11-1 lecture 11 introduction to risk, return, and the opportunity cost of capital
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11-11-11
Lecture 11
Introduction to Risk, Return, and the Opportunity Cost of Capital
11-11-22
Risk and Return
Risk and Return are related.
How?
This chapter will focus on risk and return and their relationship to the opportunity cost of capital.
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Equity Rates of Return: A Review
Capital Gain + Dividend Initial Share PricePercentage Return =
Capital GainInitial Share PriceCapital Gain Yield =
Dividend Initial Share PriceDividend Yield =
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Rates of Return: ExampleExample: You purchase shares of GE stock at $15.13 on December 31, 2009. You sell them exactly one year later for $18.29. During this time GE paid $.46 in dividends per share. Ignoring transaction costs, what is your rate of return, dividend yield and capital gain yield?
$18.29 $15.13 $.46
$15.1323.93%Percentage Return
$18.29 $15.13$15.13 20.89%Capital Gain Yield
$.46Dividend Yield = 3.04%
$15.13
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Real Rates of Return
1 + nominal rate of return1 + inflation rate1 real rate of return =
Example: Suppose inflation from December 2009 to December 2010 was 1.5%. What was GE stock’s real rate of return, if its nominal rate of return
was 23.93%?
Recall the relationship between real rates and nominal rates:
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Capital Market History:Market Indexes
• Market Index - Measure of the investment performance of the
overall market.
• Dow Jones Industrial Average (The Dow)
• Standard & Poor’s Composite Index (S&P 500)
Other Market Indexes?
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Total Returns for Different Asset Classes
The Value of an Investment of $1 in 1900
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What Drives the Difference in Total Returns?
Maturity Premium: Extra average return from investing in long- versus short-term Treasury securities.
Risk Premium: Expected return in excess of risk-free return as compensation for risk.
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Risk Premium: ExampleInterest Rate on Normal Risk
Expected Market Return = +Treasury Bills Premium
1981: 21.6% = 14% + 7.6%
2008: 9.8% = 2.2% + 7.6%
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Returns and Risk
How are the expected returns and the risk of a security related?
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Measuring Risk
Variance: Average value of squared deviations from mean. A measure of volatility.
Standard Deviation: Square root of variance. Also a measure of volatility.
What is risk?
How can it be measured?
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Variance and Standard Deviation: Example
Coin Toss Game: calculating variance and standard deviation
(assume a mean of 10)
(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%
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Histogram of Returns
What is the relationship between the volatility of these securities and their expected returns?
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Historical Risk(1900-2010)
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Risk and DiversificationDiversification
Strategy designed to reduce risk by spreading a 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.”
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Diversification: Building a Portfolio
fraction of portfolio rate of returnPortfolio Rate of Return = x
in first asset on first asset
fraction of portfolio rate of return+ x
in second asset on second asset
A portfolio’s rate of return is the weighted sum of each asset’s rate of return.
Two Asset Case:
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Building a Portfolio: ExampleConsider the following portfolio:
Stock Weight Rate of Return
IBM
Starbucks
Walmart
What is the portfolio rate of return?
50%IBMw
25%SBUXw
25%Ww
Portfolio Rate of Return =
(50% 8.3%) 25% 12.5% 25% 4.7%
8.45%
IBM IBM SBUX SBUX W Ww r w r w r
8.3%IBMr
12.5%SBUXr
4.7%Wr
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Do stock prices move together?
What effect does diversification have on a portfolio’s total risk, unique risk and market risk?
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Risk and Diversification
11-11-2020
Thinking About Risk
Message 1• Some Risks Look Big and Dangerous but Really Are
Diversifiable
Message 2• Market Risks Are Macro Risks
Message 3• Risk Can Be Measured
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