# Financial Management: Principles & Applications, Thirteenth ...

Financial Management: Principles & Applications Thirteenth Edition Chapter 8 Risk and Return Capital Market Theory Copyright Education, 2018, 2014, 2011 Pearson Inc. All Reserved Rights Reserved Copyright 2018, 2014, 2011 Pearson Inc. Education,

All Rights Learning Objectives 1. Calculate the expected rate of return and volatility for a portfolio of investments and describe how diversification affects the returns to a portfolio of investments. 2. Understand the concept of systematic risk for an individual investment and calculate portfolio systematic risk (beta). 3. Estimate an investors required rate of return using the Capital Asset Pricing Model. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Principles Applied in This Chapter

Principle 2: There is a Risk-Return Tradeoff. Principle 4: Market Prices Reflect Information. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved 8.1 PORTFOLIO RETURNS AND PORTFOLIO RISK Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Portfolio Returns and Portfolio Risk With appropriate diversification, you can lower the risk of your portfolio without lowering its expected rate of return. Those risks that can be eliminated by diversification are not necessarily rewarded in the

financial marketplace. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Calculating the Expected Return of a Portfolio (1 of 2) To calculate a portfolios expected rate of return, we weight each individual investments expected rate of return using the fraction of the portfolio that is invested in each investment. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Calculating the Expected Return of a Portfolio (2 of 2)

Portfolio Expected Rate of Return E (rportfolio ) [W1 E ( r1 )] [W2 E (r2 )] [W3 E (r3 )] [Wn E (rn )] E(rportfolio) = the expected rate of return on a portfolio of n assets. Wi = the portfolio weight for asset i. E(ri ) = the expected rate of return earned by asset i. W1 E(r1) = the contribution of asset 1 to the portfolio expected return. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved CHECKPOINT 8.1: CHECK YOURSELF Calculating a Portfolios Expected Rate of Return Evaluate the expected return for Pennys portfolio where she places a quarter of her money in Treasury bills, half in Starbucks stock, and the remainder in Emerson Electric

stock. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 1: Picture the Problem Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 2: Decide on a Solution Strategy (1 of 2) The portfolio expected rate of return is simply a weighted average of the expected rates of return of the investments in the portfolio. We can use equation 8-1 to calculate the expected rate of return for Pennys portfolio.

Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 2: Decide on a Solution Strategy (2 of 2) We have to fill in the third column (Product) to calculate the weighted average. Portfolio E(Return) X Weight = Product Treasury bills

4.0% .25 Blank EMR stock 8.0% .25 Blank SBUX stock

12.0% .50 Blank We can also use equation 8-1 to solve the problem. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 3: Solve (1 of 2) Portfolio Expected Rate of Return E (rportfolio ) [W1 E (r1 )] [W2 E (r2 )] [W3 E (r3 )] [Wn E (rn )]

E(rportfolio) = .25 .04 + .25 .08 + .50 .12 = .09 or 9% Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 3: Solve (2 of 2) Alternatively, we can fill out the following table from step 2 to get the same result. Portfolio E(Return) X Weight = Product

Treasury bills 4.0% .25 1% EMR stock 8.0% .25

2% SBUX stock 12.0% .50 6% Expected Return on Portfolio Blank Blank

9% Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 4: Analyze The expected return is 9% for a portfolio composed of 25% each in treasury bills and Emerson Electric stock and 50% in Starbucks. If we change the percentage invested in each asset, it will result in a change in the expected return for the portfolio. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Evaluating Portfolio Risk: Portfolio Diversification The effect of reducing risks by including a large number of investments in a portfolio is called diversification. The diversification gains achieved will depend on the degree of correlation among the investments, measured by correlation coefficient. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Portfolio Diversification The correlation coefficient can range from 1.0 (perfect negative correlation), meaning that two

variables move in perfectly opposite directions to +1.0 (perfect positive correlation). Lower the correlation, greater will be the diversification benefits. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Diversification Lessons 1. A portfolio can be less risky than the average risk of its individual investments. 2. The key to reducing risk through diversification is to combine investments whose returns are not perfectly positively correlated. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Calculating the Standard Deviation of a Portfolios Returns portfolio W12 12 W22 22 2W1W2 1,2 1 2 Important Definitions and Concepts: Portfolio = the standard deviation in portfolio returns. W1, W2, and W3 = the proportions of the portfolio that are invested in assets 1, 2, and 3, respectively. 1, 2, and 3 = the standard deviations in the rates of return earned by assets 1, 2, and 3, respectively. i, j = the correlation between the rates of return earned by assets i and j. The symbol 1, 2 (pronounced rhoB) represents correlation between the rates of return for asset 1 and asset 2. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Figure 8-1 Diversification and the Correlation Coefficient Apple and CocaCola (1 of 2) Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Figure 8-1 Diversification and the Correlation Coefficient Apple and CocaCola (2 of 2) Legend: Correlation Expected Return Standard Deviation 1.00

0.14 0% 0.80 0.14 6% 0.60 0.14

9% 0.40 0.14 11% 0.20 0.14 13% 0.0

0.14 14% 0.20 0.14 15% 0.40 0.14

17% 0.60 0.14 18% 0.80 0.14 19% 1.00

0.14 20% All portfolios are comprised of equal investments in Apple and Coca-Cola shares. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved The Impact of Correlation Coefficient on the Risk of the Portfolio We observe (from figure 8.1) that lower the correlation, greater is the benefit of diversification. Correlation between investment returns

Diversification Benefits +1 No benefit 0.0 Substantial benefit 1 Maximum benefit. Indeed, the risk of portfolio can be reduced to zero.

Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved CHECKPOINT 8.2: CHECK YOURSELF Evaluating a Portfolios Risk and Return Evaluate the expected return and standard deviation of the portfolio of the S&P500 index fund and the international fund where the correlation is estimated to be .20 and Sarah still places half of her money in each of the funds. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 1: Picture the Problem Sarah can visualize the expected return, standard deviation and weights as shown below, with the need to determine the numbers for the empty

boxes. Investment Fund Expected Return Standard Deviation Investment Weight S&P500 fund 12% 20%

50% International Fund 14% 30% 50% Portfolio Blank Blank

100% Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 2: Decide on a Solution Strategy The portfolio expected return is a simple weighted average of the expected rates of return of the two investments given by equation 8-1. The standard deviation of the portfolio can be calculated using equation 8-2. We are given the correlation to be equal to 0.20. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Step 3: Solve (1 of 2) Portfolio Expected Rate of Return E (rportfolio ) [W1 E (r1 )] [W2 E (r2 )] [W3 E (r3 )] [Wn E (rn )] E(rportfolio) = WS&P500 E(rS&P500) + WInternational E(rInternational) = .5 (12) + .5(14) = 13% Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 3: Solve (2 of 2) 2 1

2 1 2 2 2 2 portfolio W W 2W1W2 1,2 1 2 Standard deviation of Portfolio = { (.52x.22)+(.52x.32)+(2x.5x.5x.20x.2x.3)} = {.0385} = .1962 or 19.62%

Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 4: Analyze A simple weighted average of the standard deviation of the two funds would have resulted in a standard deviation of 25% (20 x .5 + 30 x .5) for the portfolio. However, the standard deviation of the portfolio is less than 25% (19.62%) because of the diversification benefits (with correlation being less than 1). Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Risk and Return of a 3 Assets Portfolio Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved 8.2 SYSTEMATIC RISK AND THE MARKET PORTFOLIO Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Systematic Risk and Market Portfolio (1 of 3) CAPM theory assumes that investors chose to hold the optimally diversified portfolio that includes all of the economys assets (referred to as the market portfolio). According to the CAPM, the relevant risk of an investment is determined by how it contributes

to the risk of this market portfolio. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Systematic Risk and Market Portfolio (2 of 3) To understand how an investment contributes to the risk of the portfolio, we categorize the risks of the individual investments into two categories: Systematic risk, and Unsystematic risk Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Systematic Risk and Market Portfolio (3 of 3) The systematic risk component measures the

contribution of the investment to the risk of the market portfolio. For example: War, recession. The unsystematic risk is the element of risk that does not contribute to the risk of the market and is diversified away. For example: Product recall, labor strike, change of management. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Diversification and Unsystematic Risk Figure 8-2 illustrates that, as the number of securities in a portfolio increases, the contribution of the unsystematic risk to the standard deviation of the portfolio declines while the systematic risk is not reduced. Thus large portfolios will not be affected by

unsystematic risk. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Figure 8.2 Portfolio Risk and the Number of Investments in the Portfolio Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Systematic Risk and Beta Systematic risk is measured by beta coefficient, which estimates the extent to which a particular investments returns vary with the returns on the market portfolio. In practice, it is estimated as the slope of a straight line (see figure 8-3).

Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Figure 8.3 Estimating Home Depots (HD) Beta Coefficient (1 of 2) Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Figure 8.3 Estimating Home Depots (HD) Beta Coefficient (2 of 2) Observation Date S&P 500 Return

Home Depot Stock Return 1 Nov-10 0.23% 1.47% 2 Dec-10

6.53% 16.05% 3 Jan-11 2.26% 4.88% 4 Feb-11

3.90% 1.90% 5 Mar-11 0.10% 0.43% 6

Apr-11 2.85% 0.24% 7 May-12 1.35% 2.34% 8

Jun-12 1.83% 0.52% 9 Jul-12 2.15% 3.56%

10 Aug-12 5.68% 3.72% 11 Sep-12 7.18% 1.53%

12 Oct-12 10.77% 8.91% Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Table 8.1 Beta Coefficients for Selected Companies Company Yahoo Finance

(Yahoo.com) Microsoft Money Central (MSN.com) Blank Blank Apple Inc. (AAPL) 2.90 2.58

Hewlett Packard (HPQ) 1.27 1.47 Blank Blank American Electric Power Co. (AEP) 0.74 0.73

Duke Energy Corp. (DUK) 0.40 0.56 Centerpoint Energy (CNP) 0.82 0.91 Computers and Software

Utilities Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Beta Table 8-1 illustrates the wide variation in Betas for various companies. Utilities companies can be considered less risky because of their lower betas. For example, based on the beta estimates, a 1% drop in market could lead to a .74% drop in AEP but a much greater 2.9% drop in AAPL. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Calculating Portfolio Beta (1 of 2)

The portfolio beta measures the systematic risk of the portfolio. Beta for Proportion of Beta for Beta for Proportion of Proportion of Portfolio Portfolio Invested Asset 1 Portfolio Invested Asset 2 Portfolio Invested Asset n Beta

in Asset 1 (W ) in Asset n (W ) ( 1 ) in Asset 2 (W2 ) ( 2 ) ( n ) 1 n Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Calculating Portfolio Beta (2 of 2) Example Consider a portfolio that is comprised of four investments with betas equal to 1.50, 0.75,

1.80 and 0.60 respectively. If you invest equal amount in each investment, what will be the beta for the portfolio? = .25(1.50) + .25(0.75) + .25(1.80) + .25 (0.60) = 1.16 Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved 8.3 THE SECURITY MARKET LINE AND THE CAPM Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved The Security Market Line and the CAPM (1 of 3)

CAPM describes how the betas relate to the expected rates of return. The key insight of CAPM is that investors will require a higher rate of return on investments with higher betas. Figure 8-4 provides the expected returns and betas for portfolios comprised of market portfolio and risk-free asset. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Figure 8.4 Risk and Return for Portfolios Containing the Market and the RiskFree Security (2 of 2) Legend: Blank

Blank Blank % Market Portfolio, WM % Risk-Free Asset, Wrf Portfolio Beta, Portfolio Expected Portfolio

Return, E(rPortfolio) 0% 100% 0.0 6.0% 20% 80% 0.2

7.0% 40% 60% 0.4 8.0% 60% 40%

0.6 9.0% 80% 20% 0.8 10.0% 100% 0%

Figure 8.4 Risk and Return for Portfolios Containing the Market and the RiskFree Security (1 of 2) Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved The Security Market Line and the CAPM (2 of 3) CAPM describes how the betas relate to the expected rates of return. The key insight of CAPM is that investors will require a higher rate of return on investments with higher betas. Figure 8-4 provides the expected returns and betas for portfolios comprised of market portfolio and risk-free asset.

Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved The Security Market Line and the CAPM (3 of 3) SML is a graphical representation of the CAPM. SML can be expressed as the following equation, which is often referred to as the CAPM pricing equation: E (rAsset j ) rf Asset j [E (rMarket ) rf ] Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Using the CAPM to Estimate the Expected Rate of Return Equation 8-6 implies that higher the systematic risk of an investment, other things remaining the same, the higher will be the expected rate of return an investor would require to invest in the asset. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved CHECKPOINT 8.3: CHECK YOURSELF Estimating the Expected Rate of Return Using the CAPM Estimate the expected rates of return for the three utility companies, found in Table 81, using the 4.5% risk-free rate and market risk premium of 6%. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

Step 1: Picture the Problem (1 of 2) Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 1: Picture the Problem (2 of 2) The graph shows that as beta increases, the expected return also increases. When beta = 0, the expected return is equal to the risk free rate of 4.5%. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 2: Decide on a Solution Strategy We can determine the required rate of return by using CAPM equation 8-6. The betas for the three

utilities companies (Yahoo Finance estimates) are: AEP = 0.74, DUK = 0.40, CNP = 0.82 Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 3: Solve (1 of 2) E (rAsset j ) rf Asset j [E (rMarket ) rf ] Exp. Return (AEP) = 4.5% + 0.74(6) = 8.94% Exp. Return (DUK) = 4.5% + 0.40(6) = 6.9% Exp. Return (CNP) = 4.5% + 0.82(6) = 9.42% Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 3: Solve (2 of 2)

Blank Beta Yahoo MSN E(r ) Yahoo MSN Apple Inc. (APPL) 2.90

2.58 21.90% 19.98% Hewlett Packard (HPQ) 1.27 1.47 12.12% 13.32%

Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Step 4: Analyze The expected rates of return on the stocks vary depending on their beta. Higher the beta, higher is the expected return. Copyright 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved Key Terms (1 of 2) Beta coefficient Capital asset pricing model (CAPM) Correlation coefficient Diversification

Table 8.1 Beta Coefficients for Selected Companies Company Yahoo Finance (Yahoo.com) Microsoft Money Central (MSN.com) Blank Blank Apple Inc. (AAPL)

2.90 2.58 Hewlett Packard (HPQ) 1.27 1.47 Blank Blank

American Electric Power Co. (AEP) 0.74 0.73 Duke Energy Corp. (DUK) 0.40 0.56 Centerpoint Energy (CNP) 0.82