Chapter 10: Capital Markets and the Pricing of Risk

Size: px

Start display at page:

Download "Chapter 10: Capital Markets and the Pricing of Risk"

Clifford Simon
5 years ago
Views:

1 Chapter 0: Capital Markets and the Pricing of Risk- Chapter 0: Capital Markets and the Pricing of Risk Big Picture: ) To value a project, we need an interest rate to calculate present values ) The interest rate will depend on the risk of the project 3) To determine this interest rate, we need to be able to: a) measure returns b) measure risk c) figure out the relationship between risk and return I. Estimating Risk and Return Basic approaches: ) peer into the future ) look at the past and assume future will be like the past. A. Estimates based on forecasts (Review) Key: need probability distributions for investments => probability (p R ) of each possible return (R). Expected return: R p E (0.) R R R => return around which possible returns scattered. Variance and Standard deviation: R R Var p R R R E R (0.) SD Var R (0.3) => measure of how widely scattered are the possible returns => the higher the number, the more widely scattered the possible returns

2 Chapter 0: Capital Markets and the Pricing of Risk- Ex. Given the following possible returns on General Electric (GE) stock, what is the expected return and standard deviation of returns on GE stock? Prob Return.5-6%.40 %.35 44% E[R] =.5(-6) +.4() +.35(44) = 3.3% Var(R) =.5(-6-3.3) +.4(-3.3) +.35(44-3.3) = 78. SD(R) = 78. = 6.8% Ex. Assume that the expected return on General Mills (GIS) is 5% and that the standard deviation of returns on GIS is 0%. => General Mills has a lower expected return but less volatility than GE. Note: if returns were normally distributed, then can compare distributions of GE and GIS. B. Estimates based on historical returns Key assumption: future will be like the past

3 Chapter 0: Capital Markets and the Pricing of Risk-3. Realized return: R t Divt Pt Pt (0.4) P P t t ) must calculate a return any time a dividend is paid ) can calculate at any non-dividend date by assuming a dividend of 0 3) R t+ = return between now (t) and some future date (t+) 4) Div t+ = dividend at the future date (t+) 5) P t = stock price now (t) 6) P t+ = stock price at the future date (t+) Ex. Assume the following prices and dividends for General Electric (GE) stock Date Dividend Price /3 $0.00 $5.3 /5 $0.0 $5.9 6/7 $0.0 $5.9 9/6 $0. $6.3 / $0.4 $8.06 /3 $0.00 $8.9 What is return between 9/6 and /? R / =.4 =.4% = Realized return over longer periods Key: usually think in terms of annual returns a. Allow dividend-period returns to compound => +R L = (+R S ) (+R S ) (+R S3 ). (0.5) Note: assumes reinvesting all of dividends so earn return on them

4 Chapter 0: Capital Markets and the Pricing of Risk-4 Ex. Returns per period (previous GE example): Date Dividend Price Return /3 $0.00 $5.3 n.a. /5 $0.0 $ % 6/7 $0.0 $ % 9/6 $0. $6.3.77% / $0.4 $8.06.4% /3 $0.00 $8.9.7% +R year =.47 = (.0588)(.0057)(.077)(.4)(.07) => R year = 4.7% b. Solve for rate that sets PV of inflows equal to PV of outflows => NPV = 0 => => essentially solving for IRR Ex. ) this is not in the book and not in homework from the book, but there are some problems on old exams ) no assumption that reinvest dividends 3) outflows = purchase (or beginning) price of security 4) inflows = dividends (or other payments), sales (or ending) price of securities Date Dividend Price Days /3 $0.00 $5.3 0 /5 $0.0 $ /7 $0.0 $ /6 $0. $ / $0.4 $ /3 $0.00 $ NPV r r r r r => Using Excel: r =.40 = 4.%

5 Chapter 0: Capital Markets and the Pricing of Risk-5 T 3. Average Annual Returns: R R t T t => difficult to get your mind wrapped around a list of returns => need to summarize data (0.6) where: T = number of historical returns => return around which past returns are scattered 4. Variance and Volatility of Returns Var R R t R T T t (0.7) Note: dividing by T- rather than T gives unbiased estimator Volatility = SDR VarR => gives spread of possible returns => the higher the volatility, the more spread out the returns Ex. Based on the following returns on General Electric (GE), how did the average returns and volatility of GE compare to those of General Mills (GIS) which had an average return of 9% and a standard deviation of returns of 9%? Year Return +4% % 3 54% 4 +3% 5 +9% 6 % R GE % Var R GE SD(R GE ) = 70. = 6.50% => GE s return is lower and its range of possible returns (or risk) is higher

6 Chapter 0: Capital Markets and the Pricing of Risk-6 5. Standard Deviation of Averages (Standard Error) => Need some way to measure uncertainty about our estimate of the average return Standard Deviation of Averages (Standard Error): SD SE (0.8) N Where: SD = standard deviation of the observations (individual returns) N = number of observations (size of sample) Ex. SE (Average return on GE) = 0.8% = ) the calculated average return is only an estimate of the true average ) averages vary less than individual observations 3) the bigger our sample, the more confident we are in the average we calculated II. Information, risk, and return (Review) ) Firm-specific news: good or bad news about company itself Risk from firm-specific news called: firm-specific, idiosyncratic, unsystematic, unique, diversifiable risk ) Market-wide news: about economy and thus impacts all stocks Risk from market-wide news called: systematic, undiversifiable, market risk ) individual stocks contain firm-specific risk that averages out in large portfolios ) investors will only earn a premium for systematic risk => no premium for firm-specific risk since diversifies away in a portfolio

Chapter 10: Capital Markets and the Pricing of Risk

Chapter 10: Capital Markets and the Pricing of Risk Chapter 0: Capital Markets and the Pricing of Risk- Chapter 0: Capital Markets and the Pricing of Risk Big Picture: ) To value a project, we need an interest rate to calculate present values ) The interest