INVESTMENTS | BODIE, KANE, MARCUS Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 4 Risk and Portfolio Theory

INVESTMENTS | BODIE, KANE, MARCUS LEARNING OBJECTIVES 1.Identify the sources of risk. 2. Identify the relationship between securities that is necessary to achieve diversification. 3. Contrast the sources of return and differentiate between expected and realized returns. 4. Explain how standard deviations and beta coefficients measure risk, and interpret the difference between beta coefficients of 1.5, 1.0, and 0.

INVESTMENTS | BODIE, KANE, MARCUS LEARNING OBJECTIVES 5. Contrast efficient and inefficient portfolios and identify which portfolio the individual will select. 6. Compare the explanation of a stock’s return according to the Capital Asset Pricing Model and arbitrage pricing theory

INVESTMENTS | BODIE, KANE, MARCUS Portfolio Theory and the Trade Off Between Risk and Return Return: income plus capital appreciation Differences among –Expected return –Required return –Realized return

INVESTMENTS | BODIE, KANE, MARCUS Expected Return –Expected return The expected return is the anticipated flow of income and/or price appreciation.

INVESTMENTS | BODIE, KANE, MARCUS Required return Required return, which is the return necessary to induce the investor to bear the risk associated with a particular investment. Which includes (1) what the investor may earn on alternative investments. (2) a premium for bearing risk that includes compensation for the expected rate of inflation and for fluctuations in security prices.

INVESTMENTS | BODIE, KANE, MARCUS The realized return The realized return is the return actually earned on an investment and is essentially the sum of the flow of income generated by the asset and the capital gain..

INVESTMENTS | BODIE, KANE, MARCUS Risk The uncertainty associated with earning the expected return Sources of risk

INVESTMENTS | BODIE, KANE, MARCUS Risk

INVESTMENTS | BODIE, KANE, MARCUS Systematic Risk Systematic risk: Associated with fluctuation in security prices; e.g., market risk. Market risk refers to the tendency of security prices to move together. Interest rate risk refers to the tendency of security prices, especially fixed- income securities, to move inversely with changes in the rate of interest. Reinvestment rate risk refers to the risk associated with reinvesting funds generated by an investment.

INVESTMENTS | BODIE, KANE, MARCUS Systematic Risk Purchasing power risk is the risk that inflation will erode the buying power of the investor’s assets and income. Exchange rate: the fluctuation of the price of a foreign currency in terms of another currency.

INVESTMENTS | BODIE, KANE, MARCUS Unsystematic Risk Unsystematic risk, which is also referred to as diversifiable risk, depends on factors that are unique to the specific asset. Business risk is the risk associated with the nature of the enterprise itself. Financial risk is the risk associated with a firm’s sources of financing.

INVESTMENTS | BODIE, KANE, MARCUS Unsystematic Risk and Total Risk Decline as more securities are added to the portfolio Systematic Market Risk : not affected by diversification

INVESTMENTS | BODIE, KANE, MARCUS Total Risk (Portfolio RISK) The total risk associated with owning a portfolio; the sum of systematic and unsystematic risk. Systematic Market Risk : not affected by diversification. Diversification is the process of accumulating different securities to reduce the risk of loss.

INVESTMENTS | BODIE, KANE, MARCUS Unsystematic Risk and Total Risk

INVESTMENTS | BODIE, KANE, MARCUS Measures of Risk The variability of returns (standard deviation) The volatility of returns (beta)

INVESTMENTS | BODIE, KANE, MARCUS Dispersion Around Investment Retune Stock B Stock A /2 11 1/ /2 12 1/2 14 1/ /2 15 1/ /4 18 1/ /2 5-17

INVESTMENTS | BODIE, KANE, MARCUS Increased Variability

INVESTMENTS | BODIE, KANE, MARCUS 5-19 Expected Return E(r)= Expected Return E(D) = Expected Dividends P 0 = The initial price of asset Rates of Return: Single Period

INVESTMENTS | BODIE, KANE, MARCUS 5-20 Ending Price =110 Beginning Price = 100 Dividend = 4 E ( r )= ( )/ (100) = 14% Expected Rates of Return:

INVESTMENTS | BODIE, KANE, MARCUS 5-21 Expected returns as probabilities p(s) = probability of a state r(s) = return if a state occurs s = state Expected Return and Standard Deviation

INVESTMENTS | BODIE, KANE, MARCUS StateProb. of Stater in State Excellent Good Poor Crash E(r) = (.25)(.31) + (.45)(.14) + (.25)(-.0675) + (0.05)(-0.52) E(r) =.0976 or 9.76% Scenario Returns: Example

INVESTMENTS | BODIE, KANE, MARCUS Variance (VAR): Variance and Standard Deviation Standard Deviation (STD):

INVESTMENTS | BODIE, KANE, MARCUS 5-24 Scenario VAR and STD Example VAR calculation: σ 2 =.25( ) ( ) ( ) ( ) 2 =.038 Example STD calculation:

INVESTMENTS | BODIE, KANE, MARCUS 5-25 The Return and Standard Deviation of a Portfolio Return on a Portfolio is the weighted average of returns on the individual assets in the portfolio. Standard Deviation of a portfolio’s returns is calculated using all of the individual assets in the portfolio.

INVESTMENTS | BODIE, KANE, MARCUS 5-26 Return on Portfolio

INVESTMENTS | BODIE, KANE, MARCUS Return and Standard deviation Return Stock 8.3% Weighted Average W Return % E (R)

INVESTMENTS | BODIE, KANE, MARCUS 5-28 Correlation: Why Diversification Works! Correlation is a statistical measure of the relationship between two series of numbers representing data. Positively Correlated items move in the same direction. Negatively Correlated items move in opposite directions. Correlation Coefficient is a measure of the degree of correlation between two series of numbers representing data.

INVESTMENTS | BODIE, KANE, MARCUS 5-29 Correlation Coefficients Perfectly Positively Correlated describes two positively correlated series having a correlation coefficient of +1 Perfectly Negatively Correlated describes two negatively correlated series having a correlation coefficient of -1 Uncorrelated describes two series that lack any relationship and have a correlation coefficient of nearly zero

INVESTMENTS | BODIE, KANE, MARCUS 5-30 The Correlation Between Series M, N, and P

INVESTMENTS | BODIE, KANE, MARCUS 5-31 Correlation: Why Diversification Works! To reduce overall risk in a portfolio, it is best to combine assets that have a negative (or low-positive) correlation. Uncorrelated assets reduce risk somewhat, but not as effectively as combining negatively correlated assets. Investing in different investments with high positive correlation will not provide sufficient diversification.

INVESTMENTS | BODIE, KANE, MARCUS = Variance of Security D = Variance of Security E = Covariance of returns for Security D and Security E Two-Security Portfolio: Risk

INVESTMENTS | BODIE, KANE, MARCUS  D,E = Correlation coefficient of returns Cov(r D, r E ) =  DE  D  E  D = Standard deviation of returns for Security D  E = Standard deviation of returns for Security E Covariance

INVESTMENTS | BODIE, KANE, MARCUS Three-Asset Portfolio

INVESTMENTS | BODIE, KANE, MARCUS Calculating the Standard Deviation of a Portfolio Returns Determine the expected return and standard deviation of the following portfolio consisting of two stocks that have a correlation coefficient of.75. PortfolioWeightExpected Return Standard Deviation Apple Coca-Cola

INVESTMENTS | BODIE, KANE, MARCUS Calculating the Standard Deviation of a Portfolio Returns Expected Return =.5 (.14) +.5 (.14) =.14 or 14%

INVESTMENTS | BODIE, KANE, MARCUS Calculating the Standard Deviation of a Portfolio Returns Standard deviation of portfolio = √ { (.5 2 x.2 2 )+(.5 2 x.2 2 )+(2x.5x.5x.75x.2x.2)} = √.035 =.187 or 18.7% Correlation Coefficient

INVESTMENTS | BODIE, KANE, MARCUS 7-38 Range of values for  1, >  >-1.0 If  = 1.0, the securities are perfectly positively correlated If  = - 1.0, the securities are perfectly negatively correlated Correlation Coefficients: Possible Values

INVESTMENTS | BODIE, KANE, MARCUS 5-39 Interpreting Beta Higher stock betas should result in higher expected returns due to greater risk If the market is expected to increase 10%, a stock with a beta of 1.50 is expected to increase 15% If the market went down 8%, then a stock with a beta of 0.50 should only decrease by about 4% Beta values for specific stocks can be obtained from Value Line reports or online websites such as yahoo.com

INVESTMENTS | BODIE, KANE, MARCUS 5-40 Interpreting Beta

INVESTMENTS | BODIE, KANE, MARCUS 5-41 Capital Asset Pricing Model (CAPM) Model that links the notions of risk and return Helps investors define the required return on an investment As beta increases, the required return for a given investment increases