deposited the sum will be given 0.4% per month. Interest has two types; compound interest and simple interest. The simple interest is only applied to the original amount. Like if a person deposited £100 in bank at the rate of 5% simple interest annually, he will be given interest on £100 every year. The compound interest in applied on the original amount plus the interest amount. In practical, the financial organization or the banks cut some amount of taxes and apply compound tax on the deposited amount. Probability is the possibility of a random outcome to occur. The probability is defined as the term that defines the possible results to occur at random. For example, if a die is rolled, what will be probability of 1 to occur? The probability of 1 is about 1/6, as the die has six sides. The probability of each side is 1/6. On the other hand, the coin has two sides and if it is tossed ones, the probability of each side is ½. Thus, it can be said that the probability of a certain event remains between 0 and 1. The probability depicts the risk factor (Wang, Lecture 2, n.d.,). Discrete returns are liked most due to the fact that the calculation based on the discrete returns is simpler and the rate of profit represents the real profit. There is less formulation required to evaluate the discrete returns. For example, Mr. X buy a stock share for £10, the very next day, he wanted to sell the share and sold it in £11. Thus the profit, he attained while selling the stock share is about £1, which is about 10% of the £10 or original investment. On the other hand, the logarithmic value of the whole scenario give the percentage profit of about 9.53%, which is less than the original profit. Thus, the discrete returns have remained to be correct in the given scenario but the log returns proved to be incorrect. Log returns are regarded as to be most likely to generate statistical information and thus, the financial modellers like the concept of the log returns. It shows the statistical information for some period of time and thus the financial efficiency of the financial asset can be modelled. It creates an approximation of the true value of the financial asset. The log normal distribution creates a financial value over a period of time regarding the total financial asset. Log normal distributions do not generate a negative value. The two images above show the difference between the Normal Density and Log normal density. Value at Risk (VAR) Value at risk is a Statistical method that is utilized to evaluate the intensity of the financial risk factor regarding the financial assets of an organizations or person in a fixed period of time. A particular financial risk manager within an organization works to evaluate the intensity of financial risk and the investment that is on risk and methods to reduce the financial risk. A financial risk manager may not allow all the investment of the organization to be invested. He may suggest that the invested amount should be such invested that the organization could recover, if the company faces a big loss, in terms of invested financial investment. The major factors that Value at Risk (VAR) enables are statistical analysis through log returns, probability of the risk factor, and the discrete returns on financial assets. Monte Carlo VAR Monte Carlo VAR utilizes the Monte Carlo Simulations that produce random numbers that are further utilized to evaluate the mathematical formula that is not in the closed form. The formula is such designed that there is a need to pick the random number in a large number, so that the approximation should have the correct value. The paths generate should be similarly taken. The nature of the modelling problems should be determined to evaluate the returns associated with each path. The image shows the convergence of price estimate through the Monte Carlo simulation. Methodology The method of evaluating the VAR through Monte Carlo simulation utilizes the fixed pattern that is utilized in the historical simulation. The major difference is that the in Monte Carlo simulation random number is picked; while in historical analysis, historical data is searched and number is picked from historical information. The stem in evaluation the VAR through the Monte Carlo is to divide the time period T into equal N parts. For example, The Daily VAR can be computed by dividing the minutes or seconds. The change in time should be enough large to depict a continuous value. If n = sample size, possible resamples = nn The next step is to take a random number and upgrade the cost of the financial asset obtained after stating of the time interval. As the Monte Carlo utilizes the Theoretical distribution, the generator of the random number take number from the distribution. The image shows the normal (Theoretical) distributions and the Empirical distribution of the information. Step three is the resample the data by repeating the Step two and analyzes the T till end and dividing it with the N intervals. The step involves the evaluation of other random variables. The process continues until the value of the T is reached. Step four is also a repetition step that repeats both the step two and step three. This step generates a large number of times that allow producing the equal number of paths for the financial asset over T time frame. Before this step only one path is produced but after the step four many paths are produced. The step four gives the estimated value of the terminal price of financial asset (Wang, Lecture four, n.d.,). Step 5 is comprised of many single and small steps. First the different prices that are generated through different paths in the step four are evaluated and arranged according to the ranks (Smaller to larger). Then the value in the corresponding rank is read and confidence level is achieved and thus the relevant VAR is calculated, which is most the difference between the lowest value and the lowest terminal value of the financial asset. For example, if there is a 99% confidence level, the calculation of the VAR requires first to arrange the terminal values from smallest to the largest. Then there is need to read the one percent lowest in the rank. Then the expected terminal price would mean that the current asset price will fall 1% during the period under predictable market conditions. Historical Analysis / Bootstrap VAR Statistical technique and random numbers are utilized in the Historical Analysis technique. The techniques of historical analysis give the non-random values. Historical analysis method and Monte Carlo methods have some difference and similarities. The Major difference is that Monte Carlo VAR is parametric and Historical analysis method is non-parametric. The returns are not in certain distribution in a historical analysis method (Wang, Lecture four, n.d.,). Historical data is often utilized in the historical analysis method. The method is simple and makes use of random number form the historical data regarding the returns on the day randomly selected. Then the individual paths are generated and then geometric Brownian motion is utilized. The sample method can be considered as the empirical distribution of returns. One thing should be clear that the method is applied to the returns not the actual investment. However, log or discrete returns can be utilized. Bootstrap VAR method provides an easy method to understand the relation of the correlated data and the VAR. In order to utilize the bootstrap method, there is a need to resample the data in pairs, when comparing the VAR of two different projects or organizations. In this way, correlation can be kept between the VAR of two different financial assets. Discussion Continuous distribution is also considered as the normal distribution in finance. As the general concepts of continuous distribution are distinguished by the mean μ and a standard deviation, the financial terms are the similar than those of the general terms. Similarly, the standard deviation depicts the width of the distributions. However, considering the finance the distribution always remains symmetrical. Returns is a significant terms in finance. Returns are the measure to determine the alternating in the value of the assets over a fixed period of time. The returns could be daily, monthly, yearly, etc. However, there can be different between the expected value of the assets and the real value of the assets. On the other hand, the statistical properties of returns may determine the efficiency of the financial assets. Having knowledge of the statistical properties also makes it easier to evaluate the efficiency of the financial assets. The financial assets are then modelled for better knowledge of the returns (Wang, Lecture 3, n.d.,). There are two different types of returns, one is discrete and the other is log returns. The modelling of the efficiency of the financial assets is calculated through the log returns, as it the way, the future value of the returns can be predicted. On the other hand the discrete returns are liked by the persons who are practically involved in the buying and selling of the financial assets. Mathematically, the discrete returns can be written as: Where, are the discrete returns, is the price of the financial assets at time‘t’ and is the price of the financial assets at time t-1. On the other hand the Log returns can be mathematically represented as: Here, represents the log returns. Bibliography Wang, Qingwei. ASB4416 Financial Modelling: Lecture Six: Event Studies. Bangor Business School Wang, Qingwei. ASB4416 Financial Modelling: Lecture Five: Lecture Five: Portfolio Analysis and VAR. Bangor Business School Wang, Qingwei. ASB4416 Financial Modelling: Lecture Four: Monte Carlo Simulation and Bootstrap Methods. Bangor Business School Wang, Qingwei. ASB4416 Financial Modelling: Lecture Three: Brownian Motion. Bangor Business School Wang, Qingwei. ASB4416 Financial Modelling: Lecture Two: Probability Distribution and Returns in Finance. Bangor Business School Wang, Qingwei. ASB4416 Financial Modelling: Time Value of Money. Bangor Business School Read More