### Finance&ExcelCh10

```Lessons From Capital Market History:
Return & Risk
Chapter 10
1
Topics
• Calculate 1 Period Returns
• Five Important Types of Financial Investments
– Risk-Free Investment
• What We Can Learn From Capital Market History
– Using Past To Predict Future
– Average Returns: There Is Reward For Bearing Risk
– Variability In Returns: The Greater The Potential Reward,
The Greater The Risk
• Risk & Return
• Arithmetic V Geometric Mean
• Markets Are Only Efficient In The Long Run
2
1 Year Percent Return
Dividend Yield
Capital Gains
Yield
Dt  1
DY 
Pt
Pt 1  Pt
CGY 
Pt
% Re turn DY  CGY
Dt 1  Pt  1  Pt
% Re turn
Pt
3
Period Returns = Holding Returns = 1 Year Returns
Returns On Investment For 1 Year (Holding
Period Return)
(Regardless of whether you sell the stock or
not)
Stock Price Time 0 = (Beg) = Pt
\$25.00
Stock Price Time 1 = (End) = Pt+1
\$26.00
Dividend Paid at Time 1 = Dt+1
\$2.00
Capital Gain = Pt+1 - Pt
\$1.00
Dollar Returns = Dividend Paid +
Capital Gain
\$3.00
% Return = (Dollar Return)/(End
Stock Price)
12.00%
Dividend Yield = Dt+1/Pt
8.00%
Capital Gain Yield = Pt+1/Pt - 1
4.00%
% Return = Dividend Yield +
Capital Gain Yield
12.00%
% Return + 1 = (Dt+1 + Pt+1)/Pt
112.00%
Returns On Investment For 1 Year (Holding
Period Return)
(Regardless of whether you sell the stock or
not)
Stock Price Time 0 = (Beg) = Pt
\$25.00
Stock Price Time 1 = (End) = Pt+1
\$19.50
Dividend Paid at Time 1 = Dt+1
\$2.00
Capital Gain = Pt+1 - Pt
-\$5.50
Dollar Returns = Dividend Paid +
Capital Gain
-\$3.50
% Return = (Dollar Return)/(End
Stock Price)
-14.00%
Dividend Yield = Dt+1/Pt
8.00%
Capital Gain Yield = Pt+1/Pt - 1
-22.00%
% Return = Dividend Yield +
Capital Gain Yield
-14.00%
% Return + 1 = (Dt+1 + Pt+1)/Pt
86.00%
4
Five Important Types of Financial Investments
• Roger Ibbotson & Rex Sinquefield did famous study that
looked at the nominal-pretax-returns for five important types
of financial investments in US markets during the period
1926 - 2008:
1. Large Company Stocks Portfolio based on S & P 500 Index (in
terms of MV of outstanding stock)
2. Small Company Stocks Portfolio based on smallest 20% of
companies listed on NYSE (in terms of MV of outstanding stock)
3. Long-term High Quality Corporate Bonds Portfolio (20 Years to
Maturity)
4. Long-term US Government Bonds Portfolio (20 Years to
maturity)
5. US Treasury Bills (T-bills) with one-month maturity
•
•
Virtually free of any default risk because government can raise taxes to
pay bills, especially since the time frame is one monrth.
T-bill return is considered the “risk-free return”
5
US Capital Market History
• Looking at the past can perhaps provide some
insight into the future.
• Using the past to predict the future can be
dangerous if the past isn’t representative of
what the future will bring.
– 2000 to 2007 people around the world looked at
past house prices to predict future house prices.
– 1995 to 2000 people looked at past prices for
internet stocks prices to help predict future prices.
6
U.S.
Financial
Markets
The Historical
Record: 19252008
7
Year-to-Year Total Returns
Large-Company Stock Returns
8
Year-to-Year Total Returns
Long-Term Government Bond Returns
9
Year-to-Year Total Returns
U.S. Treasury Bill Returns
10
Year To Year Returns (Hand typed from tables in textbook)
Year
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
Large Company
Down Large
Stocks
Company Stocks
11.14%
37.13%
43.31%
-8.91%
-8.91%
-25.26%
-25.26%
-43.86%
-43.86%
-8.85%
-8.85%
52.88%
-2.34%
-2.34%
47.22%
32.80%
-35.26%
-35.26%
33.20%
-0.91%
-0.91%
-10.08%
-10.08%
-11.77%
-11.77%
21.07%
25.76%
19.69%
36.46%
-8.18%
-8.18%
5.24%
5.10%
18.06%
30.58%
24.55%
18.50%
-1.10%
-1.10%
52.40%
31.43%
Long Term
Government
Bonds
7.90%
10.36%
-1.37%
5.23%
5.80%
-8.04%
14.11%
31.00%
12.98%
5.88%
8.22%
-0.13%
6.26%
5.71%
10.34%
-8.66%
2.67%
2.50%
2.88%
5.17%
4.07%
-1.15%
2.10%
7.02%
-1.44%
-3.53%
1.82%
-0.88%
7.89%
-1.03%
Down Long Term
Government
Bonds
-1.37%
-8.04%
-0.13%
-8.66%
-1.15%
-1.44%
-3.53%
-0.88%
-1.03%
Consumer Price
US Treasury Bills Index
3.30%
-1.12%
3.15%
-2.26%
4.05%
-1.16%
4.47%
0.58%
2.27%
-6.40%
1.15%
-9.32%
0.88%
-10.27%
0.52%
0.76%
0.27%
1.52%
0.17%
2.99%
0.17%
1.45%
0.27%
2.86%
0.06%
-2.78%
0.04%
0.00%
0.04%
0.71%
0.14%
9.93%
0.34%
9.03%
0.38%
2.96%
0.38%
2.30%
0.38%
2.25%
0.38%
18.13%
0.62%
8.84%
1.06%
2.99%
1.12%
-2.07%
1.22%
5.93%
1.56%
6.00%
1.75%
0.75%
1.87%
0.75%
93.00%
-0.74%
1.80%
0.37% 11
Year To Year Returns (Hand typed from tables in textbook)
Year
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Large Company
Down Large
Stocks
Company Stocks
6.63%
-10.85%
-10.85%
43.34%
11.90%
48.00%
26.81%
-8.78%
-8.78%
22.69%
16.36%
12.36%
-10.10%
-10.10%
23.94%
11.00%
-8.47%
-8.47%
3.94%
14.30%
18.99%
-14.69%
-14.69%
-26.47%
-26.47%
37.23%
23.93%
-7.16%
-7.16%
6.57%
18.61%
32.50%
-4.92%
-4.92%
21.55%
22.56%
6.27%
31.73%
Long Term
Down Long Term
Government
Government
Consumer Price
Bonds
Bonds
US Treasury Bills Index
-3.14%
-3.14%
2.66%
2.99%
5.25%
3.28%
2.90%
-6.70%
-6.70%
1.71%
1.76%
-1.35%
-1.35%
3.48%
1.73%
7.74%
2.81%
1.36%
3.02%
2.40%
0.67%
4.63%
2.82%
1.33%
1.37%
3.23%
1.64%
4.43%
3.62%
0.97%
1.40%
4.06%
1.92%
-1.61%
-1.61%
4.94%
3.46%
-6.38%
-6.38%
4.39%
3.04%
5.33%
5.49%
4.72%
-7.45%
-7.45%
6.90%
6.20%
12.24%
6.50%
5.57%
12.67%
4.36%
3.27%
9.15%
4.23%
3.41%
-12.66%
-12.66%
7.29%
8.71%
-3.28%
-3.28%
7.99%
12.34%
4.67%
5.87%
6.94%
18.34%
5.07%
4.86%
2.31%
5.45%
6.70%
-2.07%
-2.07%
7.64%
9.02%
-2.76%
-2.76%
10.56%
13.29%
-5.91%
-5.91%
12.10%
12.52%
-0.16%
-0.16%
14.60%
8.92%
49.99%
10.94%
3.83%
-2.11%
-2.11%
8.99%
3.79%
16.53%
9.90%
3.95%
39.03%
7.71%
3.80% 12
Year To Year Returns (Hand typed from tables in textbook)
Year
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Long Term
Down Long Term
Large Company
Down Large
Government
Government
Consumer Price
Stocks
Company Stocks Bonds
Bonds
US Treasury Bills Index
18.67%
32.51%
6.09%
1.10%
5.25%
-8.09%
-8.09%
5.88%
4.43%
16.61%
8.71%
6.94%
4.42%
31.69%
22.15%
8.44%
4.65%
-3.10%
-3.10%
5.44%
7.69%
6.11%
30.46%
20.04%
5.43%
3.06%
7.62%
8.09%
3.48%
2.90%
10.08%
22.32%
3.03%
2.75%
1.32%
-11.46%
-11.46%
4.39%
2.67%
37.58%
37.28%
5.61%
2.54%
22.96%
-2.59%
-2.59%
5.14%
3.32%
33.36%
17.70%
5.19%
1.70%
28.58%
19.22%
4.86%
1.61%
21.04%
-12.76%
-12.76%
4.80%
2.68%
-9.10%
-9.10%
22.16%
5.98%
3.39%
-11.89%
-11.89%
5.30%
3.33%
1.55%
-22.10%
-22.10%
14.08%
1.61%
2.38%
28.68%
1.62%
1.03%
1.88%
10.88%
10.34%
1.43%
3.26%
4.91%
10.35%
3.30%
3.42%
15.79%
28.00%
4.97%
2.54%
5.49%
10.85%
4.52%
4.08%
-37.00%
-37.00%
39.46%
1.24%
0.09%
13
Arithmetic Mean = “Average”
•
•
•
•
•
Arithmetic Mean =
Mean =
“Average” (everyday language) =
“Typical Value” =
One Value that Can Represent All The Values =
14
Historical Average Returns
• Historical Averages For Asset Classes =
Arithmetic Mean of Asset Class = (Add then all
up)/Count
• Reward For Risk = Risk Premium = Historical
Arithmetic Mean of Asset Class – Historical
Arithmetic Mean of T-Bill
15
Historical Averages, Reward For Risk, Real Rate
RH - Rf = Reward
RH - I = Real
Historical Average
Investment
For Risk
Historical Rate
Return = RH
Large Stocks
11.70%
7.90%
8.60%
Small Stocks
16.40%
12.60%
13.30%
Long-term Corporate Bonds
6.20%
2.40%
3.10%
Long-term Government Bonds
6.10%
2.30%
3.00%
U.S. Treasury Bills = R f
3.80%
0.00%
0.70%
Inflation = I
3.10%
0.00%
• What We Can Learn From Capital Market History
– Lesson 1: There Is Reward For Bearing Risk
•
But why do some investments get more reward?
– The answer lies in “variability of returns”
16
Variability In Returns = Volatility In
Returns = Risk
•
•
•
•
Variability seen with Line & Column Chart
Variability seen with X-Y scatter chart
Variability seen with Frequency Distribution
Risk Measured by calculating Standard
Deviation
17
U.S.
Financial
Markets
The Historical
Record: 19252008
18
Year-to-Year Total Returns
Large-Company Stock Returns
19
Year-to-Year Total Returns
Long-Term Government Bond Returns
20
Year-to-Year Total Returns
U.S. Treasury Bill Returns
21
Variability seen with X-Y scatter chart
Which set of data is more spread out?
Which mean represents its data points more fairly?
If the data points are all clustered around the mean, then there is less variability, less risk
that your return will be different than the mean.
22
Variability seen with Frequency Distribution
23
Variability seen with Frequency Distribution
2006 - 16%
2004 - 11%
1993 - 10%
1988 - 17% 2003 - 29% 1997 - 33%
2000 - -9%
2007 - 5% 1986 - 19% 1999 - 21% 1995 - 38%
1990 - -3%
2005 - 5% 1979 - 19% 1998 - 29% 1991 - 30%
1981 - -5%
1994 - 1% 1972 - 19% 1996 - 23% 1989 - 32%
1977 - -7%
1992 - 8% 1971 - 14% 1983 - 23% 1985 - 32%
1969 - -8%
1987 - 5% 1968 - 11% 1982 - 22% 1980 - 33%
1962 - -9%
1984 - 6% 1965 - 12% 1976 - 24% 1975 - 37%
2001 - -12%1953 - -1%
1978 - 7% 1964 - 16% 1967 - 24% 1955 - 31%
1973 - -15%1946 - -8%
1970 - 4% 1959 - 12% 1963 - 23% 1950 - 31%
1966 - -10%1939 - -1%
1960 - 0% 1952 - 19% 1961 - 27% 1945 - 36%
2002 - -22% 1957 - -11%1934 - -2%
-60%-50%
1956 - 7% 1949 - 18% 1951 - 25% 1938 - 33% 1958 - 43%
2008 - -37% 1974 - -26% 1941 - -12%1932 - -9%
1948 - 5% 1944 - 20% 1943 - 26% 1936 - 33% 1935 - 47% 1954 - 52%
1931 - -44% 1937 - -35% 1930 - -25% 1940 - -10%1929 - -9%
1947 - 5% 1926 - 11% 1942 - 21% 1927 - 37% 1928 - 43% 1933 - 53%
-50%-40%
-40%-30%
-30%-20%
-20%-10%
-10%0%
0%10%
10%20%
20%30%
30%40%
40%50%
60%70%
50%60%
24
Which Stock Would You Prefer?
Each Has a Mean Return Of 4.1%
Why?
Count
15
Mean
4.1%
Year Stock Return Deviation = R = Mean
1995
2.0%
-2.1%
1996
4.0%
-0.1%
1997
3.5%
-0.6%
1998
5.5%
1.4%
1999
4.0%
-0.1%
2000
4.2%
0.1%
2001
4.3%
0.2%
2002
4.7%
0.6%
2003
5.0%
0.9%
2004
5.1%
1.0%
2005
3.0%
-1.1%
2006
2.9%
-1.2%
2007
4.6%
0.5%
2008
4.9%
0.8%
2009
4.1%
0.0%
Total
0
Count
15
Mean
4.1%
Year Stock Return Deviation = R = Mean
1995
5.0%
0.9%
1996
10.0%
5.9%
1997
12.0%
7.9%
1998
17.0%
12.9%
1999
19.0%
14.9%
2000
1.0%
-3.1%
2001
-15.0%
-19.1%
2002
-3.0%
-7.1%
2003
3.0%
-1.1%
2004
5.5%
1.4%
2005
10.0%
5.9%
2006
6.5%
2.4%
2007
-2.0%
-6.1%
2008
-22.0%
-26.1%
2009
15.0%
10.9%
25
Total
0
Which Stock Would You Prefer?
Each Has a Mean Return Of 4.1%
Why?
26
But Now We Need A
Number To Measure The
Volatility of Returns
27
Variability Measured By Calculating
Standard Deviation
• Risk is measured by the dispersion,
• Standard Deviation will be calculated
number that measures variability, or
volatility, or dispersion, or simply RISK
28
How Far Does Each Actual Return Deviate From The
Mean In A Typical Year?
Mean
Year
•
•
•
•
Deviation tells you how far each return
is from the mean
Deviation = Return – Mean
If we average these deviations, it will
give us an indication of the volatility of
the stock.
Sum of Deviations = 0
• This means we can’t calculate the
mean in the normal way.
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
4.1%
Stock Return Deviation
5.0%
0.9%
10.0%
5.9%
12.0%
7.9%
17.0%
12.9%
19.0%
14.9%
1.0%
-3.1%
-15.0%
-19.1%
-3.0%
-7.1%
3.0%
-1.1%
5.5%
1.4%
10.0%
5.9%
6.5%
2.4%
-2.0%
-6.1%
-22.0%
-26.1%
15.0%
10.9%
Total
0
29
Standard Deviation Is A Numerical
Measure Of Volatility Or “Risk” Of Stock
30
Standard Deviation Is A Numerical
Measure Of Volatility Or “Risk” Of Stock
31
What We Can Learn From Capital Market History
Lesson 2: The Greater The Potential Reward, The Greater The Risk
32
Standard Normal Curve
Do Our Historical Distributions Look Bell Shaped?
33
Risk And The Standard Normal Curve
Only Past Distributions That Fit The “Normal” Curve
Can Use The Standard Normal Curve
• Normal distribution:
– A symmetric frequency distribution
– The “bell-shaped curve”
– Completely described by the mean and
variance
• Example: Mean = 11.7%, Standard Deviation
= 20.6%, the 68% of the values should lie
between 11.7%-20.6% and 11.7% + 20.6% or
-8.9% and 32.3%.
34
If Assume Bell Shaped
If bell shaped Distributions
68% chance that in any given year
the returns will lie between:
Historical Average
Stabndard
Investment
Devaition (risk)
Lower
Return = RH
Large Stocks
11.70%
20.60%
Small Stocks
16.40%
33.00%
Long-term Corporate Bonds
6.20%
8.40%
Long-term Government Bonds
6.10%
9.40%
U.S. Treasury Bills = Rf
3.80%
3.10%
Inflation = I
3.10%
4.20%
Upper
-8.90%
-16.60%
-2.20%
-3.30%
0.70%
-1.10%
32.30%
49.40%
14.60%
15.50%
6.90%
7.30%
35
(Conclusion To Chapter 10)
• Two key lessons from capital market
history:
– There is a reward for bearing risk
– The greater the potential reward, the
greater the risk
10-36
Capital Market History
• Average Returns: There Is Reward For Bearing
Risk
• Variability In Returns: The Greater The
Potential Reward, The Greater The Risk
37
Mean Return & Standard Deviation
• For Historical Returns we use Mean &
Standard Deviation
• For Projected Future Returns we use
“Expected Returns” based probability theory
to calculate returns and risk (standard
deviation). Chapter 11
38
Arithmetic vs. Geometric Mean
• Arithmetic average:
– Return earned in an average period over multiple periods
average year over a particular period?”
• Geometric average:
– Average compound return per period over multiple
periods
return per year over a particular period?”
• Geometric average < arithmetic average unless all
the returns are equal
10-39
Geometric Average Return:
Formula
Equation 10.4

GAR  ( 1  R1 )  ( 1  R2 )  ...  ( 1  RN)

1 /T
1
Where:
Ri = return in each period
T = number of periods
10-40
Arithmetic vs. Geometric Mean
Which is better?
• The arithmetic average is overly optimistic for long
horizons
• The geometric average is overly pessimistic for short
horizons
• Depends on the planning period under consideration
• 15 – 20 years or less: use arithmetic
• 20 – 40 years or so: split the difference between them
• 40 + years: use the geometric
10-41
Efficient Markets Hypothesis
• Efficient Markets = new information is assimilated quickly &
correctly into financial asset prices. The correctly priced
assets help to efficiently allocate resources in the capitalist
system.
• Financial Markets are efficient in that when new
information becomes available, people buying and selling
stocks and bonds try to incorporate new information into
their estimates of the security.
– Competition between investors means that people study
companies very closely, trying to find the mispriced stock.
When everyone is doing this, prices tend to be not mispriced.
– EMH implies that all investments are NPV = 0. This is because if
prices are not too high or low:
• NPV (investors estimate) – MV (Price in market) = 0
42
Efficient Markets Hypothesis
• Strong Efficient
– All public and private info is reflected in security price.
• Semistrong Efficient
• All public info is reflected in security price.
• If true, financial statement analysis or studying current
mortgage rate defaults is futile.
– People study info like this all the time.
– Weak Form Efficient
• Past Security Price info is reflected in security price.
– If true, searching for patterns in historical prices is futile.
– People do this all the time “Technical Analysis”.
43
Efficient Markets Theory As Currently Stated Is False
• Herd mentality or “animal spirits” tend to make people
follow certain trends in the market even when the trend is
unreasonable (1990 Internet Stocks, 2000 Housing Prices).
Fisher, Keynes and Minsky all wrote extensively about such
behavior.
• Often times Financial Market Bubbles are fueled by firms
and individuals borrowing money to buy up assets, the
increased demand for assets increases the price of the
assets, the increased value of the assets allows people to
borrow more because they have more collateral. In
essence, “easy credit” can contribute to assets price
increases that do not reflect the underlying fundamentals
of the asset.
– Examples: Depression and the 2007-2010 Housing Crisis.
– 2007-2010 Housing Crisis: housing prices where well above the
present value of future rent cash flows.
44
Efficient Markets Theory As Currently Stated Is False
• The idea that markets always price financial assets correctly
has been proven false a number of times in history.
– Example: Public information about default rates on houses was
available in the years 2005 - 2007, and yet prices on mortgage
back securities did not adjust downward until late 2007. As a
result of the overpriced financial assets, people continued to
take out loans and buy houses. This is an example of how
resources are inefficiently allocated when prices are not correct
based on inefficient markets. The result: many people got
seriously hurt when the prices finally did adjust (late).
– AOL was priced high at the height of the Internet Bubble in the
late 1990s.
– If markets are efficient, how come AOL stock was valued so high
for so long? How come mortgage backed securities with loans
from 2004 – 2007 had a price at all?
45
Efficient Markets Are Only Efficient In
The Long Run
• In the long run, markets tend to be efficient
(eventually, internet stocks and mortgage back
securities did fall).
46
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