1. Goal of the Lecture: Understand how to properly measure business risk.

2. Measuring Risk I.Uncertain Cash Flows - Risk Adjustment II.We Want a Measure of Risk With the Following Features a. Easy to Calculate b. Ranks Assets According to Compensated Risk c. Can be Translated into a Discount Rate, k III.Economy-Wide or Systemic Risk -> Beta Works best for a portfolio of assets. IV. Non-Systematic or Company Specific Risk -> Variance Works best for a single asset.

3. Measuring Risk TO MEASURE RISK WE NEED A GOAL VARIABLE. INVESTORS’ GOAL VARIABLE IS RETURNS % Return= = + = % capital gain (loss) + % Dividend Yield % R = =.40 or 40% QUESTION: What is risk, or, what does risk-free mean? ANSWER: If exante expected returns always equal expost returns for an investment then we say it is risk- free. If actual returns are sometimes larger and sometimes smaller than expected, the investment carries risk. (we are happy with large ones but unhappy with small ones). A measure of risk should tell us the likelihood that we will not get what we expect and the magnitude of how different our returns will be from the expected.

4. HOW TO MEASURE WHAT TO EXPECT Enumerate outcomes i.e., the different risk scenarios. Generate a probability distribution - attach probabilities to each scenario that sum to 1 (remember statistics course) EXAMPLE Economic ScenariosProbIBM Return High growth ( 5%).30.25 Low growth (3%).40.15 Recession (-3%).30.05 Sum = 1 See probabilities from Intrade. Get mean return - expected return - best guess E(R) = P i R i = Where P i is the probability of a particular return i E(R) = (.3 *.25) + (.4 *.15) + (.3 *.05) =.15 Measuring Risk

5. USE VARIANCE TO MEASURE TOTAL RISK  2 = (R i - ) 2 P i OR STANDARD DEVIATION;  = SquareRoot[  2 ] = [  2 ].5 For IBM  2 IBM = (.25 -.15) 2 (.3) + (.15 -.15) 2 (.4) + (.05 -.15) 2 (.3) =.006 Measuring Risk (Return Volatility) QUESTION: What is the variance of a stock which has a mean of.15 and returns of.15 in all states of the economy? - Zero! VARIANCE FOR A SINGLE ASSET CONTAINS a. Diversifiable Risk (Firm Specific) - easily by diversification at little or no cost. b. Undiversified (System) Risk - cannot be eliminated through diversification.

6. Variance Measures the Dispersion of a Distribution Around Its Mean

7. A Standarized Risk Measure Coefficient of Variation = Standard Deviation / Mean = Standard Deviation / E(R) = Standard Deviation / E(R) For IBM in the previous slide we would have Coefficient of Variation = SquareRoot(0.006)/0.15 = 0.077/0.15 = 0.513

8. Portfolio Mean Return and Variance TO GET THE VARIANCE OF A PORTFOLIO WE NEED TO CALCULATE THE PORTFOLIO MEAN RETURN. Portfolio mean return is a linear, weighted average of individual mean returns of the assets in the portfolio. GETTING THE WEIGHTS INVESTMENT$ INVESTEDW i 1100100/500 =.2.10 2200200/500 =.4.05 3200200/500 =.4.15 E(R p ) = W 1 + W 2 + W 3 =.2(.1) +.4(.05) +.4(.15) =.10 GENERAL => E(R p ) = W i =

9. For a two asset portfolio:  p 2 = W 1 2  1 2 + W 2 2  2 2 + 2W 1 W 2 Cov 12 where: Cov 12 = Corr 12  1  2 Cov 12 = covariance between asset 1 and 2 Corr 12 = correlation between asset 1 and 2  1 2 = variance of asset 1  2 2 = variance of asset 1 QUESTION: Diversification reduces variance of portfolio even when corr=0. WHY?- Some asset-specific risk offset one another. Portfolio Variance is More Complex - A Nonlinear Function

10. It’s usually best to diversify, except in this case.

11. Correlation Statistical Measure of the Degree of Linear Relationship Between Two Random Variables Range: + 1.0 to -1.0 + 1.0 - Move Up and Down Together - Exactly the Same Rate 0.0 - No Relationship Between the Returns - 1.0 - Move Exactly Opposite Each Other Measuring Risk (Correlation)

12. Covariance Measures How Closely Returns For Two AssetsTrack Each Other Other (Closeness to the Regression Line) All else equal, covariance is large when the data points fall along the regression line instead of away from it because, on the line, the deviations from the means of each variable are equal – the products are squares - larger than otherwise. Covariance is a Measure of Risk and Beta is a Standardized Covariance

13. Beta Is a Standardized Covariance We Need Beta (Standardized Covariance Measure) in Order to Make Comparisons of Risk Between Assets or Portfolios. Measured Relative to the Market Portfolio Slope of the Regression Line Slopes Measured Relative to Market Return General Formula Beta i = = Cov im = covariance between asset i and the market Corr im = correlation between asset i and the market  m 2 = variance of the market  i = standard deviation of asset I  m = standard deviation of the market Beta = 1 - Same as Market Risk Beta > 1 - Riskier than Market Beta < 1 - Less Risky than Market

14. Positive Beta

15. Negative Beta

16. Zero Beta

17. Negative vs. Positive Beta Over a Business Cycle

18. High vs. Low Beta Over a Business Cycle

19. Portfolio Beta GENERAL FORMULA B p = W i B i Example: Beta for a portfolio containing three stocks. INVESTMENT$ INVESTED W i B i 1100100/1000 =.12.0 2400400/1000 =.41.5 3500500/1000 =.50.5 B p = W 1 B 1 + W 2 B 2 + W 3 B 3 =.1(2) +.4(1.5) +.5(.5) = 1.05

20. CAPM “Beta is Useful Because it Can Be Precisely Translated into a Required Return, k, Using the Capital Asset Pricing Model” CAPM (Capital Asset Pricing Model) General Formula E(R i ) = k i = R f + B i (R m - R f ) = time value + (units of risk) x (price per unit) = time value + risk premium where,R f = Risk-Free Rate -> T-Bill R m = Expected Market Return -> S&P 500 B i = Beta of Stock i E(R i ) = Expected Return of Stock i Example: Suppose that a firm has only equity, is twice as risky as the market and the risk free rate is 10% and expected market return is 15%. What is the firm’s required rate? R i = k i = R f + B i (R m - R f ) = 10% + 2(15% - 10%) = 10% + 10% = 20%

21. QUESTION: If an asset has a B = 0, what is its return? -> R f QUESTION: If an asset has a B = 1, what is its return? -> R m QUESTION: Suppose E(R 1 ) > E(R 2 ) AND B 1 < B 2, which asset do you choose? -> 1 QUESTION: How about if E(R 1 ) > E(R 2 ) and B 1 > B 2 ? Now we need to know B 1 and B 2 and use the CAPM Measuring Risk (Beta)

22. CONSIDER STOCK PRICE AND CAPM P = R i = k i = R f + B i (R m - R f ) Where D 1 is stock dividend per share next year g = growth in dividends per share QUESTIONS: What happens to price as growth increases? P increases! What happens to price if k increases? P Decreases! What happens to price if Beta decreases? P increases! What happens to price if R f increases? B >1->P increase B P decrease What happens to price if R m decreases? P increases! QUESTION: As financial managers, what variables should we try to change and in what directions? 1. Increase cash flows - or growth in CF’s - make superior investment decisions, use the lowest cost financing or manipulate debt/equity ratio 2. Bring cash flows in closer to the present 3. Decrease Beta - Manipulate assets (Labor- Capital ratio). Measuring Risk (Beta)

23. Bond Ratings and Risk 1.Companies like Standard and Poor’s, Moody’s, Fitch and Duff and Phelps put out alphabetic ratings from AAA, AA, …D to grade the risk level of a bond. 2.A rating represents the probability and issuer will pay principal and interest on time. 3.All bonds of the same rating are in a risk group but do not have identical risk. 4.Ratings are supposed to reflect long-term risk based on statistical and non statistical considerations. 5.The lower the rating, the more risk and usually the higher return (yield) that must be offered by the issuing company to investors.

26. Important issues involving ratings 1.Many institutional investors are restricted to owning only “investment grade” bond where investment grade is BBB or above. Some can own some below investment grade (junk) bonds but must reserve more for potential losses. 2. Ratings agencies charge the bond issuer a fee for ratings and company can decide not to issue (selection bias). 3. Some agencies rate companies without being paid (incentive issues).

27. What is considered when an analyst sets a rating? 1.Bond indenture provisions – bond is a contract. A. Subsidiaries restricted on debt issuance? B. Restricts unsubordinated debt? C. Provides for sinking fund? D. Mortgage lien on assets or income? E. Constrains company’s decisions (investments, dividends) too much or too little? F. Sets minimum working capital, net worth, capitalization, liquidity, interest coverage etc.? G. Is the bond senior? H. Effects of regulations (regulatory commission)? Courts rewriting mortgage-backed bond indentures.

28. 2. Asset protections A. Composition of assets – liquid vs. illiquid B. Ability to value – toxic waste mortgage-backed bonds C. Plant and equipment condition – rundown or outdated? D. Book value and depreciation adequacy E. Leases and off balance sheet liabilities – AIG – U.S. gov F. Real or market value of assets (intangibles) 3. Future earnings power A. Industry of company B. Market Share C. Cost structure compared to competitors D. Accounting, tax, and depreciation practices E. Financial monitoring and risk controls

29. 4. Financial resources A. Cash flow from operations is paramount B. Ability to issue equity, preferred or other securities less important C. Ability to raise cash by selling assets even less. D. Ability to issue long term debt 5. Management A. Acquisition policy and practice – far afield B. Reputation and track record Academic studies show that ratings rely most highly on: 1.Subordination 2.Size of issuer 3.Financial leverage 4.Interest coverage 5.Stability of earnings and dividends Implication: Much detailed financial analysis is redundant.