Risk Management

Posted: August 26th, 2021

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Risk Management

As global market stocks continue becoming volatile, investors are increasingly looking for appropriate strategies to manage their investment portfolios. Sometimes choices to invest may be based on an oversimplified understanding of objectives(Johnathan 213). Hence, putting into consideration some factors such as liquidity needs, risk tolerance, time horizon, and other income requirements can help enhance consistency in the performance of the preferred portfolio. There are several methods for managing portfolio risks(Fusai, Gianluca, and Roncoroni, 563). However, this paper looks at the use of the Monte-Carlo Simulation method for assessing value at risk (VaR) for a selected stock portfolio. The aim is to build an excel spreadsheet for calculating the VaR of a portfolio on two lognormal stocks via Monte Carlo simulation (Completed on Excel) and show how to simulate discrete-time stock path scenarios.

How Monte Carlo Simulation is implemented for Discrete Stock Time

Using Monte Carlo simulation is one of the conventional methods for estimating VaR for a portfolio. In this study, VaR for a portfolio with two lognormal stocks are simulated using the method. The aim is to help predict the worst most likely lose that may occur within the portfolio based on a confidence level of 99% and a specified period. For the implementation process, the geometric Brownian motion is employed(Fries 467). Notably, Monte Carlo simulation refers to an attempt to estimate the future several times. Once the simulation is completed, thousands of trials are obtained, which produces a distribution of outcomes that are eventually analyzed. The following are the steps that were employed;

            The first step was to specify the model; in this case, the Geometric Brownian Motions that technically refers to the Markov process was considered for the exercise. In this case, the stock prices were assumed to adopt a random walk, thus almost consistent with the efficient market hypothesis (albeit in its weak form)(Birbil and Gregoriou 176). The past stock prices, that is, historical costs are incorporated while the subsequent prices movement is assumed to be conditionally independent of the previous changes in prices. According to the GBM model, the following formula was utilized;

Whereby;

S refers to the stock price

 Shows change in the stock price

 refers to the standard deviation for the returns,

 Refers to the random variable and,

 refers to the elapsed period

Primarily, once the above equation is rearranged, the following equation is obtained;

From the equation, the first term shows a “drift,” while the second term is a “shock.” At every time, the model assumes that the portfolio prices will increase (drift up) based on the expected returns. The drift could be shocked, that is, gain or loss randomly. In this case, the random shock represents the standard deviation that is indicated by “s” multiplied by the random value “e”(Birbiland Gregoriou 189). Thus, this represents a strategy for the standard deviation scaling.

Generating Random Trials (initial input spot, interest rate, volatility and correlation parameters)

Once the model is established, the next step is to run the trials. Here, several parameters can be tried. In the analysis (excel), about 1,000 tests are run for 30 days. Assuming that stock starts on day 0, the following movement will be exhibited

Figure 2: Geometric Brownian motion

Process Output

Based on the hypothetical output, several things can be done. For instance, it can be used to estimate VaR with a 95% or 99% confidence interval. For a 99% confidence interval, the located ranks the 999^th outcome. Hence, the following is the illustration of the result (see excel for calculations)

In summary, therefore, the Monte Carlo simulation utilizes a particular model to simulate a set of significant random variables and predict future outcomes. In this study, discrete-time stock prices were simulated, thereby yielding various predictions that could help manage the risks associated with the portfolio.

Works Cited

Birbil, S I., and Greg N. Gregoriou. The VaR implementation handbook: financial risk and applications in asset management, measurement, and modeling. New York: McGraw-Hill, 2009. Print.

Fries, Christian. Mathematical finance: theory, modeling, implementation. Hoboken, N.J: Wiley-Interscience, 2007. Print.

Fusai, Gianluca, and Andrea Roncoroni. Implementing models in quantitative finance: methods and cases. Berlin-New York: Springer, 2008. Print.

Mun, Johnathan. Modeling Risk Applying Monte Carlo Risk Simulation, Strategic Real Options, Stochastic Forecasting, and Portfolio Optimization. New York, NY: John Wiley & Sons, 2010. Print.