1) The chapter discusses sources of investment returns including income returns from cash flows and returns from changes in the value of investments. 2) It describes how to measure returns such as dollar returns, holding period returns, and annualized returns which allow comparisons over different time periods. 3) Risk is defined as the uncertainty of investment returns and can be measured by the variability of returns using metrics like variance and standard deviation. The higher the risk, the higher the expected return required by investors.

1. Chapter 2
RISK AND RETURN BASICS

2. Chapter 2 Questions
• What are the sources of investment returns?
• How can returns be measured?
• What is risk and how can we measure risk?
• What are the components of an investment’s
required return to investors and why might
they change over time?

3. Sources of Investment Returns
• Investments provide two basic types of
return:
• Income returns
– The owner of an investment has the right
to any cash flows paid by the investment.
• Changes in price or value
– The owner of an investment receives the
benefit of increases in value and bears the
risk for any decreases in value.

4. Income Returns
• Cash payments,
usually received
regularly over the
life of the
investment.
• Examples: Coupon
interest payments
from bonds,
Common and
preferred stock
dividend payments.

5. Returns From Changes in
Value
• Investors also
experience capital
gains or losses as the
value of their
investment changes
over time.
• For example, a stock
may pay a $1 dividend
while its value falls from
$30 to $25 over the
same time period.

6. Measuring Returns
• Dollar Returns
– How much money was made on an investment
over some period of time?
– Total Dollar Return = Income + Price Change
• Holding Period Return
– By dividing the Total Dollar Return by the
Purchase Price (or Beginning Price), we can
better gauge a return by incorporating the size of
the investment made in order to get the dollar
return.

7. Annualized Returns
• If we have return or income/price change
information over a time period in excess of
one year, we usually want to annualize the
rate of return in order to facilitate
comparisons with other investment returns.
• Another useful measure:
Return Relative = Income + Ending Value
Purchase Price

8. Annualized Returns
Annualized HPR = (1 + HPR)1/n – 1
Annualized HPR = (Return Relative)1/n – 1
• With returns computed on an annualized
basis, they are now comparable with all other
annualized returns.

9. Measuring Historic Returns
• Starting with annualized Holding Period
Returns, we often want to calculate
some measure of the “average” return
over time on an investment.
• Two commonly used measures of
average:
– Arithmetic Mean
– Geometric Mean

10. Arithmetic Mean Return
• The arithmetic mean is the “simple average”
of a series of returns.
• Calculated by summing all of the returns in
the series and dividing by the number of
values.
RA = (ΣHPR)/n
• Oddly enough, earning the arithmetic mean
return for n years is not generally equivalent
to the actual amount of money earned by the
investment over all n time periods.

11. Arithmetic Mean Example
Year Holding Period Return
1 10%
2 30%
3 -20%
4 0%
5 20%
RA = (ΣHPR)/n = 40/5 = 8%

12. Geometric Mean Return
• The geometric mean is the one return that, if
earned in each of the n years of an
investment’s life, gives the same total dollar
result as the actual investment.
• It is calculated as the nth root of the product
of all of the n return relatives of the
investment.
RG = [Π(Return Relatives)]1/n – 1

13. Geometric Mean Example
Year Holding Period Return Return Relative
1 10% 1.10
2 30% 1.30
3 -20% 0.80
4 0% 1.00
5 20% 1.20
RG = [(1.10)(1.30)(.80)(1.00)(1.20)]1/5 – 1
RG = .0654 or 6.54%

14. Arithmetic vs. Geometric
To ponder which is the superior measure,
consider the same example with a $1000
initial investment. How much would be
accumulated?
Year Holding Period Return Investment Value
1 10% $1,100
2 30% $1,430
3 -20% $1,144
4 0% $1,144
5 20% $1,373

15. Arithmetic vs. Geometric
• How much would be accumulated if you
earned the arithmetic mean over the same
time period?
Value = $1,000 (1.08)5 = $1,469
• How much would be accumulated if you
earned the geometric mean over the same
time period?
Value = $1,000 (1.0654)5 = $1,373
• Notice that only the geometric mean gives
the same return as the underlying series of
returns.

16. Investment Strategy
• Generally, the income returns from an investment are
“in your pocket” cash flows.
• Over time, your portfolio will grow much faster if you
reinvest these cash flows and put the full power of
compound interest in your favor.
• Dividend reinvestment plans (DRIPs) provide a tool
for this to happen automatically; similarly, Mutual
Funds allow for automatic reinvestment of income.
• See Exhibit 2.5 for an illustration of the benefit of
reinvesting income.

17. What is risk?
• Risk is the uncertainty associated with the
return on an investment.
• Risk can impact all components of return
through:
– Fluctuations in income returns;
– Fluctuations in price changes of the investment;
– Fluctuations in reinvestment rates of return.

18. Sources of Risk
• Systematic Risk Factors
– Affect many investment returns simultaneously;
their impact is pervasive.
– Examples: changes in interest rates and the state
of the macro-economy.
• Asset-specific Risk Factors
– Affect only one or a small number of investment
returns; come from the characteristics of the
specific investment.
– Examples: poor management, competitive
pressures.

19. How can we measure risk?
• Since risk is related to variability and
uncertainty, we can use measures of
variability to assess risk.
• The variance and its positive square root, the
standard deviation, are such measures.
– Measure “total risk” of an investment, the
combined effects of systematic and asset-specific
risk factors.
• Variance of Historic Returns
σ2 = [Σ(Rt-RA)2]/n-1

20. Standard Deviation of Historic
Returns
Year Holding Period Return
1 10% RA = 8%
2 30% σ2 = 370
3 -20% σ = 19.2%
4 0%
5 20%
σ2 = [(10-8)2+(30-8)2+(-20-8)2+(0-8)2+(20-8)2]/4
= [4+484+784+64+144]/4
= [1480]/4

21. Using the Standard Deviation
• If returns are normally distributed, the
standard deviation can be used to
determine the probability of observing a
rate of return over some range of
values.

22. Coefficient of Variation
• The coefficient of variation is the ratio of the
standard deviation divided by the return on
the investment; it is a measure of risk per unit
of return.
CV = σ/RA
• The higher the coefficient of variation, the
riskier the investment.
• From the previous example, the coefficient of
variation would be:
CV =19.2%/8% = 2.40

23. Components of Return
• The required rate of return on an
investment is the sum of the nominal
risk-free rate (Nominal RFR) and a risk
premium (RP) to compensate the
investor for risk.
• Required Return = Nominal RFR + RP
• Or to be more technically correct:
• RR = (1 + Nom RFR) x (1 + RP) - 1

24. The Risk-Return Relationship
• The Capital Market Line (CML) is a
visual representation of how risk is
rewarded in the market for investments.
• The greater the risk, the greater the
required return, so the CML slopes
upward.

25. Components of Return Over
Time
• What changes the required return on an
investment over time?
• Anything that changes the risk-free rate or
the investment’s risk premium.
– Changes in the real risk-free rate of return and the
expected rate of inflation (both impacting the
nominal risk-free rate, factors that shift the CML).
– Changes in the investment’s specific risk (a
movement along the CML) and the premium
required in the marketplace for bearing risk
(changing the slope of the CML).