1. Corporate Finance Introduction to risk Prof. André Farber SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES

2. A.Farber Vietnam 2004 |2|2 Introduction to risk Objectives for this session : –1. Review the problem of the opportunity cost of capital –2. Analyze return statistics –3. Introduce the variance or standard deviation as a measure of risk for a portfolio –4. See how to calculate the discount rate for a project with risk equal to that of the market –5. Give a preview of the implications of diversification

3. A.Farber Vietnam 2004 |3|3 Setting the discount rate for a risky project Stockholders have a choice: –either they invest in real investment projects of companies –or they invest in financial assets (securities) traded on the capital market The cost of capital is the opportunity cost of investing in real assets It is defined as the forgone expected return on the capital market with the same risk as the investment in a real asset

4. A.Farber Vietnam 2004 |4|4 Three key ideas 1. Returns are normally distributed random variables Markowitz 1952: portfolio theory, diversification 2. Efficient market hypothesis Movements of stock prices are random Kendall 1953 3. Capital Asset Pricing Model Sharpe 1964 Lintner 1965 Expected returns are function of systematic risk

5. A.Farber Vietnam 2004 |5|5 Preview of what follow First, we will analyze past markets returns. We will: –compare average returns on common stocks and Treasury bills –define the variance (or standard deviation) as a measure of the risk of a portfolio of common stocks –obtain an estimate of the historical risk premium (the excess return earned by investing in a risky asset as opposed to a risk-free asset) The discount rate to be used for a project with risk equal to that of the market will then be calculated as the expected return on the market: Expected return on the market Current risk- free rate Historical risk premium =+

6. A.Farber Vietnam 2004 |6|6 Implications of diversification The next step will be to understand the implications of diversification. We will show that: –diversification enables an investor to eliminate part of the risk of a stock held individually (the unsystematic - or idiosyncratic risk). –only the remaining risk (the systematic risk) has to be compensated by a higher expected return –the systematic risk of a security is measured by its beta (  ), a measure of the sensitivity of the actual return of a stock or a portfolio to the unanticipated return in the market portfolio –the expected return on a security should be positively related to the security's beta

7. A.Farber Vietnam 2004 |7|7 Capital Asset Pricing Model (CAPM) Risk – expected return relationship: Expected return Risk-free interest rate Market risk premium Risk

8. A.Farber Vietnam 2004 |8|8 Returns The primitive objects that we will manipulate are percentage returns over a period of time: The rate of return is a return per dollar (or £, DEM,...) invested in the asset, composed of –a dividend yield –a capital gain The period could be of any length: one day, one month, one quarter, one year. In what follow, we will consider yearly returns

9. A.Farber Vietnam 2004 |9|9 Ex post and ex ante returns Ex post returns are calculated using realized prices and dividends Ex ante, returns are random variables –several values are possible –each having a given probability of occurence The frequency distribution of past returns gives some indications on the probability distribution of future returns

10. A.Farber Vietnam 2004 | 10 Frequency distribution Suppose that we observe the following frequency distribution for past annual returns over 50 years. Assuming a stable probability distribution, past relative frequencies are estimates of probabilities of future possible returns.

11. A.Farber Vietnam 2004 | 11 Mean/expected return Arithmetic Average (mean) –The average of the holding period returns for the individual years Expected return on asset A: –A weighted average return : each possible return is multiplied or weighted by the probability of its occurence. Then, these products are summed to get the expected return.

12. A.Farber Vietnam 2004 | 12 Variance -Standard deviation Measures of variability (dispersion) Variance Ex post: average of the squared deviations from the mean Ex ante: the variance is calculated by multiplying each squared deviation from the expected return by the probability of occurrence and summing the products Unit of measurement : squared deviation units. Clumsy.. Standard deviation : The square root of the variance Unit :return

13. A.Farber Vietnam 2004 | 13 Return Statistics - Example

14. A.Farber Vietnam 2004 | 14 Normal distribution Realized returns can take many, many different values (in fact, any real number > -100%) Specifying the probability distribution by listing: –all possible values –with associated probabilities as we did before wouldn't be simple. We will, instead, rely on a theoretical distribution function (the Normal distribution) that is widely used in many applications. The frequency distribution for a normal distribution is a bellshaped curve. It is a symetric distribution entirely defined by two parameters – the expected value (mean) – the standard deviation

15. A.Farber Vietnam 2004 | 15 Belgium - Monthly returns 1951 - 1999

16. A.Farber Vietnam 2004 | 16 Normal distribution illustrated

17. A.Farber Vietnam 2004 | 17 Risk premium on a risky asset The excess return earned by investing in a risky asset as opposed to a risk-free asset U.S.Treasury bills, which are a short-term, default-free asset, will be used a the proxy for a risk-free asset. The ex post (after the fact) or realized risk premium is calculated by substracting the average risk-free return from the average risk return. Risk-free return = return on 1-year Treasury bills Risk premium = Average excess return on a risky asset

18. A.Farber Vietnam 2004 | 18 Total returns US 1926-1999 Arithmetic Mean Standard Deviation Risk Premium Common Stocks13.3%20.1%9.5% Small Company Stocks17.633.613.8 Long-term Corporate Bonds5.98.72.1 Long-term government bonds5.59.31.7 Intermediate-term government bond 5.45.81.6 U.S. Treasury bills3.83.2 Inflation3.24.5 Source: Ross, Westerfield, Jaffee (2002) Table 9.2

19. A.Farber Vietnam 2004 | 19 Market Risk Premium: The Very Long Run 1802-19701871-19251926-19991802-1999 Common Stock6.88.513.39.7 Treasury Bills5.44.13.84.4 Risk premium1.44.49.55.3 Source: Ross, Westerfield, Jaffee (2002) Table 9A.1 The equity premium puzzle: Was the 20th century an anomaly?

20. A.Farber Vietnam 2004 | 20 Notions of Market Efficiency An Efficient market is one in which: –Arbitrage is disallowed: rules out free lunches –Purchase or sale of a security at the prevailing market price is never a positive NPV transaction. –Prices reveal information Three forms of Market Efficiency (a) Weak Form Efficiency Prices reflect all information in the past record of stock prices (b) Semi-strong Form Efficiency Prices reflect all publicly available information (c) Strong-form Efficiency Price reflect all information

21. A.Farber Vietnam 2004 | 21 Efficient markets: intuition Expectation Time Price Realization Price change is unexpected

22. A.Farber Vietnam 2004 | 22 Weak Form Efficiency Random-walk model: –P t -P t-1 = P t-1 * (Expected return) + Random error –Expected value (Random error) = 0 –Random error of period t unrelated to random component of any past period Implication: –Expected value (P t ) = P t-1 * (1 + Expected return) –Technical analysis: useless Empirical evidence: serial correlation –Correlation coefficient between current return and some past return –Serial correlation = Cor (R t, R t-s )

23. A.Farber Vietnam 2004 | 23 Random walk - illustration

24. A.Farber Vietnam 2004 | 24 Semi-strong Form Efficiency Prices reflect all publicly available information Empirical evidence: Event studies Test whether the release of information influences returns and when this influence takes place. Abnormal return AR : ARt = Rt - Rmt Cumulative abnormal return: CAR t = AR t0 + AR t0+1 + AR t0+2 +... + AR t0+1

25. A.Farber Vietnam 2004 | 25 Strong-form Efficiency How do professional portfolio managers perform? Jensen 1969: Mutual funds do not generate abnormal returns R fund - R f =  +  (R M - R f ) Insider trading Insiders do seem to generate abnormal returns (should cover their information acquisition activities)