Bob LeClair's Finance and Markets Newsletter
For the Week Ending:
Change
Change
1/1/14
1/4/14
1/11/14
(Week)
(Yr-to-Date)
Dow Jones Ind. Avg.
16,577
16,470
16,437
(33)
(140)
(% Change)
-0.20%
-0.84%
S & P 500 Index
1,848
1,831
1,842
11
(6)
(% Change)
0.60%
-0.32%
NASDAQ Composite
4,177
4,132
4,175
43
(2)
(% Change)
1.03%
-0.05%
S & P 500 P/E Ratio
S & P 500 Div. Yield
T-bill - S&P 500 Yield
19.0
1.94%
-1.87%
19.0
1.94%
-1.88%
19.0
1.91%
-1.86%
0.0
-0.03%
0.02%
0.0
-0.03%
0.02%
30-Year T-Bond Yield
10-Year T-Bond Yield
91-Day T-Bill Yield
Yield Spread
3.97%
3.03%
0.07%
3.90%
3.93%
2.99%
0.07%
3.87%
3.80%
2.86%
0.06%
3.75%
-0.13%
-0.13%
-0.01%
-0.12%
-0.17%
-0.17%
-0.02%
-0.16%
30-Year Mortgage
15-Year Mortgage
1-Year Adjustable Rate
30-Yr. - 1-Yr. ARM Rate
4.48%
3.52%
2.56%
1.92%
4.53%
3.55%
2.56%
1.97%
4.51%
3.56%
2.56%
1.95%
-0.02%
0.01%
0.00%
-0.02%
0.03%
0.04%
0.00%
0.03%
$ Value of Euro (€)
Japanese Yen (¥/$)
Crude Oil, Spot Price
Gasoline, Reg. ($/Gal.)
$1.3754
105.33
$98.42
$3.32
$1.3589
104.86
$95.44
$3.33
$1.3665
104.17
$91.66
$3.31
$0.0076
-0.69
-$3.78
-$0.01
-$0.0089
-1.16
-$6.76
-$0.01
2
3
Chapter
1
McGraw-Hill/Irwin
A Brief History
of Risk and
Return
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Learning Objectives
To become a wise investor (maybe even one with too
much money), you need to know:
• How to calculate the return on an investment using different
methods.
• The historical returns on various important types of investments.
• The historical risk on various important types of investments.
• The relationship between risk and return.
1-5
A Brief History of Risk and Return
• Our goal in this chapter is to see what financial market history can
tell us about risk and return.
• There are two key observations:
– First, there is a substantial reward, on average, for bearing risk.
– Second, greater risks accompany greater returns.
• These observations are important investment guidelines.
1-8
Return on Investment
• “The level of profit from an
investment - the reward for
investing.”
• Postponement of consumption
9
Components of Return
• Current income:
– dividends (stocks)
– interest (bonds)
– rent (real estate)
• Capital Gain (Loss):
– change in market value
10
“Total Return”
• “The sum of the current income
and the capital gain (or loss)
earned on an investment over a
specified period of time.”
11
Total Return  Income  Capital Gain (Loss)
Total Return  Income  Capital Gain (Loss)
TR  I  (EV - BV)
Total Return  Income  Capital Gain (Loss)
TR  I  (EV - BV)
TR(%) 
I  (EV - BV)
BV
Total Return (%)
•
•
•
•
•
•
TR(%) = (I + (EV – BV)) ÷ BV
I ÷ BV = ???
I ÷ BV = Dividend Yield
(EV – BV) ÷ BV = ???
(EV – BV) ÷ BV = Capital Gain Yield
Total Return = Dividend Yield +
Capital Gain yield
Example: Calculating Total Dollar
and Total Percent Returns
•
•
•
Suppose you invested $1,400 in a stock with a share price of $35.
After one year, the stock price per share is $49.
Also, for each share, you received a $1.40 dividend.
•
What was your total dollar return?
–
–
–
–
•
$1,400 / $35 = 40 shares
Capital gain: 40 shares times $14 = $560
Dividends: 40 shares times $1.40 = $56
Total Dollar Return is $560 + $56 = $616
What was your total percent return?
–
–
–
Dividend yield = $1.40 / $35 = 4%
Capital gain yield = ($49 – $35) / $35 = 40%
Total percentage return = 4% + 40% = 44%
Note that $616
divided by
$1,400 is 44%.
1-19
Annualizing Returns, I
• You buy 200 shares of Lowe’s Companies, Inc. at $18
per share. Three months later, you sell these shares for
$19 per share. You received no dividends. What is your
return? What is your annualized return?
• Return: (Pt+1 – Pt) / Pt = ($19 - $18) / $18
= .0556 = 5.56%
This return is
known as the
holding period
percentage return.
• Effective Annual Return (EAR): The return on an
investment expressed on an “annualized” basis.
Key Question: What is the number of holding periods in a year?
1-20
Annualizing Returns, II
1 + EAR = (1 + holding period percentage return)m
m = the number of holding periods in a year.
•
In this example, m = 4 (12 months / 3 months).
Therefore:
1 + EAR = (1 + .0556)4 = 1.2416.
So, EAR = .2416 or 24.16%.
1-21
$1 Invested in Different Portfolios:
1926-2009
Investment
Ending Value ($)
Small-Company Stocks
12,971.38
Large-Company Stocks
2,382.68
L-T Govt. Bonds
75.33
U. S. Treasury Bills
22.33
Inflation
12.06
22
A $1 Investment in Different Types
of Portfolios, 1926—2009
The Historical Record:
Total Returns on Large-Company Stocks
The Historical Record:
Total Returns on Small-Company Stocks
The Historical Record:
Total Returns on Long-term U.S. Bonds
The Historical Record:
Total Returns on U.S. T-bills
The Historical Record:
Inflation
Holding Period Return (HPR)
• “The total return earned from holding
an investment for a specified holding
period (usually 1 year or less).”
HPR 
I  (V e  V b )
Vb
30
S & P 500 Annual Returns
Year
Total Return (%)
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
+37.58
+22.96
+33.36
+28.58
+21.04
-9.10
-11.89
-22.10
+28.69
+10.88
S & P 500 Annual Returns
Year
Total Return (%)
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
+28.69
+10.88
+ 4.91
+15.79
+ 5.49
- 37.00
+26.46
+15.06
+ 2.05
+16.00
S & P 500 Annual Returns
Year
Total Return (%)
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
+10.88
+ 4.91
+15.79
+ 5.49
- 37.00
+26.46
+15.06
+ 2.05
+16.00
??????
S & P 500 Annual Returns
Year
Total Return (%)
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
+10.88
+ 4.91
+15.79
+ 5.49
- 37.00
+26.46
+15.06
+ 2.05
+16.00
+32.40
Historical Average Returns
•
A useful number to help us summarize historical financial data is the
simple, or arithmetic average.
•
Using the data in Table 1.1, if you add up the returns for large-company
stocks from 1926 through 2009, you get about 987 percent.
•
Because there are 84 returns, the average return is about 11.75%. How
do you use this number?
•
If you are making a guess about the size of the return for a year selected
at random, your best guess is 11.75%.
•
The formula for the historical average return is:
n
Historical
Average
Return

 yearly
return
i1
n
1-39
Average Annual Returns for
Five Portfolios and Inflation
Table 1.3: Historical Returns &
Risk Premiums (1926-2009)
Investment
Avg. Return
Premium
Large Co. Stocks
11.7%
7.9%
Small Co. Stocks
17.7%
13.9%
L-T Corp. Bonds
6.5%
2.7%
L-T Govt. Bonds
5.9%
2.1%
U. S. T-bills
3.8%
0.0%
Average Returns: The First Lesson
• Risk-free rate: The rate of return on a riskless, i.e., certain
investment.
• Risk premium: The extra return on a risky asset over the risk-free
rate; i.e., the reward for bearing risk.
• The First Lesson: There is a reward, on average, for bearing risk.
• By looking at Table 1.3, we can see the risk premium earned by
large-company stocks was 7.9%!
– Is 7.9% a good estimate of future risk premium?
– The opinion of 226 financial economists: 7.0%.
– Any estimate involves assumptions about the future risk
environment and the risk aversion of future investors.
Why Does a Risk Premium Exist?
• Modern investment theory centers on this question.
• Therefore, we will examine this question many times in the chapters
ahead.
• We can examine part of this question, however, by looking at the
dispersion, or spread, of historical returns.
• We use two statistical concepts to study this dispersion, or variability:
variance and standard deviation.
•
The Second Lesson: The greater the potential reward, the greater the
risk.
1-46
Return Variability: The Statistical Tools
• The formula for return variance is ("n" is the number of returns):
 R
N
VAR(R)
σ
2

i
R

2
i1
N 1
• Sometimes, it is useful to use the standard deviation, which is
related to variance like this:
SD(R)  σ 
VAR(R)
Return Variability Review and Concepts
• Variance is a common measure of return dispersion.
Sometimes, return dispersion is also call variability.
• Standard deviation is the square root of the variance.
– Sometimes the square root is called volatility.
– Standard Deviation is handy because it is in the same "units" as the
average.
• Normal distribution: A symmetric, bell-shaped
frequency distribution that can be described with only an
average and a standard deviation.
• Does a normal distribution describe asset returns?
Frequency Distribution of Returns on
Common Stocks, 1926—2009
Historical Returns & Standard
Deviations, 1926-2009
Series
Avg. Return
Std. Dev.
Large Co. Stocks
11.7%
20.5%
Small Co. Stocks
17.7%
6.5%
5.9%
5.6%
3.8%
3.1%
37.1%
7.0%
11.9%
8.1%
3.1%
4.2%
L-T Corp. Bonds
L-T Govt. Bonds
Int.-Term Govts.
U. S. T-bills
Inflation (CPI)
52
Historical Returns, Standard Deviations,
and Frequency Distributions: 1926—2009
The Normal Distribution and
Large Company Stock Returns
Arithmetic Averages versus
Geometric Averages
• The arithmetic average return answers the question:
“What was your return in an average year over a
particular period?”
• The geometric average return answers the question:
“What was your average compound return per year
over a particular period?”
• When should you use the arithmetic average and when
should you use the geometric average?
• First, we need to learn how to calculate a geometric
average.
1-56
Arithmetic Averages versus
Geometric Averages
• The arithmetic average tells you what you earned in a
typical year.
• The geometric average tells you what you actually
earned per year on average, compounded annually.
• When we talk about average returns, we generally are
talking about arithmetic average returns.
• For the purpose of forecasting future returns:
– The arithmetic average is probably "too high" for long forecasts.
– The geometric average is probably "too low" for short forecasts.
Compound Annual Return
• Geometric mean return
GM 
n
(1  r1 )(1  r2 )...( 1  rn )  1
59
Compound Annual Return on the
S&P 500, 1995-99
GM
95  99

5
(1 . 37 )( 1 . 23 )( 1 . 33 )( 1 . 28 )( 1 . 21 )  1
60
Compound Annual Return on the
S&P 500, 1995-99
GM
GM
95  99

5
(1 . 37 )( 1 . 23 )( 1 . 33 )( 1 . 28 )( 1 . 21 )  1
95  99

5
3 . 4711  1
61
Compound Annual Return on the
S&P 500, 1995-99
95  99

5
(1 . 37 )( 1 . 23 )( 1 . 33 )( 1 . 28 )( 1 . 21 )  1
GM
95  99

5
3 . 4711  1
GM
95  99
 1 . 2826  1  28 . 26 %
GM
62
Risk and Return
• The risk-free rate represents compensation for just
waiting.
• Therefore, this is often called the time value of money.
• First Lesson: If we are willing to bear risk, then we can
expect to earn a risk premium, at least on average.
• Second Lesson: Further, the more risk we are willing to
bear, the greater the expected risk premium.
1-64
Historical Risk and Return Trade-Off
A Look Ahead
• This textbook focuses exclusively on financial assets:
stocks, bonds, options, and futures.
• You will learn how to value different assets and make
informed, intelligent decisions about the associated risks.
• You will also learn about different trading mechanisms
and the way that different markets function.
1-69
Useful Internet Sites
•
cgi.money.cnn.com/tools/millionaire/millionaire.html (millionaire link)
•
finance.yahoo.com (reference for a terrific financial web site)
•
www.globalfinancialdata.com (reference for historical financial market
data—not free)
•
www.robertniles.com/stats (reference for easy to read statistics review)
1-70
Assignment
• Calculate the compound annual
return (geometric mean) of the
Standard & Poor’s 500 Stock Index
for the period 2004-2013.
• S&P 500 Return2004-2013 = ???
Problems: Chapter 2
• 2.19
• 2.20
• 2.25