Financial Markets 11-1

Transcription

1 Financial Markets Laurent Calvet John Lewis Topic 11: Measuring Financial Risk HEC MBA Financial Markets 11-1

2 Risk There are many types of risk in financial transactions Liquidity Currency Political Inflation Natural Disaster Solvency/Counterparty Interest rate Regulatory Fraud Market Investors seek to reduce uncertainty of cash flows HEC MBA Financial Markets 11-2

3 $100 Invested at the End of

4 A First Look at Risk and Return Small stocks had the highest long-term return while T-Bills had the lowest. Small stocks had the largest price fluctuations while T-Bills had the lowest. Higher risk requires a higher return 11-4

5 Expected Return Weighted average of all possible returns, where the weights are the probabilities. Expected Return [ ] = = R R E R P R Example: [ ] 25%( 0.20) 50%(0.10) 25%(0.40) ER = + + = 10% 11-5

6 Variance and Standard Deviation Variance The expected squared deviation from the mean [ ] ( ) 2 Var( R) = PR R E R R Standard Deviation SD( R) = Var( R) Both are measures of risk In finance, the standard deviation of a return is also called its volatility 11-6

7 Example 1 TXU stock has the following probability distribution: Probability Return.25 8%.55 10%.20 12% Compute TXU s expected return and standard deviation. 11-7

8 Solution TXU E[R] and Std Dev Expected Return E[R] = (.25)(.08) + (.55)(.10) + (.20)(.12) E[R] = = = 9.9% Standard Deviation SD(R) = [(.25)( ) 2 + (.55)( ) 2 + (.20)( ) 2 ] 1/2 SD(R) = [ ] 1/2 SD(R) = /2 = = 1.338% HEC MBA Financial Markets 11-8

9 Historical Returns Realized Return The return that actually occurs over a particular time period. R t + 1 ( P + Div ) P Div P P = = + P P P t+ 1 t+ 1 t t+ 1 t+ 1 t t t t R Div + P t+ 1 t+ 1 t + 1 = 1 Pt Dividend yield Capital gain 11-9

10 Numerical Example: Ford Motor Company Date End-of-month Prices Dividend Montly Return (%) Jun ,24 Jul ,74 0,1 5,86% Aug ,97-7,17% Sep ,86-1,10% Oct ,32 0,1-14,60% Nov ,13-2,28% Dec ,72-5,04% Jan ,58 0,1 12,44% Feb ,97-7,11% Mar ,96-0,13% Apr ,95 0,1-11,43% May ,16 3,02% Jun ,93-3,21% ( )/

11 Historical Average and Variance Average Return: 1 1 T R R R R R ( ) = T = T T t = 1 where R t is the realized return of a security in year t. Show that average monthly return is -2.56% for Ford Variance: T 1 Var( R) = R R 1 T t = 1 ( ) 2 t The square root of the variance is an estimate of volatility Show that monthly variance is 0.55% for Ford t 11-11

12 Tradeoff Between Risk and Return There is a positive relationship between the volatility and average return of large portfolios

13 Individual Stocks Is there a positive relationship between volatility and average returns for individual stocks? NO, as is apparent in the next slide. Larger stocks tend to have lower volatility than smaller stocks. All individual stocks tend to have higher risk and lower returns than large portfolios 11-13

14 500 Individual Stocks by Size

15 Common Versus Independent Risk Common Risk Risk that is perfectly correlated Affects all securities Independent Risk Risk that is uncorrelated Affects only a particular security Diversification The averaging out of independent risks in a large portfolio 11-15

16 Diversification in Stock Portfolios Firm-Specific Risk Good or bad news about an individual company Example: CEO died in a plane accident Systematic Risk due to Market-Wide News News that affects all stocks Examples: Economic downturn that adversely affects the demand for the products of all firms, sovereign default

17 Large Portfolio When many stocks are combined in a large portfolio, the firm-specific risks for each stock will average out and be diversified The systematic risk, however, will affect all firms and will not be diversified 11-17

18 No Arbitrage and Risk Premium Investors are not compensated for firm-specific risk Otherwise, investors could buy the stocks, earn the additional premium, and simultaneously sell the portfolio. The risk premium of a security is determined only by its systematic risk This implies that a stock s volatility, which is a measure of total risk (that is, systematic risk plus diversifiable risk), is not especially useful in determining the risk premium that investors will earn

19 Estimating the Expected Return Estimating the expected return of a security will require two steps: 1. Measure the investment s systematic risk 2. Determine the risk premium required to compensate for that amount of systematic risk. Systematic risk is measured relative to an efficient benchmark

20 Efficient Benchmark Efficient Portfolio A portfolio that contains only systematic risk. There is no way to reduce the volatility of the portfolio without lowering its expected return. Market Portfolio An efficient portfolio that contains all shares and securities in the market. The S&P 500 is often used as a proxy for the market portfolio. Market Risk Premium = E RMkt r f 11-20

21 Measuring Systematic Risk To determine how sensitive a stock is to systematic risk, look at the average change in the return for each 1% change in the return of the efficient portfolio. Beta (β): The expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio Beta differs from volatility. Volatility measures total risk (systematic plus unsystematic risk), while beta is a measure of systematic risk

22 What drives β? A security s beta is related to how sensitive its underlying revenues and cash flows are to general economic conditions. Stocks in cyclical industries, are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive industries

23 10-23

24 A Low β Stock: AIR LIQUIDE 11-24

25 A High β Stock: INTEL CORP 11-25

26 Estimating a Security s Risk Premium We estimate a traded security s expected return from its beta. [ ] = Risk-Free Interest Rate + Risk Premium E R = rf + β ( E RMkt rf) 11-26

27 Problem There is a 60% chance that the market return will be 15% next year and a 40% chance that the market return will be 5% next year. Assume the risk-free rate is 6%. If Microsoft s beta is 1.18, what is its expected return next year? 11-27

28 Solution MSFT E[R] E[R Mkt ] = (60% 15%) + (40% 5%) = 11% E[R] = r f + β (E[R Mkt ] r f ) E[R] = 6% (11% 6%) E[R] = 6% + 5.9% = 11.9% HEC MBA Financial Markets 11-28