Chapter 10: Risk and return:
lessons from market history
Corporate Finance
Ross, Westerfield, and
Jaffe
Outline
1. Returns
2. Capital market returns
3. Portfolio risk statistics
Dollar return
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Suppose that you bought a bond for $1050 a year
ago. You have received two semiannual coupons of
$50 each. The market price of the bond today is
$1100. What is your total dollar return?
Income = 50 + 50 = $100.
Capital gain = 1100 – 1050 = $50.
Total dollar return = 100 + 50 = $150.
Total dollar return = income + capital gain (loss).
Percentage return
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It is more intuitive to think of returns in terms of
percentages.
Return = (ending value – beginning value) /
beginning value.
Return = ((1100 + 100) – 1050) / 1050 = 14.29%.
Return = income yield (return) + capital gain yield
(return) = 100 / 1050 + 50 / 1050 = 9.52% + 4.76% =
14.29%.
A sample question
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Six months ago, you purchased 100 shares of stock
in ABC Co. at a price of $43.89 a share. ABC stock
pays a quarterly dividend of $.10 a share. Today,
you sold all of your shares for $45.13 per share.
What is the total dollar amount of your capital gains
on this investment of 100 shares?
a.
$1.24
b.
$1.64
c.
$40.00
d.
$124.00
e.
$164.00
Holding period return
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Holding period return: the cumulative
return that an investor would obtain
when holding an investment over a
period of N years.
Holding period return example
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Suppose that an investment yielded 4%, 7%,
8%, 0%, and 10% for the past 5 years. What
is the holding period return for the 5 years?
Holding period return = (1 + 4%) × (1 + 7%)
× (1 + 8%) × (1 + 0%) × (1 + 10%) – 1 =
32.2%.
Why capital market returns?
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Examining capital market returns helps us
determine the appropriate returns on nonfinancial assets (e.g., firm projects).
Lessons from capital market return history:
–
–
–
There is a reward for bearing risk.
Return is positively related to risk.
This is called the “risk-return tradeoff.”
Average return, I
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The simple average of a series of returns is
called arithmetic average return.
Geometric average return: average
compound return per period over multiple
periods.
Average return example
Year Ret Arithmetic R 1 + Ret Power of 1/N Geometric R
1
0.08
0.076
1.08 1.074811381 0.07481138
2
-0.01
0.99
3
0.12
1.12
GR < AR
4
0.13
1.13
5
0.06
1.06
Multiplication term 1.4344
Average return, II
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The geometric average will be less than the
arithmetic average unless all the returns are equal.
The arithmetic average is overly optimistic for
multiple horizons.
If the investment horizon is only 1 period, the
arithmetic average is a better measure of likely
return.
Arithmetic average return based on historical returns
are often used as an estimate of expected return in
real life.
A sample question
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The average compound return earned per
year over a multi-year period is called the
_____ average return.
a.
arithmetic
b.
standard
c.
variant
d.
geometric
e.
real
Portfolio risk statistics
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An investor cares about the return variability
of her/his portfolio.
This variability at the portfolio level is usually
measured by variance and/or standard
deviation (std.).
Portfolio risk statistics, based on a sample
Year
1
2
3
4
5
Ret
0.08
-0.01
0.12
0.13
0.06
Arithmetic R
0.076
Diff
0.004
-0.086
0.044
0.054
-0.016
Sum
Diff^2
0.000016
0.007396
0.001936
0.002916
0.000256
0.01252
Var
Std
0.00313 0.055946
Historical performance, 1926-2011
Large stocks
Small Stocks
L-T Corporate Bonds
L-T Government Bonds
U.S. Treasury Bills
Inflation
Average Return
(Geometric Mean)
11.8% (9.8%)
16.5% (11.9%)
6.4% (6.1%)
6.1% (5.7%)
3.6% (3.6%)
3.1% (3.0%)
Std
20.3%
32.5%
8.4%
9.8%
3.1%
4.2%
Market risk premium
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Market risk premium is the difference
between expected equity market return and
the risk-free rate.
Approximately 6.9%.
Based on 1900-2010 data, across 17
countries.
If normally distributed?
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If we are willing to assume that asset returns
are normally distributed, can you draw a
return distribution based on the previous
slide?
Hint: about 95% within +/– 2 std.
End-of-Chapter
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Concept questions: 1-10.
Questions and problems: 1-16 and 19-23.