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Determination of Risk and The Appropriate Discount Rate

Determination of Risk and The Appropriate Discount Rate. What is “risk” in an investment context?. Value is determined by expected payoffs discounted for risk Investment risk is the risk of earning an abnormally low return and/or the loss of initial capital.

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Determination of Risk and The Appropriate Discount Rate

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  1. Determination of Risk and The Appropriate Discount Rate

  2. What is “risk” in an investment context? • Value is determined by expected payoffs discounted for risk • Investment risk is the risk of earning an abnormally low return and/or the loss of initial capital. • Risk can be viewed as the likelihood of getting payoffs that are lower than the expected payoff • Risk is characterized by the set of possible outcomes that an investor faces and the probabilities of these outcomes: a payoff (or return) distribution.

  3. Models of the Distribution of Returns: The Normal Distribution

  4. Best and Worst Performers, 1998: Wall Street Journal Shareholder Scorecard

  5. The Actual Distribution of Annual Stock Returns

  6. Diversification and Risk: the Effect on Standard Deviation from Adding More Securities to a Portfolio

  7. The Normal Distribution for the S&P 500 Portfolio Mean annual return = 13% Standard deviation of returns = 20%

  8. Number of Times Observed -50% -40% -30% -20% -10% 1% 10% 20% 30% 40% 50% The Actual Distribution of S&P 500 Portfolio Annual Returns, 1926-98 Source: Based on data from the Center for Research in Security Prices, University of Chicago

  9. Historical Betas

  10. Betas revert towards their average of 1.0 Investors are interested in the future beta over the period they hold the investment. High and low historical betas tend to move closer to 1.0 over time. A rough rule for forecasting future betas from historical betas: This adjustment pulls betas towards 1.0.

  11. The Problems with “Asset Pricing Models” • Risk factors are hard to identify • Risk premiums on risk factors are very hard to measure • Models often assume normal distributions of returns

  12. The CAPM is “Seductively Precise” • Normally distributed stock returns are assumed • The market risk premium is a big guess • Is it 3½%, 4½%, 8%, or 9½%? • Has the market risk premium declined in the 1990s? • Betas are estimated with error • Estimates of the cost of capital are made from market prices and assume that the market is efficient

  13. Fundamental Betas: Forecasting Future Betas from Fundamentals Two steps: • Estimate relationship between historical betas and fundamental attributes (say, FLEV and OLEV) in the cross section • Use estimates of b0, b1, and b2 to predict future beta for a firm using the most recent measures of the fundamentals for that firm:

  14. Some Fundamental Measures that have been Used to Predict Betas • Earnings variability • Cash flow variability • Size • Growth in earnings or sales • Growth in assets • P/E ratio • P/B ratio • Dividend yield

  15. Fundamental Risk • Risk is determined by a firm’s business • activities and so is understood by analyzing • those activities • A basic distinction: operating and financing risk

  16. A Framework for Analysis of Fundamental Risk Risk is the chance of earning poor residual earnings

  17. Profitability Risk: The Chance of Getting Poor ROCE

  18. The Analysis of Fundamental Risk

  19. The Analysis of Growth Risk Sales Risk Sales risk is the primary business risk

  20. Price Risk and Fundamental Risk • Fundamental Risk is the risk of value not being realized because of fundamental factors that affect the firm’s activities • Price Risk is the risk of value not being realized in prices because of factors other than fundamentals

  21. Price Risk Market Inefficiency Risk The market price may not reflect the “fundamental value” • Scenario A risk • Scenario B risk Fundamental analysis reduces Scenario A risk, but Scenario B risk can still affect a diligent fundamental investor

  22. P C T V C T P V = 0 0 Price Risk:Scenario A and Scenario B Scenario A: Price gravitates to fundamental value Cum-dividend Value P = V C C T T Normal return, Actual return, V 0 Abnormal return, P 0 Time 0 1 2 3 4 T Scenario B: Price deviates from fundamental value Cum-dividend Value Abnormal return, Actual return, Normal return, Time 0 1 2 3 4 T

  23. Inferring Cost of Capital from Market Prices Given an estimate of growth (g), the cost of capital can be estimated from prices and forecasts of earnings

  24. Perceived Risk

  25. Building in a Margin of Safety • Use a high discount rate in evaluating a BUY; use a low discount rate in evaluating a SELL • Be conservative (for a BUY) or optimistic (for a SELL) in forecasting

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