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Lecture Financial modeling - Topic 14: Selecting distributions, distribution fitting and the normal curve using @Risk

Topic 14 - Selecting distributions, distribution fitting and the normal curve using @Risk. After completing this unit, you should be able to: Select distributions other than the normal distribution, simulate portfolio returns and free cash flows by fitting a distribution, insert distributions using @Risk menu. | Financial Modeling Topic 14: Selecting Distributions, Distribution Fitting and The Normal Curve using @Risk L. Gattis Learning Objectives Select distributions other than the normal distribution Simulate portfolio returns and free cash flows by fitting a distribution Insert distributions using @Risk menu Simulation Process 1. Create a model that estimates a future outcome which has a stochastic variable E.g., Estimate PV of FCF/share to value a stock, FCF, Option Value, Profits 2. Specify the distribution of the stochastic variables (and their correlations) E.g., Normal, Uniform, Triangular, General Distribution Correlate or assume zero (uncorrelated independent variables) 3. Simulate many possible outcomes by randomly sampling from the specified distribution E.g., Simulate 10,000 sets of values for each stochastic variable (correlated or uncorrelated) 4. Evaluate the distribution of the outcome Riskmean, riskpercentile, risktarget 3 @Risk Distributions Symmetry (Skew), Peak, Bounds (Min/Max), Slope, Continuous (or discrete) Coin toss Prices Returns Wait Time Grades Bond Recovery Rates “Fat” Normal Financial Asset Distributions Asset Returns: Normal (Gaussian) distribution is often utilized. Unbounded, symmetric, single-peaked Asset Prices: Lognormal distribution is often utilized. Bounded (prices are non-negative) and positively skewed If asset returns are normally distributed, it follows that asset prices are lognormally distributed. In other words, a lognormal price distribution implies a normal return distribution – and vice versa. Let’s now look at the historical distribution of the S&P 500, T-Bonds, and T-Bills. Data and Portfolio Mean and Vol (Copy into excel) S&P 500 Market Returns and Histogram (1928-2013) S&P 500 Market Returns Impirical Distribution S&P 500 Market Returns and Normal Distribution Formula Predictions @Risk Normal Distribution Modeling Insert RISKNORMAL(μ,σ) Functions in Excel for SP500, Bonds, and Bills using historical μ and σ Add . | Financial Modeling Topic 14: Selecting Distributions, Distribution Fitting and The Normal Curve using @Risk L. Gattis Learning Objectives Select distributions other than the normal distribution Simulate portfolio returns and free cash flows by fitting a distribution Insert distributions using @Risk menu Simulation Process 1. Create a model that estimates a future outcome which has a stochastic variable E.g., Estimate PV of FCF/share to value a stock, FCF, Option Value, Profits 2. Specify the distribution of the stochastic variables (and their correlations) E.g., Normal, Uniform, Triangular, General Distribution Correlate or assume zero (uncorrelated independent variables) 3. Simulate many possible outcomes by randomly sampling from the specified distribution E.g., Simulate 10,000 sets of values for each stochastic variable (correlated or uncorrelated) 4. Evaluate the distribution of the outcome Riskmean, riskpercentile, risktarget 3 @Risk Distributions Symmetry (Skew), Peak, Bounds .