Chapter 10
RISK AND RETURN: LESSONS FROM MARKET
HISTORY
SLIDES
CHAPTER WEB SITES
Section Web Address
10.1 finance.yahoo.com
www.marketwatch.com/markets
10.2 bigcharts.marketwatch.com
CHAPTER ORGANIZATION
10.1 Returns
Dollar Returns
Percentage Returns
10.2 Holding Period Returns
10.1 Key Concepts and Skills
10.2 Chapter Outline
10.3 Returns
10.4 Returns
10.5 Returns: Example
10.6 Returns: Example
10.7 Holding Period Return
10.8 Holding Period Return: Example
10.9 Historical Returns
10.10 Return Statistics
10.11 Historical Returns, 1926-2007
10.12 Average Stock Returns and Risk-Free Returns
10.13 Risk Premiums
10.14 The Risk-Return Tradeoff
10.15 Risk Statistics
10.16 Normal Distribution
10.17 Normal Distribution
10.18 Example – Return and Variance
10.19 More on Average Returns
10.20 Geometric Return: Example
10.21 Geometric Return: Example
10.22 The U.S. Equity Risk Premium
10.23 Quick Quiz
10.3 Return Statistics
10.4 Average Stock Returns and Risk-Free Returns
10.5 Risk Statistics
Variance
Normal Distribution and Its Implications for Standard Deviation
10.6 More on Average Returns
Arithmetic versus Geometric Averages
Calculating Geometric Average Returns
Arithmetic Average Return or Geometric Average Return?
10.7 The U.S. Equity Risk Premium: Historical and International Perspectives
10.8 2008: A Year of Financial Crisis
ANNOTATED CHAPTER OUTLINE
Slide 10.0 Chapter 10 Title Slide
Slide 10.1 Key Concepts and Skills
Slide 10.2 Chapter Outline
Slide 10.3 Returns
10.1. Returns
.A Dollar Returns
Income component – direct cash payments such as dividends or interest
Price change – loosely, capital gain or loss
Total dollar return = income component + capital gain (loss)
The return (ignoring taxes) is unaffected by the decision to sell or hold
securities.
Lecture Tip: The issues discussed in this section need to be stressed. Many
students feel that if you do not sell a security, you will not have to
consider the capital gain or loss involved. (This is a common
investor mistake – holding a loser too long because of reluctance
to admit a bad decision was made.) Point out that non-recognition
is relevant for tax purposes – only realized income must be
reported. However, whether or not you have liquidated the asset is
irrelevant when measuring a security’s pre-tax performance.
.B Percentage Returns
Percentage return = dollar return / initial investment
= dividend yield + capital gains yield
Dividend yield = Dt+1 / Pt
Capital gains yield = (Pt+1 – Pt) / Pt
Slide 10.4 Returns
Slide 10.5 –
Slide 10.6 Returns: Example
10.2. Holding Period Returns
Defined as the total return an investor would earn from holding an
investment over n periods.
1)1(*…*)1(*)1( 21 n
RRRHPR
Slide 10.7 Holding Period Return
Slide 10.8 Holding Period Return: Example
The following are the basis for the nominal pretax rates of return
reported by Ibbotson and Singuefield and presented in the figures
throughout the chapter:
-Large-company stocks – S&P 500 index, which contains 500 of
the largest companies in terms of total market value in the U.S.
Lecture Tip: An interesting trivia fact is that the S&P500 may
actually contain 501 different stocks. In 2014, Google initiated a
stock split, but rather than issuing the same class of shares, a
separate share class was used. To keep the index unaffected, both
share classes are included in the S&P500.
-Small-company stocks – Smallest 20% of stocks listed on the
NYSE based on market value of outstanding stock
-Long-term corporate bonds – High quality corporate bonds with
20 years to maturity
-Long-term government bonds – Portfolio of U.S. government
bonds with 20 years to maturity
-U.S. Treasury bills – Portfolio of T-bills with a three-month
maturity
Slide 10.9 Historical Returns
10.3. Return Statistics
Slide 10.10 Return Statistics
The arithmetic average return equals the sum of the observed returns, divided
by the number of observations.
Lecture Tip: Some students may not recall their statistics, so a brief review is
in order. Security returns are examples of random variables –
categories of numbers for which in any particular instance more
things can happen than will happen – and the things that can
happen have an associated probability of occurrence.
Random variables are typically characterized by their probability
distributions (i.e., a graph, a table, or function that relates the
potential values of the random variable to its associated
probabilities) along with measures of central tendency and
dispersion (the deviation from that central tendency). The normal
distribution is a common probability distribution; mean, median,
and mode measure central tendency; and variance and standard
deviation are common measures of dispersion.
Slide 10.11 Historical Returns, 1926-2014
10.4. Average Stock Returns and Risk-Free Returns
Using the T–bill rate as the risk-free return, define excess return as the
difference between a particular asset class’ return and the return on
T-bills.
Risk premium – reward for bearing risk, the difference between a risky
investment return and the risk-free rate.
Slide 10.12 Average Stock Returns and Risk-Free Returns
Slide 10.13 Risk Premiums
Slide 10.14 The Risk-Return Tradeoff
Risky investments earn a risk premium. For large company stocks, the average
annual risk premium has been approximately 8.6% since 1926. For
smaller (and presumably riskier) firms, the average annual risk
premium has been closer to 13.2% over the same period. As we
will discuss below, this rate is relatively high as compared to more
historical periods, as well as versus international markets.
10.5. Risk Statistics
Slide 10.15 Risk Statistics
.A Variance
Variance – the average squared deviation between actual returns and their
mean
Lecture Tip: Occasionally, students ask why we include the above-mean
returns in measuring dispersion, since these are desirable from the
investor’s viewpoint. This question provides a natural springboard
for a discussion of alternative variability measures. Here we
discuss semivariance as an alternative to variance.
In Portfolio Selection (1959), Harry Markowitz states:
“Analyses based on [semivariance] tend to produce
better portfolios than those based on [variance].
Variance considers extremely high and extremely
low returns equally undesirable. An analysis based
on [variance] seeks to eliminate extremes. An
analysis based on [semivariance] on the other
hand, concentrates on reducing losses.”
Semivariance is computed in a manner similar to the traditional
variance, except that if the deviation is positive, its value is
replaced by zero. We still tend to use variance instead of
semivariance because semivariance tends to complicate the risk-
return issue, and if returns are symmetrically distributed, then
variance is two times semivariance.
The Sharpe ratio, or reward to risk ratio, can be calculated as the
risk premium (or excess return) divided by the standard deviation.
.B Normal Distribution and Its Implications for Standard Deviation
Historical returns on securities have probability distributions that are
approximately normal. The normal distribution is completely
described by its mean and variance. Since 1926, annual returns on
large company stocks have averaged about 12.1%, with a standard
deviation of about 20.1%. An observation on a normally
distributed random variable has a ~68% chance of being within
plus or minus one standard deviation from the mean, a ~95%
chance of being within plus or minus two standard deviations from
the mean, and a ~99% chance of being within plus or minus three
standard deviations from the mean.
Slide 10.16 –
Slide 10.17 Normal Distribution
Slide 10.18 Example – Return and Variance
Based upon the historical risk premium for large company common stocks, an
investment of “average risk” should return about 8.6% above the
T-bill rate.
Lecture Tip: It is sometimes difficult to get students to appreciate the risk
involved in investing in common stocks. They see the large average
returns and miss the variance. A simple exercise illustrating the
risk of the different securities can be performed using Table 10.1.
Each student (or the entire class) is given an initial investment.
They are then allowed to choose a security class. Use a random
number generator and the last two digits of the year to sample the
distribution. The initial investment is then increased or decreased
based on the return. This works best if the trials are limited to
between one and five.
Lecture Tip: The wealth of financial information makes it easy to have
students collect historical prices and compute averages and
standard deviations. One of the easiest free sites is
finance.yahoo.com. Have the students enter a ticker symbol for a
company that they are interested in and select historical data. They
can then download historical daily, weekly, monthly, or yearly
stock quotes. The quotes will appear on the screen, and at the
bottom of the page there is an option to download the quotes into a
“csv” file that can be opened by Excel. The students can then use
Excel to examine the volatility of their chosen company.
10.6. More on Average Returns
.A Arithmetic versus Geometric Averages
Slide 10.19 More on Average Returns
Geometric average – average compound return earned per year over multiple
years
Arithmetic average – return earned in an average year over multiple years
.B Calculating Geometric Average Returns
Arithmetic average is just the typical average that we are used to computing:
add the returns for each period and divide by the number of
periods.
Geometric average = [(1+R1)*(1+R2)*…*(1+RT)]1/T – 1
Geometric means will always be smaller than arithmetic means, unless all the
returns are equal.
Slide 10.20 –
Slide 10.21 Geometric Return: Example
.C Arithmetic Average Return or Geometric Average Return?
The geometric average tells you the return you earned per year over the time
period based on annual compounding. The arithmetic average tells
you what you earned in an average year.
The appropriate average depends on the question you are asking.
If you are using estimates of annual returns to determine future values, then
the arithmetic average is probably too high if you have a long
horizon, and the geometric average is probably too low if you have
a short horizon. The arithmetic average is probably best for short
planning horizons, and the geometric average is probably best for
very long planning horizons.
Lecture Tip: Blumes’ Formula can be used to estimate returns:
where, T is the forecast horizon and N is the number of years of
historical data we are working with. T must be less than N.
10.7. The U.S. Equity Risk Premium: Historical and International Perspectives
Slide 10.22 Perspectives on the Equity Risk Premium
AverageArithmetic
N
TN
verageGeometricA
N
T
TR
11
1
)(
Over the period (1926-2011) examined, the U.S. equity premium
has been quite large compared to earlier years in the U.S., as well
as to, a lesser extent, the premiums earned in foreign countries.
For example, using U.S. data from 1802, the historical equity risk
premium was 5.4%. The overall world equity risk premium for
1900 to 2010 is 6.9%, versus 7.2% for the U.S.
A good estimate for the future risk premium in the U.S. may be
7%, although somewhat higher or lower estimates could also be
considered reasonable.
10.8. 2008: A Year of Financial Crisis
The S&P500 index plunged -37 percent in 2008, which is behind
only 1931 at -43 percent. Moreover, there were 18 days during
2008 on which the value of the S&P changed by more than 5
percent. From 1956 to 2007 there were only 17 such days.
Slide 10.23 Quick Quiz