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Copyright © 2006 McGraw Hill Ryerson Limited 10-1
prepared by:Sujata Madan
McGill University
Fundamentals
of Corporate
Finance
Third Canadian Edition
Copyright © 2006 McGraw Hill Ryerson Limited 10-2
Chapter 10 Introduction to Risk, Return and the Opportunity Cost of Capital
Rates of Return: A Review
79 Years of Capital Market History
Measuring Risk
Risk and Diversification
Thinking about Risk
Copyright © 2006 McGraw Hill Ryerson Limited 10-3
Rates of Return: A ReviewMeasuring Rate of Return
The total return on an investment is made up of:
Income (dividend or interest payments). Capital gains (or losses).
Percentage Return = Capital Gain + DividendInitial share Price
Copyright © 2006 McGraw Hill Ryerson Limited 10-4
Rates of Return: A Review
D iv id e n d Y ie ld = D iv id e n d In i t ia l S h a re P r ic e
C a p i t a l G a in Y ie ld = C a p i t a l G a inIn i t i a l S h a r e P r i c e
rateinflation 1rate nominal1 = rate real 1
Copyright © 2006 McGraw Hill Ryerson Limited 10-5
79 Years of Capital Market History Market index: Measure of the investment
performance of the overall market
S&P/TSX Composite Index- Index of the investment performance of a portfolio of the major stocks listed on the Toronto Stock Exchange.
Dow Jones Industrial Average- Value of a portfolio holding one share in each of 30 large industrial firms.
Copyright © 2006 McGraw Hill Ryerson Limited 10-6
79 Years of Capital Market HistoryValue of a $1 investment made in 1925:
Copyright © 2006 McGraw Hill Ryerson Limited 10-7
79 Years of Capital Market HistoryAverage returns on T-bills, government bonds and common stocks (1926-2004) :
Average AnnualAverage
Portfolio Rate of ReturnRisk Premium*
Treasury Bills 4.7% -
Gov’t Bonds 6.4% 1.7%capitals
Common Stocks 11.4%6.7%capitals
Copyright © 2006 McGraw Hill Ryerson Limited 10-8
79 Years of Capital Market History Can the past tell us about the future?
The historical record shows that investors have received a risk premium for holding risky assets.
Rate of Return = Interest Rate + Market Riskon Any Security on T-bills Premium
Copyright © 2006 McGraw Hill Ryerson Limited 10-9
Measuring Risk Variance and Standard Deviation
Variance: The average value of squared deviations from the
mean.
Standard Deviation The square root of the variance.
Both variance and standard deviation are measures of volatility.
Copyright © 2006 McGraw Hill Ryerson Limited 10-10
Measuring Risk Coin Toss game
2 coins are flipped For each head, you get 20% For each tail, you lose 10%
Possible outcomes: HH: 20+20=40 HT:20-10= 10 TH:-10+20=10 TT:-10-10=-20
Copyright © 2006 McGraw Hill Ryerson Limited 10-11
Measuring Risk Calculating Standard Deviation for the
Coin Toss Game
(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%
Copyright © 2006 McGraw Hill Ryerson Limited 10-12
Measuring RiskStandard Deviation for Various Securities
Average rates of return and standard deviation for various investment classes (1926-2004):
Average Annual Average Standard Portfolio Rate of Return Risk Premium Deviation
Treasury Bills 4.7% - 4.2%
Gov’t Bonds 6.4% 1.7%capitals9.0%
Common Stocks 11.4% 6.7%capitals18.6%
Copyright © 2006 McGraw Hill Ryerson Limited 10-13
Measuring RiskStandard Deviation for Various Securities
Notice the risk-return trade-off: T-bills have the lowest average rate of return, and
the lowest level of volatility.
Stocks have the highest average rate of return and the highest level of volatility.
Bonds are in the middle.
Copyright © 2006 McGraw Hill Ryerson Limited 10-14
Risk and Diversification Definitions
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.
Copyright © 2006 McGraw Hill Ryerson Limited 10-15
Risk and DiversificationDiversification
Which stock would you pick?
Rate of ReturnScenario Probability Auto Stock Gold StockRecession 1/3 -8.0% 20.0% Normal 1/3 5.0% 3.0%Boom 1/3 18.0% -20.0%
Expected Return5.0% 1.0%Standard Deviation 10.6% 16.4%
Copyright © 2006 McGraw Hill Ryerson Limited 10-16
Risk and DiversificationDiversification
For a two-asset portfolio:
Portfolio Rate = fraction of portfolio x rate of return
of return in 1st asset on 1st asset
+ fraction of portfolio x rate of return
in 2nd asset on 2nd asset
( )( )
Copyright © 2006 McGraw Hill Ryerson Limited 10-17
Risk and DiversificationDiversification
Rate of return for a portfolio comprising 75% auto stock and 25% gold:
Rate of ReturnScenario Probability Auto Stock Gold Stock PortfolioRecession 1/3 -8.0% 20.0% -1.0% Normal 1/3 5.0% 3.0% 4.5%Boom 1/3 18.0% -20.0% 8.5%
Expected Return5.0% 1.0% 4.0%Standard Deviation 10.6% 16.4% 3.9%
Copyright © 2006 McGraw Hill Ryerson Limited 10-18
Risk and DiversificationDiversification
Addition of the gold stock stabilizes the returns on the portfolio.
Diversification reduces risk because the assets in the portfolio do not move in exact lock step with each other. When one stock is doing poorly, the other is doing
well, helping to offset the negative impact on return of the stock with the poorer performance.
Copyright © 2006 McGraw Hill Ryerson Limited 10-19
Risk and DiversificationCorrelation Coefficient
A measure of how closely two variables move together.
The correlation coefficient is always a number between -1 and +1.
Copyright © 2006 McGraw Hill Ryerson Limited 10-20
Risk and DiversificationCorrelation Coefficient
> 0 positive correlation variables move in the same direction.
< 0 negative correlation variables move in the opposite direction.
= 0 no correlation
Copyright © 2006 McGraw Hill Ryerson Limited 10-21
Risk and DiversificationMarket Risk Versus Unique Risk
If you hold two stocks with a correlation coefficient less than 1, then the risk of the portfolio can be reduced below the risk of holding either stock by itself.
Adding stocks to the portfolio, decreases the risk of the portfolio.
How much can you decrease the portfolio risk?
Copyright © 2006 McGraw Hill Ryerson Limited 10-22
Risk and Diversification
Diversification Reduces Risk
0
2
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6
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10
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0 5 10 15 20 25 30
Number of Securities
Po
rtfo
lio S
tan
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d D
evia
tio
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Market Risk
Unique Risk
Copyright © 2006 McGraw Hill Ryerson Limited 10-23
Risk and DiversificationMarket Risk Versus Unique Risk
You cannot eliminate all risk from a portfolio by adding securities.
Typically, once you get beyond 15 stocks, adding more stocks does very little to reduce the risk of the portfolio.
The risk that cannot be diversified away is called market risk.
For a reasonably well diversified portfolio, only market risk matters.
Copyright © 2006 McGraw Hill Ryerson Limited 10-24
Thinking about Risk3 Key Messages about Risk
Some risks look big and dangerous but are really diversifiable. Unique risk can be minimized by creating a diversified
portfolio.
Market risks are macro risks Example: changes in interest rates, industrial
production, inflation, exchange rates and energy cost.
Risk can be measured
Copyright © 2006 McGraw Hill Ryerson Limited 10-25
Summary of Chapter 10 Standard deviation and variance are measures of
risk.
Diversification reduces risk because stocks do not move in exact lock step, meaning that poor performance by one stock can be offset by strong performance by another.
Correlation coefficient is a measure of how two variables move with respect to each other.
Copyright © 2006 McGraw Hill Ryerson Limited 10-26
Summary of Chapter 10 Risk which can be eliminated by diversification is
known as unique risk.
Risk which cannot be eliminated by diversification is called market risk.
For a well-diversified portfolio, only market risk matters.