1. Introduction to Risk, Return and Opportunity cost of Capital
Chapters 10
Introduction to Risk, Return and Opportunity cost of Capital
Chapter Outline
Rates of Return: A Review
Capital Market History
Measuring Risk
Risk and Diversification
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2. Rates of Return: A Review
Measuring Rate of Return
The returns on an investment come in two forms:
Income (dividend or interest payments).
Capital gains (or losses).
You have learned how to measure the total rate of return on an investment:
Percentage Return = Dividend Yield+Capital Gain(%)
Percentage Return = Dividend + Capital Gain Share Price
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3. 79Years of Capital Market History
Can the past tell us about the future?
By looking at the history of security returns, you can get some idea of the return that investors might reasonably expect from various types of securities.
You could look at individual securities.
But there are thousands of such investments!
Thus financial analysts tend to rely on market indexes to summarize the return on different classes of securities.
S&P/TSX Composite Index in Canada, DJIA, S&P 500 Index in US
We will look at the historical performance of 3 portfolios:
A portfolio of 91 day Treasury bills (t-bills).
A portfolio of long-term Canadian government bonds.
A portfolio of common shares of large companies
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4. These portfolios are not equally risky.
The t-bill portfolio is a safe holding.
You are sure to get your money back from the government.
Because of its short maturity, the price of the t-bill portfolio is quite stable and predictable.
The common stock portfolio is the riskiest.
There is no promise you will get your money back.
The portfolio’s price is uncertain and not easily predicted.
The portfolio of long-term bonds falls between the t-bill portfolio and the common stock one in its level of risk.
You are certain to get your money back at maturity.
However, the price of the holdings before maturity will be uncertain and not easily predicted.
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5. Can the past tell us about the future?
Figure 10.1 on page 311 shows how much a $1 investment made in 1925 would have grown to by the end of 2003.
You should see that the performance of the portfolios fits our risk ranking:
Common stocks were the most risky and also offered the highest gains.
T-bills had the lowest risk and the lowest return.
Long-term bonds provided a return between t-bills and common stocks.
Average Annual Average Portfolio Rate of Return Risk Premium*
Treasury Bills 4.7% -
Gov’t Bonds % %
Common Stocks % %
* Avg. Risk Premium = The extra return versus a t-bill
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6. Can the past tell us about the future?
Common stock and government bonds both had a higher rate of return than t-bills.
On average, investors demanded 6.7% more on a common stock portfolio than they did on t-bill portfolio.
They demanded 1.7% more on a bond portfolio.
This excess return, over and above the risk free rate, is called the risk premium.
It is the compensation investors demand for taking on extra risk.
The historical record shows that investors have received a risk premium for holding risky assets.
They also show a relationship between risk and return:
Average returns on high risk assets exceed those on low risk assets.
Rate of Return = Interest Rate Market Risk on Any Security on T-bills Premium
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7. Estimating Today’s Cost of Capital
You learned in Chapter 7 that a project should be discounted at the opportunity cost of capital.
Measuring the cost of capital is easy if the project is riskless:
Any project which is risk free should have a rate of return which matches the rate of interest on a t-bill, which is also risk free.
But what is the cost of capital on a project which is not risk free? What if the risk of a project is equivalent to the risk of a market portfolio of common stocks?
Instead of investing in your project, the shareholders could invest in a portfolio of common stocks.
Thus the project’s opportunity cost of capital would be the market rate of return. This is what the investors are giving up by investing in your project.
But should we use the historical average rate of return on common stocks?
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8. Estimating Today’s Cost of Capital
No! Figure 10.2 shows us that the market rate of return changes dramatically from year to year.
Thus 11.4% would not be a good indicator of the market rate of return for this moment in time.
Investors right now may want 11.4%, or more than 11.4%, or less than 11.4% on the market portfolio.
Can you see another solution?
Historically, investors have demanded a 6.7% risk premium over the t-bill rate to hold common stocks.
So a better procedure for estimating the market rate of return would be to take the current interest rate on t-bills and add the normal risk premium of 6.7%:
Expected = Interest Rate Normal Risk Market Return on T-bills Premium
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9. Estimating Today’s Cost of Capital
You now know how to estimate the opportunity cost of capital for:
A risk-free project
… use the t-bill rate.
A project with market risk (an “average risk” project)
… use the rate of return on a market portfolio.
But, how should you handle a project that does not fit either of these two categories?
You do know that the opportunity cost of an investment should reflect its risk.
Therefore, it is essential for you to understand how the risk of a project is measured.
Understanding this concept will allow you to understand how to estimate the required rate of return on a project.
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10. Measuring Risk Which of the following two investments is riskier?
Investment A has an average annual return of 8%, with a range of  2%.
Returns vary from 6% to 10% in any particular year.
Investment B also has an average annual return of 8%, but with a range of  12%.
Returns vary from –4% to 20% in any particular year.
You should recognize immediately that B is the riskier investment.
There is much greater uncertainty about the possible outcome on Investment B.
Thus, intuitively, you know that risk depends on the dispersion or spread of the possible outcomes.
The greater the dispersion, the greater the risk.
How do you measure the amount of dispersion (or volatility)?
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11. Measuring Risk
In financial analysis, we have two measures of risk on an investment
Variance: Average value of squared deviations from the mean.
Standard Deviation: The square root of the variance.
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12. Measuring Risk
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13. Measuring Risk
Table 10.5 Standard Deviation of rates of return,
Portfolio
Average
Rate of Return
Average Risk Premium
Standard Deviation %
Treasury bill
4.7
4.2
LT Gvt. Bonds
6.4
1.7
9.0
Common Stocks
11.4
6.7
18.6
There is a risk-return trade-off
T-bills have the lowest average return and the lowest volatility
Stocks have the highest average return and the highest volatility
Government bonds are in the middle, offering a mid-level return with a mid-level risk
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14. Risk and Diversification
If you look at Table 10.6 on page 319, you will see the standard deviation for some representative Canadian common stocks.
Do the standard deviations look high to you?
The market portfolio’s standard deviation was about 19%.
Yet you will discover that most stocks are substantially more variable than the market portfolio.
Only a handful are less variable.
How is it possible for a market portfolio of individual stocks to have less variability than the average variability of its parts?
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15. Risk and Diversification
The answer to this question is:
“diversification”
You will discover that diversification reduces variability.
Diversification works because prices of different stocks do not move exactly together
Diversification works best when the returns are negatively correlated!
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16. Risk and Diversification
Suppose you are looking at investing in either a gold stock or an auto stock.
You have the following information about the two investments:
Gold stock is riskier than the Auto stock and gives a smaller return
Can you reduce the risk by investing in both stocks?
Rate of Return Scenario Probability Auto Stock Gold Stock
Recession 1/3 -8.0% 20.0%
Normal 1/3 5.0% 3.0%
Boom 1/3 18.0% %
Expected Return 5.0% 1.0%
Standard Deviation 10.6% 16.4%
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17. Risk and Diversification
Let’s say you have $10,000 and decide to put $7,500 in autos and $2,500 in gold.
First we need to calculate the expected return on this portfolio for each of the scenarios.
The portfolio return will be the weighted average of the returns on the individual assets.
The weight will be equal to the proportion of the portfolio invested in each asset.
rp = X1r1 + x2r2 + …+Xnrn
Where ri is the return on ith stock and xi is its weight on the portfolio.
Under the recession scenario you would calculate the portfolio return as
= (0.75 x -8%) + (0.25 x 20%) = -1.0%
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18. Risk and Diversification
Below we see the return table expanded to include the portfolio (75% auto stock and 25% gold):
Rate of Return Scenario Probability Auto Stock Gold Stock Portfolio
Recession 1/3 -8.0% 20.0% %
Normal 1/3 5.0% 3.0% 4.5%
Boom 1/3 18.0% % 8.5%
Expected Return 5.0% 1.0% 4.0%
Standard Deviation 10.6% 16.4% 3.9%
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19. Risk and Diversification
Are you surprised by the results?
When you shifted funds from the auto stock to the more volatile gold stock, the variability of the portfolio actually decreased!
In fact, the volatility for the portfolio is much less than the volatility of either stock held separately.
This is the payoff from diversification.
The gold stock offsets the swings in performance of the auto stock, reducing the best-case return, but improving the worst case return.
Thus, addition of the gold stock stabilizes the returns on the portfolio.
Diversification reduces risk in a portfolio 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.
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20. Risk and Diversification
Can we quantify how much two assets move in lock step with each other?
The correlation coefficient is a measure of the degree to which any two variables move together.
The correlation coefficient is always a number between -1 and +1.
The closer the correlation coefficient is to either -1 or +1, the stronger the relationship between the two variables.
If It is greater than zero, then the two variables tend to move in the same direction. They are said to be positively correlated.
If it is less than zero, then the two variables tend to move in the opposite direction. They are said to be negatively correlated.
If it equals zero, then a change in one variable tells you nothing about the likely change in the other. They are said to be uncorrelated.
If it equals 1, then the two variables are perfectly positively correlated. They will move in lock step with each other.
If the it equals -1, then two variables are perfectly negatively correlated. They will move exactly opposite of each other.
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21. Risk and Diversification
Correlation Coefficient
We use the Greek letter “rho” () to represent the correlation coefficient.
The standard deviation of a portfolio with two stocks, x and y, and a correlation between x and y of xy, is calculated as:
p =  Wx2 x2 + Wy2y 2 + 2WxWyxyxy
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22. Risk and Diversification
If you calculate the standard deviation of a portfolio, p, you will find the following:
xy = 1
The stocks move in lock step and there is no benefit from diversification. The risk of the portfolio will equal the weighted average of the risk of the stocks.
xy = -1
The stocks move exactly opposite to each other. There is 100% benefit from diversification. It is possible to reduce the risk of the portfolio to zero.
-1 < xy < 1
There is a benefit from diversification and the standard deviation of a portfolio, p, will be between zero and the weighted average of the the risk of the stocks.
The closer xy is to -1, the greater the benefit from diversification, and the lower the risk of the portfolio.
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23. Risk and Diversification
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24. Market Risk Versus Unique Risk
You will find that if you are holding only one stock, then you will be exposed to 100% of the risk of that stock’s price changes.
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.
As you add stocks to the portfolio, the risk steadily falls
You cannot eliminate all risk from a portfolio by adding securities.
You get the greatest risk reduction by holding a few securities.
Once you get beyond 15 stocks, adding more stocks does very little to reduce the risk of the portfolio.
There always remains some risk in a portfolio from economy-wide perils that threaten all businesses.
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25. Risk and Diversification
Diversification Reduces Risk 2 4 6 8 10 12 14 16 5 15 20 25 30
Number of Securities
Portfolio Standard Deviation
Unique Risk
Market Risk
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26. Market Risk Versus Unique Risk
The risk which cannot be eliminated from a portfolio regardless of how much you diversify is known as market risk.
The risk which can be avoided by diversifying is known as unique risk.
Unique risk exists because of the perils which are peculiar to any one company.
If you held less than 15 securities in your portfolio, you should see on the graph that you would be exposed to unique risk.
The fewer the securities you hold, the more unique risk you are exposed to.
For a reasonably well diversified portfolio, unique risk is not an issue.
Unique risk can be diversified away.
The only risk which matters in a well diversified portfolio is Market Risk
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27. Thinking About Risk
There are 3 messages which you want to take from this chapter:
1. Some risks look big and dangerous but are really diversifiable.
If a risk is a unique risk, reflecting perils specific to a particular company, investors can avoid that risk by combining it in a diversified portfolio with many other assets or securities.
From an investor’s perspective, unique risk need not be a concern.
2. Market risks are macro risks.
Diversified portfolios are not exposed to the unique risks of individual holdings.
However, they are exposed to uncertain events which affect the entire securities market or the entire economy.
These macro factors include changes in interest rates, industrial production, inflation, exchange rates and energy cost.
When these macro factors are favorable, investors do well and vice versa when they go the other way.
3. Risk can be measured.
We can measure how risky a stock is by comparing its price fluctuations to those of the market as a whole.
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