Introduction to Risk and Return and opportunity cost of capital Chapter 11 BBM 08/29/12 1

11-2 Risk and Return Risk and Return are related. How? We now focus on risk and return and their relationship to the opportunity cost of capital.

11-3 Equity Rates of Return: A Review

11-4 Real Rates of Return Example: Suppose inflation from December 2009 to December 2010 was 1.5%. What was GE stock’s real rate of return, if its nominal rate of return was 23.93%? Recall the relationship between real rates and nominal rates:

11-5 Total Returns for Different Asset Classes The Value of an Investment of $1 in 1900

11-6 What Drives the Difference in Total Returns? Maturity Premium: Extra average return from investing in longer term Treasury securities. Risk Premium: Expected return in excess of risk-free return as compensation for risk.

11-7 Risk Premium: Example

11-8 Returns and Risk How are the expected returns and the risk of a security related?

11-9 Measuring Risk Variance: Average value of squared deviations from mean. A measure of volatility. Standard Deviation: Square root of variance. Also a measure of volatility. What is risk? How can it be measured?

Market Indexes Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms. Standard & Poor’s Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues. OMX SPI index 10

OMX Stockholm PI OMX nordiska börs använder en gemensam indelning och uppbyggnad av index för de nordiska marknaderna. En enhetlig indexstandard ökar förståelsen för de nordiska indexen och underlättar jämförelser mellan olika index. OMX Stockholm 30 (OMXS30) – PI OMX Stockholm 30 är OMX Nordiska Börs Stockholms ledande aktieindex. Indexet består av de 30 mest aktivt handlade aktierna på den Nordiska Börsen i Stockholm. OMX Stockholm All-Share (OMXS) – PI OMX Nordiska Börs Stockholms All-Share-index innefattar alla aktier som är noterade på den Nordiska Börsen i Stockholm. Basdatum för All-Share-index på OMX Nordiska Börs Stockholm är den 31 december 1995, med basvärdet

Average Market Risk Premium (by country) Risk premium, % Country Market risk premium = Market rate of return – risk-free rate 12

Dividend Yield Dividend yields in the U.S.A. 1900–

Rates of Return Source: Ibbotson Associates Year Percentage Return Stock Market Index Returns 14

Measuring Risk Return % # of Years Histogram of Annual Stock Market Returns ( ) 15 Probability distribution of stock returns Ex. There has been 24 years with 20 to 30 % stock return.

Thinking About Risk Message 1 – Some Risks Look Big and Dangerous but Really Are Diversifiable Message 2 – Market Risks Are Macro Risks Message 3 – Risk Can Be Measured

11-17 Historical Risk ( )

11-18 Risk and Diversification Diversification Strategy designed to reduce risk by spreading a portfolio across many investments. Unique Risk: Risk factors affecting only that firm. Also called “diversifiable risk.” Market Risk: Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation (STD) – square root of variance. A measure of volatility. Expected value: average value with equal weight. 19

Measuring Risk Example from page: 320. Coin Toss Game-calculating variance and standard deviation

Measuring Risk You start with 100 kr. Toss two coins at a time. Head up you gain 20%, tails up you lose 10%. There are all together 4 outcomes. (HH) (HT) (TH) (TT). Coin Toss Game-calculating variance and standard deviation 21

Measuring Risk Expected return is just a weighted average of individual stock returns. 22

Dow Jones Risk Annualized Standard Deviation of the DJIA over the preceding 52 weeks (1900 – 2008) Years Standard Deviation (%) 23

Measuring Risk Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” 24

Market Index Obs: step 1, get the Mean 8,5%, step 2, get the deviations from the mean and step 3, square it to get the variance. Since we have 6 years’ observations, divide it with 6.

11-26 Risk and Diversification

Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes 27

Portfolio Risk Example Suppose you invest 60% of your portfolio in Campbell Soup and 40% in Boeing. The expected dollar return on your Campbell Soup stock is 3.1% and on Boeing is 9.5%. The expected return on your portfolio is: 28

Portfolio Risk Example Suppose you invest 60% of your portfolio in Campbell Soup and 40% in Boeing. The expected dollar return on your Campbell Soup stock is 3.1% and on Boeing is 9.5%. The standard deviation of their annualized daily returns are 15.8% and 23.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 29

11-30 Do stock prices move together? What effect does diversification have on a portfolio’s total risk, unique risk and market risk?

Portfolio Risk Example Suppose you invest 60% of your portfolio in Campbell Soup and 40% in Boeing. The expected dollar return on your Campbell Soup stock is 3.1% and on Boeing is 9.5%. The standard deviation of their annualized daily returns are 15.8% and 23.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 31 Obs: Since the correlation coefficient is 1, there is no portfolio risk reduction at all! The average standard deviation for the two stocks is the same 18,96%=15,8*0,6+23,7*0,4

Portfolio Risk Another Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is: 32

Portfolio Risk Another Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 33 Again the correlation coefficient= 1, no gain on diversification! But it sure lowered the risk and the return by averaging.

Portfolio Risk 34

Portfolio Risk Example Correlation Coefficient =.4 Stocks  % of PortfolioAvg Return ABC Corp28%60% 15% Big Corp 42% 40% 21% Standard Deviation = weighted avg. = 33.6 (this is an average of the std) Standard Deviation = Portfolio = 28.1 Real Standard Deviation: Portfolio Variance = (28 2) (.6 2 ) + (42 2 )(.4 2 ) + 2(.4)(.6)(28)(42)(.4) STD=sqrt (Variance) = 28.1 CORRECT Mean: r = (15%)(.60) + (21%)(.4) = 17.4% 35

Portfolio Risk Example Correlation Coefficient =.4 Stocks  % of PortfolioAvg Return ABC Corp28%60% 15% Big Corp 42% 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4% Let’s Add stock New Corp to the portfolio 36

Portfolio Risk Example Correlation Coefficient =.3 Stocks  % of PortfolioAvg Return Portfolio28.150% 17.4% New Corp30 50% 19% NEW Standard Deviation = weighted avg. std= NEW Standard Deviation = Portfolio = NEW Mean = weighted avg = Portfolio = 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION 37

The Variance Covariance Matrix The shaded boxes contain variance terms; the remainder contain covariance terms. Adding them up you get the portfolio variance N N STOCK To calculate portfolio variance add up the boxes 38

Portfolio Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio. 39

The Security Market Line The return on Dell stock changes on average by 1.41% for each additional 1% change in the market return. Beta = The model is the famous CAPM: Capital asset pricing model, you get the r--- required rate of return or cost of capital from this!

Portfolio Risk σ im = Covariance with the market σ m ^ 2 = Variance of the market If beta is 1,5, market volatility is 20%, Then, Covariance of the portfolio with the market return is =(20%)^2*1,5=0,06 41

Portfolio Risk Covariance with the market Variance of the market 42

Portfolio Risk The middle line shows that a well Diversified portfolio of randomly selected stocks ends up with β= 1 and a standard deviation equal to the market’s—in this case 20%. The upper line shows that a well-diversified portfolio with β= 1.5 has a standard deviation of about 30%, i.e. 1.5 times that of the market. The lower line shows that a well-diversified portfolio with β =.5 has a standard deviation of about 10%—half that of the market. 43

Beta Check the figure see if it is right! Find out how to use excel to calculate variance and mean of a portfolio. 44