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# Beta

Beta. or…. “What Is Beta and How Is It Calculated?”. Beta. A “coefficient measuring a stock’s relative volatility” Beta measures a stock’s sensitivity to overall market movements. Source:UBS Warburg Dictionary of Finance and Investment Terms.

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## Beta

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

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

3. 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

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

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

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

7. 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

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

9. Risk-Reward Curve Risk Expected Return

10. 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?

11. 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

12. 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)

13. WACC and Beta • 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 • Therefore, increasing WACC reduces the firms valuation to reflect the increase in risk

14. 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**

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

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

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