1. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -1  The Market Portfolio ◦ Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P TSX or S&P 500 Composite Index, is used to represent the market. ◦ The market portfolio is used as a benchmark to measure the risk of individual stocks  Beta ◦ Sensitivity of a stock’s return to the return on the market portfolio ◦ Beta (denoted  ) is a measure of market risk LO1, LO2

2. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -2 Measuring beta:  Example: Turbot Charged Seafood has the following returns on its stock, relative to the listed changes in the return on the market portfolio.  The first three months, every time that the market return was 1% the return for Turbot were 0.8%, 1.8% and -0.2% respectively.  In the next three months, every month the market return was -1% and the Turbot returns were -1.8%, 0.2% and -0.8% respectively. Beta of Stock j =  j = % change in return of Stock j % change in return of the market LO1, LO2

3. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -3 MonthMarket Return %Turbot Return % 1+1+0.8 2+1+1.8 3+1-0.2 4-1-1.8 5-1+0.2 6-1-0.8 Average = +0.8% Average = -0.8% 1.6% LO1, LO2

4. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -4 -0.5 0.5 1 1.5 -1.5-0.50.511.5 Market Return (%) Stock Return (%) Calculating Beta  = slope of line = 0.804 Calculating Beta for Turbot LO1, LO2

5. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -5  There are two ways of measuring beta: Beta of Stock j =  j = cov(r j, r m ) mm 2 Where: Cov (j,m) = covariance of the stock’s return with the market’s return  m = standard deviation of the market LO1, LO2

6. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -6  The other way… Where:  jm = correlation of the stock’s return with market’s return  j = standard deviation of the stock  m = standard deviation of the market Beta of Stock j =  j =  jm  j mm LO1, LO2

7. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -7 Example: Correlation of the stock’s return with the market’s return (  jm ) = 0.70 Covariance of the stock’s return with the market’s return (cov jm ) = 420 Standard deviation of the market (  m ) = 20% Standard deviation of the stock (  j ) = 30%  j = 0.7(30) 20 = 1.05 420 20 2 = 1.05 LO1, LO2

8. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -8 LO1

9. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -9  Portfolio Beta: the weighted average of the betas of the individual assets; with the weights being equal to the proportion of wealth invested in each asset  The beta of a portfolio of two assets: Portfolio Beta = ( fraction of portfolio x beta of in 1 st asset 1 st asset ) + ( fraction of portfolio x beta of in 2 nd asset 2 nd asset ) LO1

10. © 2012 McGraw-Hill Ryerson LimitedChapter 12 -10  Example: You have a portfolio with 50% of your money invested in Cameco and 50% in Royal Bank stock  The beta for Cameco is 1.51 while Royal Bank beta is 0.63 Portfolio beta = [0.5  1.51] + [0.5  0.63] = 1.07 LO1