Risk and Return (Introduction) Professor: Burcu Esmer 1
Overview Rates of Return: A Review A Century of Capital Market History Measuring Risk Risk & Diversification Thinking About Risk Measuring Market Risk Beta Risk and Return CAPM Capital Budgeting and Project Risk 2
Risk and Return People make decisions based on expected returns and risks every day Should I attend to the corporate finance class today? Return: hour of leisure time Risk: you may miss an important topic for the exams Which activity would you prefer? Shopping Gold Sky-diving Different people have different perceptions of expected returns and risk 3
Risk and Return Since financial resources are finite, there is a hurdle that projects have to cross before being deemed acceptable. This hurdle will be higher for riskier projects than for safer projects. A simple representation of the hurdle rate is as follows: Hurdle rate = Riskless Rate + Risk Premium Two basic questions that every risk and return model in finance tries to answer are: How do you measure risk? How do you translate this risk measure into a risk premium? 4
Risk Aversion How big a win would you require from Heads to take the gamble You win $10,000, if it is Heads You lose $10,000, if it is Tails It is fair game! Would you take the gamble? How big a win you require from Heads to take the gamble? İf you required less than $10,000, you are risk seeking İf you required more than $10,000, you are risk averse 5
Risk and Return (cont.) What s Risk? What s return? risk: uncertainty/variability of outcomes return: reward for bearing risk Even when expected returns and risk are known, people often make different choices about what invest in: Risk preferences Risk Averse more Risk more Required Return Risk Neutral more Risk same Required Return Risk Seeking more Risk less Required Return 6
What is Risk? Risk, in traditional terms, is viewed as a negative. Websters dictionary, for instance, defines risk as exposing to danger or hazard. The Chinese symbols for risk, reproduced below, give a much better description of risk: The first symbol is the symbol for danger, while the second is the symbol for opportunity, making risk a mix of danger and opportunity. You cannot have one, without the other. 7
What is Return? Income received on an investment (i.e. Stock or bond) plus any change in market price, usually expressed as a percent of the beginning market price of the investment Percentage Return = Capital Gain + Dividend Initial Share Price 8
Return Example The stock price for Stock A was $75.06 per share 1 year ago. The stock is currently trading at $93.29 per share, and shareholders just received a $1.37 dividend. What return was earned over the past year? $1.37 + ($93.29 - $75.06 ) R = = 26.1% 9 $75.06
Rates of Return Dividend Yield = Dividend Initial Share Price Capital Gain Yield = Capital Gain Initial Share Price 10
Rates of Return Dividend Yield = 1.37 75.06.018 or 1.8% Capital Gain Yield = 18.23 75.06 11.243 or 24.3%
Rates of Return (ror) Nominal vs. Real (assume 4.1% inflation rate) 1+ real ror = 1 + nominal ror 1 + inflation rate 1+.261 1 + real ror = 1+.041 1.211 real ror 21.1% 12
Market Indexes Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms. Standard & Poor s Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. proportional to the number of shares in the issues. Holdings are 13
Index Investment performance of three portfolios The Value of an Investment of $1 in 1900 14 Source: Ibbotson Associates T-bills here are 3-month bills T-bonds here have maturity of 10 yrs.
Average rate of returns (1900-2010) Maturity premium Remember : Hurdle rate = Riskless Rate + Risk Premium Rate of return on common stocks = interest rate on Treasury Bills (risk-free rate) + market risk premium 15
Rates of Return for Common Stocks Common Stocks (1900-2010) 16
Returns (%) 1927 1930 1933 1936 1939 1942 1945 1948 1951 1954 1957 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Stock Market vs T-Bills The stock market is much riskier than investing in T-Bills (Rf). 50 30 10-10 -30 RF Mkt -50 If individuals are risk averse we should expect the stock market to have higher average returns. 17
1927 1931 1935 1939 1943 1947 1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007 Value of $1 invested in 1927 Stock Market vs T-Bills The risk premium for investing in the stock market is around 7% per year over the last 80 years. - This is the premium necessary to compensate investors for bearing stock market risk. 2500 2000 1500 1000 $ in RF $ in Mkt 500 0 18
Returns and Risk How are the expected returns and the risk of a security related? 19
Measuring Risk What is risk? How can it be measured? Variance: Average value of squared deviations from mean. A measure of volatility. Standard Deviation: Square root of variance. Also a measure of volatility. 20
Measuring Risk Return Distributions Probability of return A Do you prefer A or B? B has higher expected return but greater risk. B Possible Returns 21
Number of Years Histogram of Returns 15 10 5 Common Stocks 0 50 40 30 20 10 0-45 -40-35 -30-25 -20-15 -10-5 0 5 10 15 20 25 30 35 40 45 50 55 Treasury Bonds -45-40 -35-30 -25-20 -15-10 -5 0 5 10 15 20 25 30 35 40 45 50 55 Treasury Bills 80 60 40 20 0-45 -40-35 -30-25 -20-15 -10-5 0 5 10 15 20 25 30 35 40 45 50 55 Return, (percent) 22
Quantifying Risk and Return Pr(r) Distance r i is from expected outcome. Pr(r i ) r j -E(r) r i -E(r) Likelihood of r i r j E(r) The most likely outcome, E(r), must be our required return. Our measure of risk must consider the distance and likelihood of the unexpected outcomes. r i r i 23
Mean and Std. Deviation N i 1 E( R) Mean P ( r ) i i Variance Prob. of r i 2 r i N i 1 P i r i E( r) 2 Squared distances or deviations from the mean Std. Dev. 2 Variance 24
Example You start by investing $100. Then two coins are flipped. for each head starting balance increases by 20%. for each tail starting balance decreases by 10%. Possible scenarios : Head + Head = 20 + 20 = 40% Head + Tail = 20 + - 10 = 10% Tail + Head = -10 + 20 = 10% Tail + Tail = -10 + -10 = -20% 25
Example (cont.) E( R) Mean P ( r ) Expected Return= 0.25 x 40 + 0.25 x 10 + 0.25 x 10 + 0.25 x -20 Variance = 10% 2 r i i 1 i 1 Variance= 0.25 x (40-10) 2 + 0.25 x (10-10) 2 + 0.25 x (10-10) 2 + 0.25 x (-20-10) 2 = 0.25 x 900 + 0.25 x 0 + 0.25 x 0 + 0.25 x 900 = 225 + 0 + 0 + 225 = 450 N N P i r i i i E( r) 2 Std. Dev. 2 Variance Standard deviation = (450) 0.5 = 21.2% 26
Measuring Risk Coin Toss Game-calculating variance and standard deviation (1) (2) (3) Percent Rate of Return Deviation from Mean Squared Deviation + 40 + 30 900 + 10 0 0 + 10 0 0-20 - 30 900 Variance = average of squared deviations = 1800 / 4 = 450 Standard deviation = square of root variance = 450 = 21.2% OR: Variance: sum of squared deviations weighted by probabilities: = 0.25 * 30 2 + 0.25 * 0 + 0.25 * 0+ 0.25 * (-30) 2 = 450 27
Variation in Stock Returns Historical Data Portfolio (1900-2010) Standard Deviation (%) Treasury Bills 2.8 Long-term government bonds 8.6 Common Stocks 20 28
Stock Market Volatility Annualized standard deviation of weekle returns in the Dow 1900-2010 29
Risk and Diversification Diversification Strategy designed to reduce risk by spreading the portfolio across many investments. 30
Calculate expected returns and volatilities: Scenario Probability Rate of Return Auto Stock Recession 1/3-8% 20% Normal 1/3 5% 3% Boom 1/3 18% -20% Rate of Return Gold Stock 31
e.g. cont. Auto Stock Expected Return = 5% Variance = 112.7 St. Dev. = 10.6% Expected return = (-8%+ 5% + 18%) / 3 Variance= ( (-8%-5%) 2 +(5%-5%) 2 + (18%-5%) 2 ) / 3 Gold Stock Expected Return =1% Variance = 268.7 St. Dev. = 16.4% Would anyone be willing to hold gold mining stocks in an investment portfolio? YES!! 32
Asset versus Portfolio Risk Portfolio rate of return ( )( ) fraction of portfolio rate of return = x in first asset on first asset ( )( ) fraction of portfolio rate of return + x in second asset on second asset Suppose autos have a weight of 0.75 and gold has weight of 0.25 in your portfolio (weights are given). Portfolio return in recession = 0.75 x -8% + 0.25 x 20% = -1% Portfolio return in normal = 0.75 x 5% + 0.25 x 3% = 4.5% Portfolio return in boom= 0.75 x 18% + 0.25 x -20% = 8.5% 33 Average Portfolio Return = (-1%+4.5%+8.5%)/3 = 4%
Example cont. Average Portfolio Return = (-1%+4.5%+8.5%)/3 = 4% Variance = (.0025+.000025+.002025)/3 =.001517 Std. Dev = Variance =.0389 34
Example cont. Portfolio Expected Return= 4% Portfolio Variance = 15.17 Potfolio Std. Dev = =3.89% Auto Stock Expected Return = 5% St. Dev. = 10.6% Gold Stock Expected Return =1% St. Dev. = 16.4% 35
Shortcut Auto Stock Expected Return = 5% St. Dev. = 10.6% Weight= 75% Gold Stock Expected Return =1% St. Dev. = 16.4% Weight= 25% Portfolio Expected Return= 0.75*5% + 0.25*1%= 4% BEWARE!! YOU CAN NOT DO THIS FOR STANDARD DEVIATION! 36
Adding stocks to a portfolio can reduce risk 37
Sum up Investors care about the expected return and risk of their portfolio of assets. The standard deviation of the returns of an individual security measures how risky that security would be if held in isolation. But for an investor with a portfolio of assets, how each security affects the risk of the entire portfolio. 38
Value (August 2004 = 100) The Value of Investments 160 140 120 100 80 60 Network Mining Ford Portfolio 40 20 0 39
Risk and Diversification Portfolio standard deviation 0 5 10 15 Number of Securities 40
Market vs Unique Risk Unique Risk - Risk factors affecting only that firm. Also called diversifiable risk or unsystematic risk or specific risk Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called systematic risk. 41
Risk and Diversification Portfolio standard deviation 0 Unique risk Market risk 5 10 15 Number of Securities 42
Thinking About Risk Message 1 Some Risks Look Big and Dangerous but Really Are Diversifiable (like insurance companies) Message 2 Market Risks Are Macro Risks (airlines, machine tool manufacturers vs food companies) Message 3 Risk Can Be Measured (by measuring the individual stock s sensitivity to the fluctuations of the overall stock market we will learn how to do it in the next chapter ). 43