LO 1 Expected Returns 13 1 Expected returns

LO 1 Expected Returns 13. 1 • Expected returns are based on the probabilities of possible outcomes • In this context, “expected” means average if the process is repeated many times • The “expected” return does not even have to be a possible return © 2013 Mc. Graw-Hill Ryerson Limited 13 -0

LO 1 Expected Returns – Example 1 • Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? • • State Boom Normal Recession Probability 0. 3 0. 5 ? ? ? C 0. 15 0. 10 0. 02 T 0. 25 0. 20 0. 01 • RC =. 3(. 15) +. 5(. 10) +. 2(. 02) =. 099 = 9. 9% • RT =. 3(. 25) +. 5(. 20) +. 2(. 01) =. 177 = 17. 7% © 2013 Mc. Graw-Hill Ryerson Limited 13 -1

LO 1 Expected Returns – Example 1 continued • This example can also be done in a spreadsheet • Click on the Excel link to see this © 2013 Mc. Graw-Hill Ryerson Limited 13 -2

LO 1 Variance and Standard Deviation • Variance and standard deviation still measure the volatility of returns • You can use unequal probabilities for the entire range of possibilities • Weighted average of squared deviations © 2013 Mc. Graw-Hill Ryerson Limited 13 -3

LO 1 Variance and Standard Deviation – Example 1 • Consider the previous example. What is the variance and standard deviation for each stock? • Stock C • 2 =. 3(. 15 -. 099)2 +. 5(. 1 -. 099)2 +. 2(. 02. 099)2 =. 002029 • =. 045 • Stock T • 2 =. 3(. 25 -. 177)2 +. 5(. 2 -. 177)2 +. 2(. 01. 177)2 =. 007441 • =. 0863 © 2013 Mc. Graw-Hill Ryerson Limited 13 -4

LO 1 Variance and Standard Deviation – Example continued • This can also be done in a spreadsheet • Click on the Excel icon to see this © 2013 Mc. Graw-Hill Ryerson Limited 13 -5

Quick Quiz I LO 1 • Consider the following information: • • • State Boom Normal Slowdown Recession Probability. 25. 50. 15. 10 ABC, Inc. . 15. 08. 04 -. 03 • What is the expected return? • What is the variance? • What is the standard deviation? © 2013 Mc. Graw-Hill Ryerson Limited 13 -6

LO 1 Portfolios 13. 2 • A portfolio is a collection of assets • An asset’s risk and return is important in how it affects the risk and return of the portfolio • The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets © 2013 Mc. Graw-Hill Ryerson Limited 13 -7

Example: Portfolio Weights LO 1 • Suppose you have $15, 000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? • • $2000 of ABC $3000 of DEF $4000 of GHI $6000 of JKL • ABC: 2/15 =. 133 • DEF: 3/15 =. 2 • GHI: 4/15 =. 267 • JKL: 6/15 =. 4 © 2013 Mc. Graw-Hill Ryerson Limited 13 -8

LO 1 Portfolio Expected Returns • The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio • You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities © 2013 Mc. Graw-Hill Ryerson Limited 13 -9

LO 1 Example: Expected Portfolio Returns • Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? • • ABC: 19. 65% DEF: 8. 96% GHI: 9. 67% JKL: 8. 13% • E(RP) =. 133(19. 65) +. 2(8. 96) +. 267(9. 67) +. 4(8. 13) = 10. 24% • Click the Excel icon for an example © 2013 Mc. Graw-Hill Ryerson Limited 13 -10

LO 1 Portfolio Variance • Compute the portfolio return for each state: R P = w 1 R 1 + w 2 R 2 + … + w m. R m • Compute the expected portfolio return using the same formula as for an individual asset • Compute the portfolio variance and standard deviation using the same formulas as for an individual asset © 2013 Mc. Graw-Hill Ryerson Limited 13 -11

LO 1 Example: Portfolio Variance • Consider the following information • • Invest 60% of your money in Asset A State Probability A B Boom. 5 70% 10% Bust. 5 -20% 30% • What is the expected return and standard deviation for each asset? • What is the expected return and standard deviation for the portfolio? © 2013 Mc. Graw-Hill Ryerson Limited 13 -12

LO 1 Portfolio Variance Example continued • This can also be done in a spreadsheet • Click on the Excel icon to see this © 2013 Mc. Graw-Hill Ryerson Limited 13 -13

LO 1 Another Way to Calculate Portfolio Variance • Portfolio variance can also be calculated using the following formula: © 2013 Mc. Graw-Hill Ryerson Limited 13 -14

Quick Quiz II LO 1 • Consider the following information • • State Boom Normal Recession Probability. 25. 60. 15 X 15% 10% 5% Z 10% 9% 10% • What is the expected return and standard deviation for a portfolio with an investment of $6, 000 in asset X and $4, 000 in asset Z? © 2013 Mc. Graw-Hill Ryerson Limited 13 -15

LO 1 Arbitrage Pricing Theory (APT) 13. 8 • Similar to the CAPM, the APT can handle multiple factors that the CAPM ignores • Unexpected return is related to several market factors © 2013 Mc. Graw-Hill Ryerson Limited 13 -16