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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 = •(Add Then All Up)/Count 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, spread, or volatility of returns. • 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 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 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 – 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 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