Chapter 6
The Meaning and
Measurement of Risk and
Return
Chapter Objectives





Define and measure the expected rate of return of
an individual investment
Define and measure the riskiness of an individual
investment
Compare the historical relationship between risk
and rates of return in the capital markets
Explain how diversifying investments affect the
riskiness and expected rate of return of a portfolio
or combination of assets
Explain the relationship between an investor’s
required rate of return and the riskiness of the
investment
Rate of Return

Determined by future cash flows, not
reported earnings
Expected Rate of Return

Weighted average of all the possible returns,
weighted by the probability that each return
will occur
Expected Rate of Return

Jazzfestival (in August) has 2 possible
outcomes
– bad weather (20% chance); return 30.000 zloty
– good weather (80% chance); return 100.000 zloty
– expected return; 86.000 zloty
Risk

Potential variability in future cash flows
 The greater the range of possible events that
can occur, the greater the risk
Standard Deviation of Return
Quantitative measure of an asset’s riskiness
 Measures the volatility or riskiness of
portfolio returns
 Square root of the weighted average
squared deviation of each possible return
from the expected return

Real Average Annual Rate of
Return
 Nominal
rate of return less the inflation
rate
For example; savings account inTurkey
 Nominal intrest rate is 40%
 Inflation (expected) is 38%
 Real intrest rate is 2% (plus - minus)
Risk Premium

Additional return received beyond the riskfree rate (Treasury Bill rate) for assuming
risk
Risk and Diversification

Diversification can reduce the risk
associated with an investment portfolio,
without having to accept a lower expected
return
Annual Rates of Return
1926 to 2000
Security
Nominal
Average
Annual
Returns
Standard
Deviation
of Returns
Real
Average
Annual
Returns
Risk
Premium
Common Stocks
Small Cmpy Stk
L-T Corp bonds
L-T Govt bonds
Int. Govt bonds
U.S. Treas. Bills
Inflation
13.0 %
20.2 %
9.8 %
9.1 %
17.3 %
33.4 %
14.1 %
13.4 %
6.0 %
8.7 %
2.8 %
2.1 %
5.7 %
9.4 %
2.5 %
1.8 %
5.5 %
5.8 %
2.3 %
1.6 %
3.9 %
3.2 %
0.7 %
0%
3.2 %
4.4 %
Diversification

If we diversify investments across different
securities, the variability in the returns
declines
Total Risk or Variability

Company-Unique Risk (Unsystematic)

Market Risk (Systematic)
Company-Unique Risk

Unsystematic risk
 Diversifiable -Can be diversified away
Market Risk

Systematic
 Non-diversifiable
 Can not be eliminated through random
diversification
Market Risk

Events that affect market risk
Changes in the general economy, major
political events, sociological changes
Examples:
Interest Rates in the economy
Changes in tax legislation that affects all
companies
Beta
Average relationship between a stock’s
returns and the market’s returns
 Measure of a firm’s market risk or the risk
that remains after diversification
 Slope of the characteristic line—or the line
that measures the average relationship
between a stock’s returns and the market

Beta

A stock with a Beta of 0 has no systematic risk
 A stock with a Beta of 1 has systematic risk equal
to the “typical” stock in the marketplace
 A stock with a Beta greater than 1 has systematic
risk greater than the “typical” stock in the
marketplace
 Most stocks have betas between .60 and 1.60
Portfolio Beta

Weighted average of the individual stock
betas with the weights being equal to the
proportion of the portfolio invested in each
security
 Portfolio beta indicates the percentage
change on average of the portfolio for every
1 percent change in the general market
Asset Allocation

Diversification among different kinds of
assets
 Examples:
Treasury Bills
Long-Term Government Bonds
Large Company Stocks
Required Rate of Return

Minimum rate of return necessary to attract
an investor to purchase or hold a security
 Considers the opportunity cost of funds
Opportunity Cost
The next best alternative
Required Rate of Return
 k=kfr

+ krp
Where:
k
= required rate of return
 kfr = Risk Free Rate
 krp = Risk Premium
Risk-Free Rate

Required rate of return for risk-less
investments
 Typically measured by U.S. Treasury Bill
Rate
Risk Premium

Additional return expected for assuming
risk
 As risk increases, expected returns increase

Risk Premium = Required Return – Risk
Free rate
 krp = k
- kfr

Where:
 k = required rate of return
 kfr = Risk Free Rate
 krp = Risk Premium
If required return is 15% and the risk free rate is
5%, then the risk premium is 10%. The 10% risk
premium would apply to any security having a
systematic risk equivalent to general market or a
Beta of 1. If beta is 2, then risk premium = 20%.
Capital Asset Pricing Model

Equation that equates the expected rate of
return on a stock to the risk-free rate plus a
risk premium for the systematic risk

CAPM
CAPM

CAPM suggests that Beta is a factor in
required returns
 kj = krf + B(market rate – risk free rate)
 Example:
 Market risk = 12%
 Risk Free rate = 5%
 5% + B(12% - 5%)
 If B = 0
Required rate = 5%
 If B = 1
Required rate = 12%
 If B = 2
Required rate = 19%