Lessons From Capital Market History: Return & Risk Chapter 10 1

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Lessons From Capital Market History:Return & Risk

Chapter 10

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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

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1 Year Percent Return

t

ttt

t

tt

t

t

P

PPD

CGYDY

P

PPCGY

P

DDY

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1

1

Return %

Return %

Dividend Yield

Capital Gains Yield

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Period Returns = Holding Returns = 1 Year ReturnsReturns On Investment For 1 Year (Holding

Period Return)(Regardless of whether you sell the stock or

not)Stock Price Time 0 = (Beg) = Pt $25.00Stock Price Time 1 = (End) = Pt+1 $19.50Dividend Paid at Time 1 = Dt+1 $2.00Capital Gain = Pt+1 - Pt -$5.50Dollar 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%

Returns On Investment For 1 Year (Holding Period Return)

(Regardless of whether you sell the stock or not)

Stock Price Time 0 = (Beg) = Pt $25.00Stock Price Time 1 = (End) = Pt+1 $26.00Dividend Paid at Time 1 = Dt+1 $2.00Capital Gain = Pt+1 - Pt $1.00Dollar 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%

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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”

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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.

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U.S. Financial Markets

The Historical Record: 1925-

2008

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Year-to-Year Total Returns

Large-Company Stock Returns

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Long-Term Government Bond Returns

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U.S. Treasury Bill Returns

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Year To Year Returns (Hand typed from tables in textbook)

YearLarge Company Stocks

Down Large Company Stocks

Long Term Government Bonds

Down Long Term Government Bonds US Treasury Bills

Consumer Price Index

1926 11.14% 7.90% 3.30% -1.12%1927 37.13% 10.36% 3.15% -2.26%1928 43.31% -1.37% -1.37% 4.05% -1.16%1929 -8.91% -8.91% 5.23% 4.47% 0.58%1930 -25.26% -25.26% 5.80% 2.27% -6.40%1931 -43.86% -43.86% -8.04% -8.04% 1.15% -9.32%1932 -8.85% -8.85% 14.11% 0.88% -10.27%1933 52.88% 31.00% 0.52% 0.76%1934 -2.34% -2.34% 12.98% 0.27% 1.52%1935 47.22% 5.88% 0.17% 2.99%1936 32.80% 8.22% 0.17% 1.45%1937 -35.26% -35.26% -0.13% -0.13% 0.27% 2.86%1938 33.20% 6.26% 0.06% -2.78%1939 -0.91% -0.91% 5.71% 0.04% 0.00%1940 -10.08% -10.08% 10.34% 0.04% 0.71%1941 -11.77% -11.77% -8.66% -8.66% 0.14% 9.93%1942 21.07% 2.67% 0.34% 9.03%1943 25.76% 2.50% 0.38% 2.96%1944 19.69% 2.88% 0.38% 2.30%1945 36.46% 5.17% 0.38% 2.25%1946 -8.18% -8.18% 4.07% 0.38% 18.13%1947 5.24% -1.15% -1.15% 0.62% 8.84%1948 5.10% 2.10% 1.06% 2.99%1949 18.06% 7.02% 1.12% -2.07%1950 30.58% -1.44% -1.44% 1.22% 5.93%1951 24.55% -3.53% -3.53% 1.56% 6.00%1952 18.50% 1.82% 1.75% 0.75%1953 -1.10% -1.10% -0.88% -0.88% 1.87% 0.75%1954 52.40% 7.89% 93.00% -0.74%1955 31.43% -1.03% -1.03% 1.80% 0.37%

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1956 6.63% -3.14% -3.14% 2.66% 2.99%1957 -10.85% -10.85% 5.25% 3.28% 2.90%1958 43.34% -6.70% -6.70% 1.71% 1.76%1959 11.90% -1.35% -1.35% 3.48% 1.73%1960 48.00% 7.74% 2.81% 1.36%1961 26.81% 3.02% 2.40% 0.67%1962 -8.78% -8.78% 4.63% 2.82% 1.33%1963 22.69% 1.37% 3.23% 1.64%1964 16.36% 4.43% 3.62% 0.97%1965 12.36% 1.40% 4.06% 1.92%1966 -10.10% -10.10% -1.61% -1.61% 4.94% 3.46%1967 23.94% -6.38% -6.38% 4.39% 3.04%1968 11.00% 5.33% 5.49% 4.72%1969 -8.47% -8.47% -7.45% -7.45% 6.90% 6.20%1970 3.94% 12.24% 6.50% 5.57%1971 14.30% 12.67% 4.36% 3.27%1972 18.99% 9.15% 4.23% 3.41%1973 -14.69% -14.69% -12.66% -12.66% 7.29% 8.71%1974 -26.47% -26.47% -3.28% -3.28% 7.99% 12.34%1975 37.23% 4.67% 5.87% 6.94%1976 23.93% 18.34% 5.07% 4.86%1977 -7.16% -7.16% 2.31% 5.45% 6.70%1978 6.57% -2.07% -2.07% 7.64% 9.02%1979 18.61% -2.76% -2.76% 10.56% 13.29%1980 32.50% -5.91% -5.91% 12.10% 12.52%1981 -4.92% -4.92% -0.16% -0.16% 14.60% 8.92%1982 21.55% 49.99% 10.94% 3.83%1983 22.56% -2.11% -2.11% 8.99% 3.79%1984 6.27% 16.53% 9.90% 3.95%1985 31.73% 39.03% 7.71% 3.80%

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1986 18.67% 32.51% 6.09% 1.10%1987 5.25% -8.09% -8.09% 5.88% 4.43%1988 16.61% 8.71% 6.94% 4.42%1989 31.69% 22.15% 8.44% 4.65%1990 -3.10% -3.10% 5.44% 7.69% 6.11%1991 30.46% 20.04% 5.43% 3.06%1992 7.62% 8.09% 3.48% 2.90%1993 10.08% 22.32% 3.03% 2.75%1994 1.32% -11.46% -11.46% 4.39% 2.67%1995 37.58% 37.28% 5.61% 2.54%1996 22.96% -2.59% -2.59% 5.14% 3.32%1997 33.36% 17.70% 5.19% 1.70%1998 28.58% 19.22% 4.86% 1.61%1999 21.04% -12.76% -12.76% 4.80% 2.68%2000 -9.10% -9.10% 22.16% 5.98% 3.39%2001 -11.89% -11.89% 5.30% 3.33% 1.55%2002 -22.10% -22.10% 14.08% 1.61% 2.38%2003 28.68% 1.62% 1.03% 1.88%2004 10.88% 10.34% 1.43% 3.26%2005 4.91% 10.35% 3.30% 3.42%2006 15.79% 28.00% 4.97% 2.54%2007 5.49% 10.85% 4.52% 4.08%2008 -37.00% -37.00% 39.46% 1.24% 0.09%

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Arithmetic Mean = “Average”

• Arithmetic Mean =• Mean =• “Average” (everyday language) =• “Typical Value” =• One Value that Can Represent All The Values =

• (Add Then All Up)/Count

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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

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Historical Averages, Reward For Risk, Real Rate

InvestmentHistorical Average Return = RH

RH - Rf = Reward For Risk

RH - I = Real Historical Rate

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 = Rf 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”

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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

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U.S. Financial Markets

The Historical Record: 1925-

2008

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Large-Company Stock Returns

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Long-Term Government Bond Returns

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U.S. Treasury Bill Returns

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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.

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Variability seen with Frequency Distribution

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Variability seen with Frequency Distribution

-60%--50%

-50%--40%

1931 - -44%

-40%--30%

1937 - -35%

2008 - -37%

-30%--20%

1930 - -25%

1974 - -26%

2002 - -22%

-20%--10%

1940 - -10%

1941 - -12%

1957 - -11%

1966 - -10%

1973 - -15%

2001 - -12%

-10%-0%

1929 - -9%

1932 - -9%

1934 - -2%

1939 - -1%

1946 - -8%

1953 - -1%

1962 - -9%

1969 - -8%

1977 - -7%

1981 - -5%

1990 - -3%

2000 - -9%

0%-10%

1947 - 5%

1948 - 5%

1956 - 7%

1960 - 0%

1970 - 4%

1978 - 7%

1984 - 6%

1987 - 5%

1992 - 8%

1994 - 1%

2005 - 5%

2007 - 5%

10%-20%

1926 - 11%

1944 - 20%

1949 - 18%

1952 - 19%

1959 - 12%

1964 - 16%

1965 - 12%

1968 - 11%

1971 - 14%

1972 - 19%

1979 - 19%

1986 - 19%

1988 - 17%

1993 - 10%

2004 - 11%

2006 - 16%

20%-30%

1942 - 21%

1943 - 26%

1951 - 25%

1961 - 27%

1963 - 23%

1967 - 24%

1976 - 24%

1982 - 22%

1983 - 23%

1996 - 23%

1998 - 29%

1999 - 21%

2003 - 29%

30%-40%

1927 - 37%

1936 - 33%

1938 - 33%

1945 - 36%

1950 - 31%

1955 - 31%

1975 - 37%

1980 - 33%

1985 - 32%

1989 - 32%

1991 - 30%

1995 - 38%

1997 - 33%

40%-50%

1928 - 43%

1935 - 47%

1958 - 43%

50%-60%

1933 - 53%

1954 - 52%

60%-70%

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Which Stock Would You Prefer?Each Has a Mean Return Of 4.1%

Why?

Count 15Mean 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 15Mean 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%

Total 0

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Which Stock Would You Prefer?Each Has a Mean Return Of 4.1%

Why?

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But Now We Need A Number To Measure The

Volatility of Returns

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Variability Measured By Calculating Standard Deviation

• Risk is measured by the dispersion, spread, or volatility of returns.

• Standard Deviation will be calculated number that measures variability, or volatility, or dispersion, or simply RISK

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How Far Does Each Actual Return Deviate From The Mean In A Typical 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.

Mean 4.1%

Year Stock Return Deviation1995 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%

Total 0

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Standard Deviation Is A Numerical Measure Of Volatility Or “Risk” Of Stock

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Standard Deviation Is A Numerical Measure Of Volatility Or “Risk” Of Stock

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What We Can Learn From Capital Market HistoryLesson 2: The Greater The Potential Reward, The Greater The Risk

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Standard Normal CurveDo Our Historical Distributions Look Bell Shaped?

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Risk And The Standard Normal CurveOnly 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%.

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If Assume Bell Shaped

If bell shaped Distributions68% chance that in any given year

the returns will lie between:

InvestmentHistorical Average Return = RH

Stabndard Devaition (risk) Lower Upper

Large Stocks 11.70% 20.60% -8.90% 32.30%Small Stocks 16.40% 33.00% -16.60% 49.40%Long-term Corporate Bonds 6.20% 8.40% -2.20% 14.60%Long-term Government Bonds 6.10% 9.40% -3.30% 15.50%U.S. Treasury Bills = Rf 3.80% 3.10% 0.70% 6.90%Inflation = I 3.10% 4.20% -1.10% 7.30%

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Risk–Return Tradeoff(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

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Capital Market History

• Average Returns: There Is Reward For Bearing Risk

• Variability In Returns: The Greater The Potential Reward, The Greater The Risk

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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

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Arithmetic vs. Geometric Mean• Arithmetic average: – Return earned in an average period over multiple periods– Answers the question: “What was your return in an

average year over a particular period?”• Geometric average: – Average compound return per period over multiple

periods– Answers the question: “What was your average compound

return per year over a particular period?”

• Geometric average < arithmetic average unless all the returns are equal

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Geometric Average Return: Formula

1R1(...)R1()R1(GAR /T1N)21

Where:

Ri = return in each period

T = number of periods

Equation 10.4

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Arithmetic vs. Geometric MeanWhich 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

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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

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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”.

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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.

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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?

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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).

Documents

Lessons From Capital Market History: Return & Risk Chapter 10 1