Chapter 5
Risk and
Return
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Learning Goals
1. Meaning and importance of risk.
2. Calculate and assess returns and risk for a
single asset.
3. Calculate and assess returns and risk for a
portfolio.
4. Diversification & the role of correlation
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Learning goals, continued
5. CAPM:
1. Beta and what it measures
2. Calculate required returns using beta
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5-3
Risk and Return Fundamentals
• If we knew in advance how decisions would turn out,
finance would be easy (and boring).
• What can we do? Use history as a basis for
understanding the future.
• We begin by evaluating the risk and return of
individual assets, and then look at portfolios of assets.
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5-4
Risk Defined
• In the context of business and finance, risk
exists whenever we are not certain what the
outcome of a decision will be.
• Two notions of risk:
– the chance of suffering a financial ______________
– the _____________________________________ or
variability of returns
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5-5
Risk and Return Fundamentals
• Risk is important in financial decisions because
most people (investors, managers, etc.) are
____________________________________
• What does risk aversion mean?
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5-6
Return Defined
• Return is the total gain or loss on an investment.
• Returns can be:
– actual or expected
– dollar or percent
Most often, we are interested in percentage returns.
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5-7
Returns
• To calculate percentage returns:
rt = Pt – Pt-1 + CFt
Pt-1
Where rt is the actual or expected percentage return
during period t, Pt is the actual or expected price at t,
Pt-1 is the price at t-1, and CFt is any cash flow from
the investment during the period from t-1 to t.
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5-8
Returns
• Calculated returns include change in
_________________________, even if the asset
is not sold.
• Capital gains and losses matter, even if they are
not realized.
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Historical Returns
Table 5.2 Historical Returns for Selected
Security Investments (1926–2006)
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5-10
Expected Returns
• Expected return can be calculated as shown above by
using the expected future price and cash flow.
• An alternative method of calculating expected return is
a weighted average of the possible values, as shown
on the next slide.
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5-11
Return Measurement for a Single Asset:
Expected Return
• The expected value of a return, r-bar, is the most likely
return of an asset.
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5-12
Measures of Risk
• As noted above, risk is sometimes defined as the probability of
suffering a financial loss.
• A better definition of risk is the uncertainty of returns.
• A simple indicator of risk is the range of possible outcomes.
• A better statistical measure of variability, or uncertainty, is
__________________________________________, which
measures dispersion around the expected value. We use it as
one measure of risk.
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5-13
Risk Measurement for a Single Asset:
Standard Deviation
• The expression for the standard deviation of returns, k,
is given in Equation 5.3 below.
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5-14
Risk Measurement for a Single Asset:
Coefficient of Variation
• The coefficient of variation, CV, is a measure
of ________________________ risk that is
useful in comparing risks of assets with differing
expected returns.
• Equation 5.4 gives the expression of the
coefficient of variation.
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5-15
Risk Measurement for a Single Asset:
Standard Deviation (cont.)
Table 5.6 Historical Returns, Standard Deviations, and
Coefficients of Variation for Selected Security Investments
(1926–2006)
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5-16
Portfolio Risk and Return
• A portfolio is a combination of assets.
• If investors are risk averse, that investor will invest in
portfolios rather than in single assets.
• In a portfolio, a portion of the risk is eliminated by
_______________________________________.
• To maximize the risk reduction from diversification,
combine securities whose returns have a low or
negative _____________________________________.
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Portfolio Return
• The return of a portfolio is a weighted average
of the returns on the individual assets from
which it is formed and can be calculated as
shown in Equation 5.5.
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5-18
Risk of a Portfolio
• Diversification is enhanced depending upon the extent to which
the returns on assets “move” together.
• This movement is typically measured by a statistic known as
“correlation” as shown in the figure below.
Figure 5.3 Correlations
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5-19
Risk of a Portfolio (cont.)
• Even if two assets are not perfectly negatively correlated, an
investor can still realize diversification benefits from combining
them in a portfolio as shown in the figure below.
Figure 5.4 Diversification
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5-20
Risk of a Portfolio:
Adding Assets to a Portfolio
Portfolio
Risk (SD)
Unsystematic (diversifiable) Risk
σM
Systematic (non-diversifiable) Risk
0
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# of Stocks
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Risk of a Portfolio:
Adding Assets to a Portfolio (cont.)
Portfolio
Risk (SD)
Portfolio of Domestic Assets Only
Portfolio of both Domestic and
International Assets
σM
0
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# of Stocks
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Risk and Return: The Capital Asset
Pricing Model (CAPM)
• If you notice in the last slide, a good part
of a portfolio’s risk (the standard deviation of returns)
can be eliminated simply by holding a lot of stocks.
• The risk you can’t get rid of by adding stocks
(systematic) cannot be eliminated through
diversification because that variability is caused by
events that affect most stocks similarly.
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5-23
Risk and Return: The Capital Asset
Pricing Model (CAPM) (cont.)
• In the early 1960s, researchers noticed that when the stock
market drops, some stocks go down more than others.
• They reasoned that if they could measure this variability—the
systematic risk—then they could develop a model to price
assets using only this risk.
• The unsystematic (company-related) risk is irrelevant because
it could easily be eliminated simply by diversifying.
• The result is the Capital Asset Pricing Model (CAPM).
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5-24
Risk of a Portfolio
Capital Asset Pricing Model (CAPM)
• CAPM is a theory of the relationship between
_______________________________________.
• If investors are risk averse, they must be
compensated for bearing risk with higher expected
returns. The question CAPM attempts to answer is,
how much higher should the return on a risky asset
be?
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5-25
Risk and Return: The Capital Asset
Pricing Model (CAPM) (cont.)
• The required return for all assets is composed
of two parts: the risk-free rate and a risk
premium.
The risk premium is a
function of both market
conditions and the asset
itself.
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The risk-free rate (RF) is
usually estimated from
the return on US T-bills
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Risk and Return: The Capital Asset
Pricing Model (CAPM) (cont.)
• The risk premium for a stock is composed of
two parts:
– The Market Risk Premium which is the return
required for investing in any risky asset rather than
the risk-free rate
– Beta, which is risk measure
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5-27
CAPM
• Beta is the part of a security’s risk that cannot be
eliminated by diversification.
• Beta is sometimes called:
– ________________________________ risk
– ________________________________ risk
• Beta measures the sensitivity of a security’s
returns to a change in market returns.
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5-28
Risk and Return: The Capital Asset
Pricing Model (CAPM) (cont.)
• According to CAPM, the required return on a risky
asset is:
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5-29
Risk and Return: The Capital Asset
Pricing Model (CAPM) (cont.)
Stock Z has a beta of 1.5. The risk-free rate of return is 2%;
the return on the market portfolio of assets is 11%.
Substituting bZ = 1.5, RF = 2%, and km = 11% into the CAPM
yields a return of:
kZ = 2% + 1. 5 [11% - 2%]
kZ = 15.5%
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