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Copyright © 2021 Pearson Education Ltd.
Financial Management
An Introduction to
Risk and Return—
History of Financial
Market Returns
– Copyright © 2021 Pearson Education Ltd.

7.1 REALIZED AND EXPECTED RATES
OF RETURN AND RISK

Calculating the Realized Return from an
Investment (1 of 4)
• Realized return or cash return measures the gain or loss on an
investment.
• Example: You invested in 1 share of Apple (AAPL) for $95 and sold a
year later for $115. The company did not pay any dividend during that
period. What will be the cash return on this investment?
−
Cash Ending CashDistribution Beginning
= +
Return Price (Dividend) Price
Cash Return = $115 + 0 −$95
= $20

Calculating the Realized Return from an
Investment
We can also calculate the rate of return as a percentage. It is simply the
cash return divided
by the beginning stock price.
−
Ending CashDistribution Beginning
+
Rate of CashReturn Price (Dividend) Price
= =
Beginning
Return BeginningPrice
Price
Example: Compute the rate of return for the previous example.
Rate of Return = ($115 + 0 −$95) ÷ 95
= 21.05%

Table 7.1 Measuring an Investor’s Realized Rate of Return
from Investing in Common Stock (1 of 2)
Blank Stock Prices Blank Cash
Distribution
(Dividend)
Return Blank
Blank Beginning (April
9, 2015)
Ending (April
8, 2016)
Blank Cash Rate
Company A B C D=C+B− A E=D/A
Duke Energy (DUK) 77.23 79.63 3.30 5.70 7.4%
Emerson Electric
(EMR)
58.40 53.84 1.90 (2.66) 24.6%
Sears Holdings (SHLD) 43.24 14.45 — (28.79) 266.6%
Walmart (WMT) 80.29 68.00 2.00 (10.29) 212.8%

Observations from Table 7-1
• Table 7-1 indicates that the returns from investing
in common stocks can be positive or negative.
• However, past performance is not an indicator of
future performance. In general, we expect to
receive higher returns for assuming more risk.

Calculating the Expected Return from an
Investment
• Expected return is what the investor expects to earn from an
investment in the future.
• It is the weighted average of the possible returns, where the weights
are determined by the probability that it occurs.
 
     
    
    
    
     
1 1 2 2
ExpectedRate Rate of Probability Rate of Probability Rate of Probability
of Return = Return1 × of Return1 + Return 2 × of Return 2 + + Return × of Return
( ) ( ) ( ) ( ) ( ) ( ) ( )
n n
n n
E r r Pb r Pb Pb Pb



Using equation 7-3,
Expected Return
= (−10%×0.2) + (12%×0.3) +
(22%×0.5)
= 12.6%

Table 7.2 Calculating the Expected Rate of Return for an
Investment in Common Stock
State of the
Economy
Probability
of the State
of the
Economya
(Pbi)
End-of-Year
Selling Price
of the Stock
Beginning
Price of the
Stock
Cash
Return
from Your
Investment
Percentage
Rate of
Return =
Cash
Return/Begin
ning Price
of the Stock
Product =
Percentage
Rate of
Return ×
Probability
of the State
of the
Economy
A B C D E = C−D F = E/D G = B × F
Recession 20% $ 9,000 $ 10,000 $(1,000) −10% =
−$1,000 
$10,000
−2.0%
Moderate
growth
30% 11,200 $ 10,000 1,200 12% = $1,200
 $10,000
3.6%
Strong
growth
50% 10,000 $ 10,000 2,200 22% = $2,200
 $10,000
11%
Sum 100% Blank Blank Blank Blank 12.6%
aThe probabilities assigned to the three possible economic conditions have to be determined subjectively, which requires
management to have a thorough understanding of both the investment cash flows and the general economy.

Measuring Risk
• In the example on Table 7-2, the expected return is 12.6%; However,
the return could range from −10% to +22%.
• This variability in returns can be quantified by computing the Variance
or Standard Deviation in investment returns.
• Variance is the average squared difference between the individual
realized returns and the expected return.
• Standard deviation is the square root of the variance and is more
commonly used to quantify risk.

Calculating the Variance and Standard Deviation
of the Rate of Return on an Investment
Assume two possible investment alternatives:
1. U.S. Treasury Bill – U.S. Treasury bill is considered risk-free as
there is no risk of default on the promised payments of 5%.
2. Common stock of the Ace Publishing Company – An investment
in common stock will be a risky investment.
The probability distribution of an investment’s return contains all
possible rates of return from the investment along with the
associated probabilities for each outcome.

Figure 7-1 Probability Distribution of Returns for a Treasury
Bill and the Common Stock of the Ace Publishing Company
Chance or Probability
of Occurrence
Rate of Return
on Investment
1 chance in 10 (10%) −10%
2 chances in 10 (20%) 5%
4 chances in 10 (40%) 15%
2 chances in 10 (20%) 25%
1 chance in 10 (10%) 40%

• The probability distribution for Treasury bill is a single spike at 5% rate
of return indicating that there is 100% probability that you will earn 5%.
• The returns for Ace Publishing company range from a low of −10% to a
high of +40%. Thus the common stock investment is risky, whereas the
Treasury bill is not.
• Using equation 7-3, expected rate of return on the stock is 15% while
the expected rate of return on Treasury bill is 5%.
• Does the higher return of stock make it a better investment? Not
necessarily – the two investments have very different risks, which must
also be taken into account.

Risk, as measured by variance:
( ) ( ) ( )
 
 
 
 
−
 
 
 
 
 
 
 
2
Rate of Expected Rate Probability
+ + Return 3 of Return × of Return
n n
n
r E r Pb

Investment Expected Return Standard Deviation
Treasury Bill 5% 0%
Common Stock 15% 12.85%
• We observe that the common stock offers a higher expected return but
also entails more risk, as measured by standard deviation. An
investor’s choice of a specific investment will be determined by their
attitude toward risk.

Table 7-3 Measuring the Variance and Standard Deviation of
an Investment in Ace Publishing’s Common Stock
State of
the World
Rate of
Return
Chance or
Probability
Blank Step 2 Step 3
A B C D = B × C E = [B − E(R)]2 F = E × C
1 −0.10 0.10 −0.01 0.0625 0.00625
3 0.05 0.20 0.01 0.0100 0.00200
4 0.15 0.40 0.06 0.0000 0.00000
4 0.25 0.20 0.05 0.0100 0.00200
5 0.40 0.10 0.04 0.0625 0.00625
• Step 1: Expected Return, E(r) = → 0.15
• Step 4: Variance = → 0.0165
• Step 5: Standard Deviation = → 0.1285

Problem??

7.2 A BRIEF HISTORY OF FINANCIAL
MARKET RETURNS

A Brief History of the Financial Markets
Investors have historically earned higher rates of return on riskier
investments. However, having a higher expected rate of return simply
means that investors “expect” to realize a higher return. Higher return is
not guaranteed.

U.S. Financial Markets—Domestic
Investment Returns
Figure 7.2 Historical Rates of Return for U.S. Financial
Securities: 1970—2015

U.S. Financial Markets—Domestic Investment
Returns
We observe a clear relationship between risk and return. International
equities have the highest annual return but higher returns are associated
with much greater risk.
Annual US Equities T. Bills Govt. Bonds Corp. Bonds International
Equities
Return 10.21% 4.89% 7.05% 7.79% 10.35%
S.D. 17.55% 3.52% 2.74% 2.57% 21.60%
1. The riskier investments have historically realized higher returns.
2. The historical returns of the higher-risk investment stocks have
higher standard deviations.

Figure 7-3 Stocks, Gold, and Real Estate

Investing in Emerging Markets
Figure 7.4 Historical Rates of Return in Global Markets:
1970–2011

What Determines Stock Prices?
In general, stock prices tend to go up when there is good news about
future profits, and they go down when there is bad news about future
profits.
Stock price movements are also affected by speculation or investor
sentiment.

The Efficient Market Hypothesis
• The efficient market hypothesis (EMH) states that securities prices
accurately reflect future expected cash flows and are based on all
information available to investors.
• An efficient market is a market in which all the available information is
fully incorporated into the prices of the securities and the returns the
investors earn on their investments cannot be predicted.
• Three forms of EMH:
• The weak-form efficient market hypothesis asserts that all past security
market information is fully reflected in securities prices.
• The semi-strong form efficient market hypothesis asserts that all
publicly available information is fully reflected in securities prices.
• The strong form efficient market hypothesis asserts that all information,
whether public or private, is fully reflected in securities prices.

The Behavioral View
• Efficient market hypothesis is based on the assumption that investors,
as a group, are rational. This view has been challenged.
• If investors do not rationally process information, then markets may not
accurately reflect even public information.
• For example, overconfident investors may under react when
management announces earnings as they have too much confidence
in their own views of the company’s true value and place little weight
on new information released by management. As
a result, this new information, even though it is publicly and freely
available, is not completely reflected in stock prices.

8.1 PORTFOLIO RETURNS AND PORTFOLIO RISK

Portfolio Returns and Portfolio Risk
• With appropriate diversification, you can lower the risk of your portfolio
without lowering it’s expected rate of return.
• Those risks that can be eliminated by diversification are not
necessarily rewarded in the financial marketplace.

Calculating the Expected Return of a
Portfolio
=  +  +  + + 
1 1 2 2 3 3
( ) [ ( )] [ ( )] [ ( )] [ ( )]
portfolio n n
E r W E r W E r W E r W E r
Portfolio Expected Rate of Return
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.
To calculate a portfolio’s expected rate of return, we weight each individual
investment’s expected rate of return using the fraction of the portfolio that is
invested in each investment.

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

• 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
Penny’s portfolio.
• 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
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%

=  +  +  + + 
1 1 2 2 3 3
( ) [ ( )] [ ( )] [ ( )] [ ( )]
portfolio n n
E(rportfolio) = .25 × .04 + .25 × .08 + .50 × .12
= .09 or 9%
•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.

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.
• 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.

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.

Calculating the Standard Deviation of a
Portfolio’s Returns
     
= + +
2 2 2 2
1 1 2 2 1 2 1,2 1 2
2
portfolio W W W W
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
“rho”) represents correlation between the rates of return for asset 1 and asset 2.

Figure 8-1 Diversification and the Correlation Coefficient—
Apple and Coca—Cola (1 of 2)

Figure 8-1 Diversification and the Correlation Coefficient—
Apple and Coca—Cola (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.

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.

CHECKPOINT 8.2: CHECK YOURSELF

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.
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%

=  +  +  + + 
1 1 2 2 3 3
( ) [ ( )] [ ( )] [ ( )] [ ( )]
portfolio n n
E(rportfolio)
= WS&P500 E(rS&P500) + WInternational E(rInternational)
= .5 (12) + .5(14)
= 13%
     
= + +
2 2 2 2
1 1 2 2 1 2 1,2 1 2
2
portfolio W W W W
Standard deviation of Portfolio
= √ { (.52x.22)+(.52x.32)+(2x.5x.5x.20x.2x.3)}
= √ {.0385}
= .1962 or 19.62%

8.2 SYSTEMATIC RISK AND THE
MARKET PORTFOLIO

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 economy’s 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.
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

Systematic Risk and Market Portfolio
• 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.

Figure 8.2 Portfolio Risk and the Number of Investments in
the Portfolio
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.

Table 8.1 Beta Coefficients for Selected Companies
Company Yahoo Finance
(Yahoo.com)
Microsoft Money
Central (MSN.com)
Computers and Software Blank Blank
Apple Inc. (AAPL) 2.90 2.58
Hewlett Packard (HPQ) 1.27 1.47
Utilities 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
Systematic Risk and Beta
Systematic 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.
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.

Calculating Portfolio Beta
The portfolio beta measures the systematic risk of the portfolio.
 
   
   
=  +  + +
   
   
   
1 1 2 2
Proportion of Beta for Proportion of Beta for Proportion of
Portfolio
Portfolio Invested Asset 1 Portfolio Invested Asset 2 Portfolio Investe
Beta
in Asset 1 ( ) ( ) in Asset 2 ( ) ( )
W W 
 
 

 
 
 
Beta for
d Asset
in Asset ( ) ( )
n n
n
n W
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

8.3 THE SECURITY MARKET LINE AND THE CAPM

The Security Market Line and the CAPM
• 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.
• 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.
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:

= + −
( ) [ ( ) ]
Asset j f Asset j Market f
E r r E r r

Figure 8.4 Risk and Return for Portfolios Containing the
Market and the Risk—Free Security

Figure 8.4 Risk and Return for Portfolios Containing the
Market and the Risk—Free Security
Legend: Blank Blank Blank
% Market Portfolio,
WM
% Risk-Free
Asset, Wrf
Portfolio Beta,
βPortfolio
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% 1.0 11.0%
120% −20% 1.2 12.0%
*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.

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