Beta “What Is Beta and How Is It Calculated?” or….

Beta A “coefficient measuring a stock’s relative volatility” A “coefficient measuring a stock’s relative volatility” Beta measures a stock’s sensitivity to overall market movements Beta measures a stock’s sensitivity to overall market movements Source:UBS Warburg Dictionary of Finance and Investment Terms

In practice, Beta is measured by comparing changes in a stock price to changes in the value of the S&P 500 index over a given time period In practice, Beta is measured by comparing changes in a stock price to changes in the value of the S&P 500 index over a given time period The S&P 500 index has a beta of 1 The S&P 500 index has a beta of 1

A Generic Example Stock XYZ has a beta of 2 Stock XYZ has a beta of 2 The S&P 500 index increases in value by 10% The S&P 500 index increases in value by 10% The price of XYZ is expected to increase 20% over the same time period The price of XYZ is expected to increase 20% over the same time period

Beta can be Negative Stock XYZ has a beta of –2 Stock XYZ has a beta of –2 The S&P 500 index INCREASES in value by 10% The S&P 500 index INCREASES in value by 10% The price of XYZ is expected to DECREASE 20% over the same time period The price of XYZ is expected to DECREASE 20% over the same time period

If the beta of XYZ is 1.5 … If the beta of XYZ is 1.5 … And the S&P increases in value by 10% And the S&P increases in value by 10% The price of XYZ is expected to increase 15% The price of XYZ is expected to increase 15%

A beta of 0 indicates that changes in the market index cannot be used to predict changes in the price of the stock A beta of 0 indicates that changes in the market index cannot be used to predict changes in the price of the stock The company’s stock price has no correlation to movments in the market index The company’s stock price has no correlation to movments in the market index

CompanyBeta AMGN0.82 BRK.B0.73 C1.37 XOM0.10 MSFT1.80 MWD2.19 NOK2.05 PXLW1.93 TXN1.70 VIA.B1.39 Source: taken from yahoo.finance.com, except PXLW from bloomberg.com

Beta and Risk Beta is a measure of volatility Beta is a measure of volatility Volatility is associated with risk Volatility is associated with risk

Risk-Reward Curve Risk Expected Return

If beta is a measure of risk, then investors who hold stocks with higher betas should expect a higher return for taking on that risk If beta is a measure of risk, then investors who hold stocks with higher betas should expect a higher return for taking on that risk What does this remind you of? What does this remind you of?

Beta and CAPM The capital asset pricing model: E(R) = Rf + B(Rm-Rf) where: E(R) = Expected return Rf = risk free rate of return B = beta Rm = market return

WACC Weighted average cost of capital: WACC = (D/V)*Rd*(1-T) + (E/V)*Re where: D = market value of firm’s debt Rd = return on debt securities T = tax rate E = market value of firm’s equity securities Re = return on equity securities (from CAPM) V = total value of firm’s securities (D + V)

WACC and Beta WACC increases as the beta and the rate of return on the equity securities increases (all else constant) WACC increases as the beta and the rate of return on the equity securities increases (all else constant) WACC is used as the discount rate in DCF models WACC is used as the discount rate in DCF models Therefore, increasing WACC reduces the firms valuation to reflect the increase in risk Therefore, increasing WACC reduces the firms valuation to reflect the increase in risk

How to Calculate Beta Beta = Covariance(stock price, market index) Variance(market index) **When calculating, you must compare the percent change in the stock price to the percent change in the market index**

How to Calculate Beta Easily calculated using Excel and Yahoo! Finance Easily calculated using Excel and Yahoo! Finance Use COVAR and VARP worksheet functions Use COVAR and VARP worksheet functions An example: An example: Calculate the beta of Citigroup stock over the 5-yr time period from Jan. 1, 1997 – Dec. 31, 2001

S&P 500 Adjusted Daily Closing Values: January 1, December 31, 1997 S&P 500 Adjusted Daily Closing Values: January 1, December 31, 1997 Citigroup Adjusted Daily Closing Prices: January 1, December 31, 1997 Citigroup Adjusted Daily Closing Prices: January 1, December 31, 1997