Introduction to risk, return, and the opportunity cost of capital So, don't ask me no questions And...
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Transcript of Introduction to risk, return, and the opportunity cost of capital So, don't ask me no questions And...
Introduction to risk, return, and the opportunity
cost of capital
So, don't ask me no questions And I won't tell you no lies So, don't ask me about my business And I won't tell you goodbye - Rossington, VanZant
Stock 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
major firms. Holdings are proportional to
the number of shares in issue.
$0.10
$1.00
$10.00
$100.00
$1,000.00
$10,000.00
$100,000.00
Large Company StocksSmall Company StocksGovernment BondsTreasury BillsInflation
Stocks, Bonds, Bills, and Inflation
Hypothetical value of $1 invested at year-end 1925. Assumes reinvestment of income and no transaction costs or taxesThis is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2010. Copyright © 2010 Ibbotson Associates, Inc.
1925 - 2009
AverageReturn
EndingWealth
1925
1935
1945
1955
1965
1975
1985
1995
2009
$12,233$2,587
$84.39 $20.53$12.14
Volatility of Stock and Bond Returns1926 - 2006
Mon
thly
Ret
urns
Monthly returns in percent from 1926-2006.This is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2006. Copyright © 2006 Ibbotson Associates, Inc..
Stocks
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
1926 1946 1966 1986 2006
Bonds
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
1926 1946 1966 1986 2006
Rates of Return 1926-2009
Source: Ibbotson Associates
-60
-40
-20
0
20
40
60
Common Stocks
Long T-Bonds
T-Bills
Year
Per
cent
age
Ret
urn
Stocks, Bonds, Bills, and Inflation
CompoundAnnualReturn
ArithmeticAnnualReturn
Risk(StandardDeviation)
*The 1933 Small Company Stock total return was 142.9%.This is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2010. Copyright © 2010 Ibbotson Associates, Inc.
Summary Statistics 1926 - 2009
Distribution of Annual Returns
LargeCompanyStocks
9.66% 11.8% 20.5%
Small CompanyStocks
*11.7% 16.5% 33.0%
GovernmentBonds 5.7% 6.1% 9.4%
Inflation 2.9% 3.1% 4.2%
Treasury Bills 3.7% 3.8% 3.1%
Large Company Stocks Histogram1926-2009
Source: Ibbotson Associates 2010
Risk Premiums 1926-2009 Average Risk Portfolio Premium
Small-firm stocks 12.24%
Common stocks 7.71 (S&P 500)
Long-term govt 2.22bonds
Treasury bills 0
Average Market Risk Premia (by country)Risk premium, %
Country
Expected return on market portfolio(= expected return on average-risk US
stock)
current expectedrm = interest + market risk rate (rf) premium
If expected risk premium = long-run average*
rm = interest rate (rf) + 7.71%*
* Note: This can change a little bit from year to year.
Risk and Return
• Expected ReturnPrefer more to less.
• Variance and Standard Deviation (Risk)Prefer less to more.
Measuring Risk
Variance - Average value of squared deviations from mean. A measure of volatility.
Standard Deviation – square root of variance.
Calculating standard deviation of returns
Deviation Rate of from Squared Year return average deviation
1988 16.8 .1 .01
1989 31.5 14.8 219.04
1990 - 3.2 -19.9 396.01
1991 30.6 13.9 193.21
1992 7.7 - 9.0 81.0
Total 83.4 889.27
Average rate of return = 83.4/5 = 16.68 = 16.7
Variance = average of squared deviations = 889.27/5 = 177.854
Std deviation = square root of variance = 177.854 = 13.34%
Calculating variance and standard deviation
of Merck returns from past monthly data Deviation from mean Squared Month Return return deviation
1 5.4% 2.6% 6.76 2 1.7 - 1.1 1.21 3 - 3.6 - 6.4 40.96 4 13.6 10.8 116.64 5 - 3.5 - 6.3 39.69 6 3.2 0.4 0.16
Total 16.8 205.41
Mean: 16.8/6 = 2.8% Variance: 205.41/6 = 34.235 Std dev: Sq root of 34.235 = 5.85% per month
Total risk (standard deviation)for common stocks, 1989 -
1994
Standard StandardStock deviation Stock deviation
AT&T 21.4% Exxon 12.1%
Biogen 51.5 Ford Motor 28.0
Bristol-Myers Squibb 18.6 General Electric 19.6
Coca Cola 21.6 McDonald’s 21.7
Compaq 43.5 Microsoft 53.6
Risk and Diversification
Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.
Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”
Diversification eliminates unique risk
deviationstandardPortfolio
Unique risk
Market risk
Number ofsecurities
5 10
Number of Randomly Selected Assets in Portfolio
Ris
kReduction of Portfolio Risk
Risk is measured by standard deviation.This is for illustrative purposes only and not indicative of any investment.Past performance is no guarantee of future results. 3/1/2000. Copyright © 2000 Ibbotson Associates, Inc.
0%
5%
10%
15%
20%
25%
30%
35%
40%
1 2 3 4 5 6 7 8
Stock Diversification
1 2 4 6 8 16 30 50 100 1000Number of Stocks in Portfolio
Ris
k
Market Risk
Diversifiable Risk
This is for illustrative purposes only and not indicative of any investment.
Past performance is no guarantee of future results. 3/1/2000. Copyright © 2000 Ibbotson Associates, Inc.
Where do Diversification Benefits Come from?
• Concepts of Correlation and Covariance
• Expected Return on portfolio
• Standard Deviation of Portfolio Returns
Portfolio Risk and Return
)rx()r(x Return Portfolio Expected 2211
)σσρxx(2σxσxVariance Portfolio 21122122
22
21
21
Portfolio ReturnExample
Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The expected return on your portfolio is:
%12)1540(.)1060(. ReturnExpected
Portfolio RiskExample
Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The standard deviation of their annualized daily returns are 19.8% and 29.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance.
% 23.8 5.564 Deviation Standard
5.56419.8x29.7)2(.40x.60x
]x(29.7)[(.40)
]x(19.8)[(.60) Variance Portfolio22
22
To calculate portfolio variance add up the boxes The shaded boxes contain variance terms; the
remainder contain covariance terms.
1
2
3
4
5
6
N
1 2 3 4 5 6 NSTOCK
STOCK
Beta and Unique RiskMarket Portfolio - Portfolio of all assets in the
economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.
How can we measure exposure to market risk?
Beta - Sensitivity of a stock’s return to the return on the market portfolio. Beta is a measure of sensitivity to market movements.
Beta Computation
2m
imiB
Covariance with the market
Variance of the market
Beta
(1) (2) (3) (4) (5) (6) (7)Product of
Deviation Squared deviationsDeviation from average deviation from average
Market Anchovy Q from average Anchovy Q from average returnsMonth return return market return return market return (cols 4 x 5)
1 -8% -11% -10% -13% 100 1302 4 8 2 6 4 123 12 19 10 17 100 1704 -6 -13 -8 -15 64 1205 2 3 0 1 0 06 8 6 6 4 36 24
Average 2 2 Total 304 456
Variance = σm2 = 304/6 = 50.67
Covariance = σim = 456/6 = 76
Beta (β) = σim/σm2 = 76/50.67 = 1.5
Calculating the variance of the market returns and the covariance between the returns on the market and those of Anchovy Queen. Beta is the ratio of
the variance to the covariance (i.e., β = σim/σm2)
Market risk (beta) for common stocks1994
Stock Beta Stock Beta
AT&T .92 Exxon .51Biogen 2.20 Ford Motor Co. 1.12Bristol Myers Squibb .97 General Electric 1.22Coca Cola 1.12 McDonald’s 1.07Compaq 1.18 Microsoft 1.23
Market risk (beta) for common stocks2010*
Stock Beta Stock Beta
AT&T .63 Exxon .39Biogen .68 Ford Motor Co. 2.79Bristol Myers Squibb .59 General Electric 1.72Coca Cola .51 McDonald’s .52Hewlett-Packard 1.03 Microsoft 1.06
* Source: Finance.yahoo.com, which is based on 36 months of data and S&P500 as market index.
Firm Goals to Diversify?
Since diversification reduces risk, should
firms be concerned about diversification?
• Investors may diversify more easily.
• Value Additivity