Expected asset risk measures are needed to construct optimal portfolios, plan for retirement, value equities and options, and forecast corporate cash flow distributions. In this lecture, students will: Compute asset return variance and standard deviation, scale standard deviations across time, compute moving average volatility, compute volatility using EWMA models, compute implied volatility using the black-scholes option pricing model. | Financial Modeling Topic #2: Estimating Asset Risk L. Gattis 1 2 References Financial Modeling 3rd Edition by Simon Benninga Ch. 8: Portfolio Models Ch. 11: Estimating Beta Ch. 35: Some Excel Hints Ch. 36: User Defined Functions with VBA Learning Objectives Expected asset risk measures are needed to construct optimal portfolios, plan for retirement, value equities and options, and forecast corporate cash flow distributions In this lecture, students will Compute asset return variance and standard deviation Scale standard deviations across time Compute moving average volatility Compute volatility using EWMA models Compute implied volatility using the Black-Scholes Option Pricing Model 3 Return Data – Copy entire range 4 Arithmetic Mean 5 Histogram of IBM Monthly Returns 6 Data, Data Analysis, Histogram, Graph Output Risk is often defined as the dispersion around the mean – often measured by standard deviation 7 History of The Normal Distribution De Moivre (18th Century statistician and gambling consultant) finds the distribution of coin flips has order Dist. of heads in 12 coin flips Galton Board This order is considered nature’s “normal” order Pattern often called a bell curve, or Gaussian distribution Central Limit Theory: A large sample of independent, random observations is often assumed to be normally distributed (under certain conditions) Normal curves are used in Living organisms’ height, weight, mass, mortality .; Male height μ=5’10”, σ =3” Intensity of light Weather – rain, snow, temperatures IQ Test Scores: μ=100, σ =10 Asset returns? Normal Distribution and Risk If you assume that asset returns are normally distributed as a computational short-cut, then you can fully describe the distribution of returns (and risk) by the mean and standard deviation statistics Standard deviation (σ) is the square root of the variance and is a measure or the “dispersion” Variance (σ2) is the average . | Financial Modeling Topic #2: Estimating Asset Risk L. Gattis 1 2 References Financial Modeling 3rd Edition by Simon Benninga Ch. 8: Portfolio Models Ch. 11: Estimating Beta Ch. 35: Some Excel Hints Ch. 36: User Defined Functions with VBA Learning Objectives Expected asset risk measures are needed to construct optimal portfolios, plan for retirement, value equities and options, and forecast corporate cash flow distributions In this lecture, students will Compute asset return variance and standard deviation Scale standard deviations across time Compute moving average volatility Compute volatility using EWMA models Compute implied volatility using the Black-Scholes Option Pricing Model 3 Return Data – Copy entire range 4 Arithmetic Mean 5 Histogram of IBM Monthly Returns 6 Data, Data Analysis, Histogram, Graph Output Risk is often defined as the dispersion around the mean – often measured by standard deviation 7 History of The Normal Distribution De Moivre (18th Century statistician and
