The Basics of Risk and Return
Corporate Finance
Dr. A. DeMaskey
Learning Objectives

Questions to be answered:
–
–
–
What is risk?
How is risk measured?
What is the relationship between risk and
return?
What Are Investment Returns?
Investment returns measure the financial
results of an investment.
 Returns may be historical or prospective
(anticipated).
 Returns can be expressed in:

–
–
Dollar terms
Percentage terms
What Is Investment Risk?
Typically, investment returns are not known
with certainty.
 Investment risk pertains to the probability
of earning a return less than that expected.
 The greater the chance of a return far below
the expected return, the greater the risk.

Probability Distribution
Stock X
Stock Y
-20
0
15
50
Rate of
return (%)
 Which stock is riskier? Why?
Measuring Stand-Alone Risk

Expected Rate of Return

Standard Deviation

Coefficient of Variation
Measuring Stand-Alone Risk
Standard deviation measures the standalone risk of an investment.
 The larger the standard deviation, the higher
the probability that returns will be far
below the expected return.
 Coefficient of variation is an alternative
measure of stand-alone risk.

Portfolio Risk and Return
^
Portfolio Return, kp
 Portfolio Risk, p

–
–
–
–
Covariance
Portfolio Variance
Portfolio Standard Deviation
Correlation Coefficient
Two-Stock Portfolio

Two stocks can be combined to form a riskless
portfolio if r = -1.0.

Risk is not reduced at all if the two stocks have r =
+1.0.

In general, stocks have r  0.65, so risk is lowered
but not eliminated.

Investors typically hold many stocks.

What happens when r = 0?
Diversifiable Risk versus Market Risk
p (%)
Company Specific
(Diversifiable) Risk
35
Stand-Alone Risk, p
20
Market Risk
0
10
20
30
40
2,000+
# Stocks in Portfolio
Diversifiable Risk versus
Market Risk
Market risk is that part of a security’s
stand-alone risk that cannot be eliminated
by diversification.
 Firm-specific, or diversifiable, risk is that
part of a security’s stand-alone risk that can
be eliminated by diversification.

Conclusion



As more stocks are added, each new stock has a
smaller risk-reducing impact on the portfolio.
p falls very slowly after about 40 stocks are
included. The lower limit for p is about 20% =
M .
By forming well-diversified portfolios, investors
can eliminate about half the riskiness of owning a
single stock.
How Is Market Risk Measured
For Individual Securities?
Market risk, which is relevant for stocks
held in well-diversified portfolios, is
defined as the contribution of a security to
the overall riskiness of the portfolio.
 It is measured by a stock’s beta coefficient,
which measures the stock’s volatility
relative to the market.

How Are Betas Calculated?
Run a regression with returns on the stock
in question plotted on the Y axis and returns
on the market portfolio plotted on the X
axis.
 The slope of the regression line, which
measures relative volatility, is defined as the
stock’s beta coefficient, or b.

How Are Betas Interpreted?
If b = 1.0, stock has average risk.
 If b > 1.0, stock is riskier than average.
 If b < 1.0, stock is less risky than average.
 Most stocks have betas in the range of 0.5
to 1.5.
 Can a stock have a negative beta?

The Capital Asset Pricing
Model (CAPM)

CAPM indicates what should be the
required rate of return on a risky asset.
–
–

Beta
Risk aversion
The return on a risky asset is the sum of the
riskfree rate of interest and a premium for
bearing risk (risk premium).
Security Market Line (SML)
The CAPM when graphed is called the
Security Market Line (SML).
 The SML equation can be used to find the
required rate of return on a stock.
 SML: ki = kRF + (kM - kRF)bi

–
–
(kM – kRF) = market risk premium, RPM
(kM – kRF)bi = risk premium
Expected Return versus
Market Risk
Security
HT
Market
USR
T-bills
Collections
Expected
return
17.4%
15.0
13.8
8.0
1.7
Risk, b
1.29
1.00
0.68
0.00
-0.86
 Which of the alternatives is best?
Portfolio Risk and Return

Calculate beta for a portfolio with 50% HT and
50% Collections.

What is the required rate of return on the
HT/Collections portfolio?
Impact of Inflation Change on SML
Required Rate
of Return k (%)
 I = 3%
New SML
SML2
SML1
18
15
11
8
Original situation
0
0.5
1.0
1.5
2.0
Impact of Risk Aversion Change
Required Rate
of Return (%)
After increase
in risk aversion
SML2
kM = 18%
kM = 15%
SML1
18
 RPM =
3%
15
8
Original situation
1.0
Risk, bi
Drawbacks of CAPM
Beta is an estimate.
 Unrealistic assumptions.
 Not testable.
 CAPM does not explain differences in
returns for securities that differ:

–
–
–
Over time
Dividend yield
Size effect