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In this chapter student will understand how VaR measures the risk of a portfolio; compute static portfolio VaR using formulas and normal distribution functions, a Monte Carlo simulation of a random walk model of asset returns, and @Risk; write VBA Macros using “For Loops” and the “Cells” objects. | Financial Modeling Topic #6: Computing Portfolio Value-At-Risk (VaR), Random Walk Simulations, Macros and @Risk Simulations L. Gattis 1 2 References Financial Modeling 3rd Edition by Simon Benninga Ch. 15: Value at Risk Ch. 22: Monte Carlo simulation Ch. 29: Generating Random Numbers Learning Objectives Understand how VaR measures the risk of a portfolio Compute static portfolio VaR using Formulas and normal distribution functions, A Monte Carlo simulation of a random walk model of asset returns, and @Risk Write VBA Macros using “For Loops” and the “Cells” objects 3 Value at Risk (VaR) VaR is the most you should expect to lose with a given confidence interval and time period. E.g. if the 95% confidence interval, 1-Year, VaR = $10,000. 95% confident that losses will not exceed $10,000 5% probability of losing $10,000 or more One-tailed test statistic 4 $10,000 Loss 95% 5% 5 Analytical VaR If portfolio returns are normally distributed with expected return “µ” and standard deviation “σ”, then the X% Confidence Interval VaR for a portfolio value of V$ is: Where Zx is derived from the normal distribution function X=90% Tail=10% Z90%=1.28 VaR(1Yr, 90%)=V(μ-1.28σ) VaR(1Yr, 95%)=V(μ-1.65σ) VaR(1Yr, 99%)=V(μ-2.33σ) X=95% Tail=5% Z95%=1.65 X=99% Tail=1% Z99%=2.33 Data 6 Analytical VaR 7 VaR=-v*((ua/252)*t-z*(sa/252^0.5)*t^0.5) Simulated VaR and GBM To estimate the risk of a portfolio over multiple periods with contributions you must simulate periodic asset price movements A standard model for simulating asset prices is Geometric Brownian Motion (GBM)-- also called the Random Walk Model The GBM model has two components (1) Drift: the likely price appreciation of the asset (r-d) Expected Total Return – Dividend Yield If assume d=0, it is assumed that dividend are reinvested (2) Noise: Random shocks which are assumed to be normally distributed 8 GBM model of asset values Assuming returns are normally distributed with annual mean (μ) and standard deviation (σ), the simulated . | Financial Modeling Topic #6: Computing Portfolio Value-At-Risk (VaR), Random Walk Simulations, Macros and @Risk Simulations L. Gattis 1 2 References Financial Modeling 3rd Edition by Simon Benninga Ch. 15: Value at Risk Ch. 22: Monte Carlo simulation Ch. 29: Generating Random Numbers Learning Objectives Understand how VaR measures the risk of a portfolio Compute static portfolio VaR using Formulas and normal distribution functions, A Monte Carlo simulation of a random walk model of asset returns, and @Risk Write VBA Macros using “For Loops” and the “Cells” objects 3 Value at Risk (VaR) VaR is the most you should expect to lose with a given confidence interval and time period. E.g. if the 95% confidence interval, 1-Year, VaR = $10,000. 95% confident that losses will not exceed $10,000 5% probability of losing $10,000 or more One-tailed test statistic 4 $10,000 Loss 95% 5% 5 Analytical VaR If portfolio returns are normally distributed with expected return “µ” and standard deviation “σ”,
