Chapter 8 Risk and Return: Capital Market...

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Risk and Return: Capital Market Theory

Chapter 8

Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-2

Chapter 8 Contents

Learning Objectives1. Portfolio Returns and Portfolio Risk

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. Systematic Risk and the Market Portfolio1. Understand the concept of systematic risk for an

individual investment and calculate portfolio systematic risk (beta).

3. The Security Market Line and the CAPM1. Estimate an investor’s required rate of return using

capital asset pricing model.


Portfolio Returns and Portfolio Risk

• With appropriate diversification, can lower risk of the portfolio without lowering the portfolio’s expected rate of return.

• Some risk can be eliminated by diversification, and those risks that can be eliminated are not necessarily rewarded in the financial marketplace.


Calculating Expected Return of a Portfolio

• To calculate a portfolio’s expected rate of return, weight each individual investment’s expected rate of return using the fraction of the portfolio that is invested in each investment.

• Example 8.1 : Invest 25% of your money in Citibank stock (C) with expected return = -32% and 75% in Apple (AAPL) with expected return=120%. Compute the expected rate of return on portfolio.

• Expected rate of return

= .25(-32%) + .75 (120%) = 82%


Calculating Expected Return of Portfolio

• E(rportfolio) = the expected rate of return on a portfolio of n assets.

• Wi = the portfolio weight for asset i.• Sum of Wi = 1• E(ri ) = the expected rate of return earned by asset i.• W1 × E(r1) = the contribution of asset 1 to the

portfolio expected return. Weight times the rate!


Checkpoint 8.1

Calculating a Portfolio’s Expected Rate of ReturnPenny Simpson has her first full-time job and is considering how to invest her savings. Her dad suggested she invest no more than 25% of her savings in the stock of her employer, Emerson Electric (EMR), so she is considering investing the remaining 75% in a combination of a risk-free investment in U.S. Treasury bills, currently paying 4%, and Starbucks (SBUX) common stock. Penny’s father has invested in the stock market for many years and suggested that Penny might expect to earn 9% on the Emerson shares and 12% from the Starbucks shares. Penny decides to put 25% in Emerson, 25% in Starbucks, and the remaining 50% in Treasury bills. Given Penny’s portfolio allocation, what rate of return should she expect to receive on her investment?



Class Problem – modify previous

Evaluate the expected return for Penny’s portfolio where she places 1/4th of her money in Treasury bills, half in Starbucks stock, and the remainder in Emerson Electric stock.

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

9%


Evaluating Portfolio Risk and Diversification

• Unlike expected return, standard deviation is not generally equal to the a weighted average of the standard deviations of the returns of investments held in the portfolio.– This is because of diversification effects.

• Effect of reducing risks by including large number of investments in portfolio is called diversification.

• As a consequence of diversification, the standard deviation of the returns of a portfolio is typically less than the average of the standard deviation of the returns of each of the individual investments.


Portfolio Diversification

• The diversification gains achieved by adding more investments will depend on the degree of correlation among the investments.

• The degree of correlation is measured by using the correlation coefficient.

• Correlation coefficient can range from -1.0 (perfect negative correlation), meaning two variables move in perfectly opposite directions to +1.0 (perfect positive correlation), which means the two assets move exactly together.

• Correlation coefficient of 0 means no relationship exists between returns earned by the two assets.


Portfolio Diversification (cont.)

• As long as the investment returns are not perfectly positively correlated, there will be diversification benefits.– However, the diversification benefits will be greater

when the correlations are low or positive.

– The returns on most investment assets tend to be positively correlated.

Diversification Lessons1. A portfolio can be less risky than the average risk of its

individual investments in the portfolio.

2. Key to reducing risk through diversification is combine investments whose returns do not move together.


Calculating the Standard Deviation of a Portfolio Returns – The Formula


Calculating the Standard Deviation of a Portfolio Returns (Example)

• Determine the expected return and standard deviation of above portfolio consisting of two stocks that have a correlation coefficient of .75.

• Expected Return = .5 (.14) + .5 (.14)= .14 or 14%

Portfolio Weight Expected Return

Standard Deviation

Apple .50 .14 .20

Coca-Cola .50 .14 .20


Calculating the Standard Deviation of a Portfolio Returns (cont.)

• Standard deviation of portfolio = √ { (.52x.22)+(.52x.22)+(2x.5x.5x.75x.2x.2)}= √ .035= .187 or 18.7%

Correlation Coefficient


Calculating the Standard Deviation of a Portfolio Returns (Example-cont.)

• Had we taken a simple weighted average of the standard deviations of the Apple and Coca-Cola stock returns, it would produce a portfolio standard deviation of .20.

• Since the correlation coefficient is less than 1 (.75), it reduces the risk of portfolio to 0.187.

Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-16Figure 8.1 cont.


Figure 8.1 cont.


Standard Deviation of a Portfolio Returns and Diversification logic

• Figure 8-1 illustrates the impact of correlation coefficient on the risk of the portfolio. We observe 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.


Systematic Risk and Market Portfolio

• An ugly task to calculate the correlations when we have thousands of possible investments.

• Capital Asset Pricing Model or the CAPM provides a relatively simple measure of risk.

• CAPM assumes that investors chose to hold the optimally diversified portfolio that includes all risky investments.– This optimally diversified portfolio that includes all of the

economy’s assets is referred to as the market portfolio.


Systematic Risk and Market Portfolio (cont.)

• According to the CAPM, the relevant risk of an investment relates to how the investment contributes to the risk of this market portfolio.

• Classify the risks of individual investments into two categories:– Systematic risk, and Unsystematic risk

• The systematic risk component measures the contribution of the investment to the risk of the market. For example: War, hike in corporate tax rate.

• The unsystematic risk is the element of risk that does not contribute to the risk of the market. This component is diversified away when the investment is combined with other investments. For example: Product recall, labor strike, change of management.


Systematic Risk and Market Portfolio

• An investment’s systematic risk is far more important than its unsystematic risk.– If the risk comes mainly from unsystematic risk, the

investment will tend to have low correlation with returns of most other stocks in the portfolio, and will make a minor contribution to the portfolio’s overall risk.

• Figure 8-2 illustrates that as the number of securities in a portfolio increases, the contribution of the unsystematic or diversifiable risk to the standard deviation of the portfolio declines.

• Figure 8-2 illustrates that systematic or non-diversifiable risk is not reduced even as we increase the number of stocks in the portfolio.



Diversification and Systematic Risk

• Systematic sources of risk (such as inflation, war, interest rates) are common to most investments resulting in a perfect positive correlation and no diversification benefit.

• Figure 8-2 illustrates that large portfolios will not be affected by unsystematic risk but will be influenced by systematic risk factors.


Systematic Risk and Beta

• Systematic (market) risk is measured by beta coefficient, which estimates the extent to which a particular investment’s 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)

– Beta could be estimated using excel or financial calculator, or readily obtained from various sources on the internet (such as Yahoo Finance and Money Central.com)

Copyright © 2011 Pearson Prentice Hall. All rights reserved. 8-25Figure 8.3 cont.

Systematic Risk and Beta – Market Model


Figure 8.3 cont.



Calculating Portfolio Beta

• The portfolio beta measures the systematic risk of the portfolio and is calculated by taking a simple weighted average of the betas for the individual investments contained in the portfolio.


Calculating Portfolio Beta (cont.)

• Example 8.2 Consider a portfolio comprised of four investments with betas equal to 1.5, .75, 1.8 and .60. If you invest equal amount in each investment, what is the beta for the portfolio?

• Portfolio Beta= .25(1.5) + .25(.75) + .25(1.8) + .25 (.6)= 1.16


The Security Market Line and the CAPM

• CAPM also describes how the betas relate to the expected rates of return that investors require on their investments.

• The key insight of CAPM is that investors will require a higher rate of return on investments with higher betas.


Security Market Line and CAPM (cont.)

Figure 8-4 provides the expected returns and betas for a variety of portfolios comprised of market portfolio and risk-free asset. However, the figure applies to all investments, not just portfolios consisting of the market and the risk-free rate.


Figure 8.4 – The Security Market Line (Beta and Portfolio Return)


Figure 8.4 cont.


The Security Market Line

• The straight line relationship between the betas and expected returns in Figure 8-4 is called the security market line (SML), and its slope is often referred to as the reward to risk ratio.

– SML is one graphical representation of the CAPM.

• SML can be expressed as the following equation, which is also referred to as the CAPM pricing equation:


The CAPM intuition

• CAPM Equation implies the higher the systematic risk of an investment, all else equal, the higher will be the expected rate of return an investor would require to invest in the asset.

– This is consistent with Principle 2: There is a Risk-Return Tradeoff.

• Example 8.2 What is the expected rate of return on AAPL stock with a beta of 1.49; the risk-free rate is 2% and the market risk premium is estimated to be 8%?

E(rAAPL ) = .02 + 1.49 (.08) = .1392 or 13.92%


Checkpoint 8.3 – Class Example

Estimating the Expected Rate of Return Using the CAPMJerry Allen graduated from Texas Tech University with a finance degree in the spring of 2010 and took a job with a Houston-based investment banking firm as a financial analyst.

One of his first assignments is to investigate the investor-expected rates of return for three technology firms: Apple (APPL), Dell (DELL), and Hewlett Packard (HPQ).

Jerry’s supervisor suggests that he make his estimates using the CAPM where the risk-free rate is 4.5%, the expected return on the market is 10.5%,and the risk premium for the market as a whole (the difference between the expected return on the market and the risk-free rate) is 6%. Use the two estimates of beta provided for these firms in Table 8.1to calculate two estimates of the investor-expected rates of return for the sample firms.


Checkpoint 8.3

Chapter 8 Risk and Return: Capital Market...

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