copyright © 2003 mcgraw hill ryerson limited 9-1 prepared by: carol edwards ba, mba, cfa...

copyright © 2003 McGraw Hill Ryerson Limited

9-19-1

prepared by:Carol EdwardsBA, MBA, CFA

Instructor, FinanceBritish Columbia Institute of Technology

Fundamentals

of Corporate

Finance

Second Canadian Edition


9-29-2

Chapter 9Introduction to Risk, Return and the Opportunity Cost of Capital

Chapter Outline Rates of Return: A Review Seventy-five Years of Capital Market

History Measuring Risk Risk and Diversification Thinking about Risk


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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 two ways to measure the total rate of return on an investment:

Percentage Return = Dividend Yield+Capital Gain(%)

Percentage Return = Dividend + Capital GainShare Price


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75 Years 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.


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• Can the past tell us about the future? There are many kinds of market indexes you

could study. In this chapter, you will look at the historical

performance of the following portfolios: A portfolio of 91 day government securities, known

as Treasury bills (t-bills). A portfolio of long-term Canadian government

bonds. A portfolio of common shares of large companies.


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• Can the past tell us about the future? 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 of the three types of portfolios. There is no promise you will get your money back. The portfolio’s price is uncertain and not easily

predicted.


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• Can the past tell us about the future? 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. The price of the bond holdings will fluctuate in

response to interest rate changes. When rates fall, bond prices rise, and vice versa.


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• Can the past tell us about the future? Look at Figure 9.1 on page 276 and you can

see how much a $1 investment made in 1926 would have grown to by the end of 2000. You should see that the performance of the

portfolios fits our risk ranking: Common stocks were the most risky and also offered

the greatest gains. T-bills had the lowest risk and the lowest return. Long-term bonds provided a return between the

returns of t-bills and common stocks.


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• Can the past tell us about the future? We can summarize the average rates of return

for each of the investment classes for the period 1926 – 2000 as follows:

* Avg. Risk Premium = The extra return as versus a t-bill

Average AnnualAverage

Portfolio Rate of ReturnRisk Premium*

Treasury Bills 4.8% -

Gov’t Bonds 6.4% 1.6%capitals

Common Stocks 11.8%7.0%capitals


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• 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 7% more on a

common stock portfolio than they did on t-bill portfolio.

They demanded 1.6% 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.


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• Can the past tell us about the future? 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. In summary:

Rate of Return = Interest Rate + Market Riskon Any Security on T-bills Premium


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• Estimating Today’s Cost of Capital You learned in Chapter 6 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?


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• Estimating Today’s Cost of Capital Suppose you found an investment with a risk

which exactly matched the risk on 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.


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•Estimating Today’s Cost of Capital Key Question:

What is the market rate of return? We could use the historical average rate

of return.From Slide #9, we know this rate to be

11.8%. Do you think this would be a good

solution to our question?


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• Estimating Today’s Cost of Capital Using the average rate of 11.8% would not be

a good solution: You know from the historical record that the rate of

return on the market varies quite dramatically from year to year.

Thus 11.8% would not be a good indicator of the market rate of return for this moment in time.

Investors right now may want 11.8%, or more than 11.8%, or less than 11.8% on the market portfolio.

Can you see another solution?


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• Estimating Today’s Cost of Capital Historically, investors have demanded a 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 7%:

Expected = Interest Rate + Normal RiskMarket Return on T-bills Premium


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• 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?


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• Estimating Today’s Cost of Capital 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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Measuring Risk• Variance and Standard Deviation

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.


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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.

The critical question is: How do you measure the amount of dispersion?


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In financial analysis, we have two measures of risk on an investment: Variance

The average value of squared deviations from the the mean.

Standard Deviation The square root of the variance.

Both standard deviation and variance are measures of volatility of return.


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Measuring Risk

• Standard Deviation for Various Securities We can now add a column to the average

rates of return for each of the investment classes for the period 1926 – 2000 :

Average Annual Average Standard Portfolio Rate of Return Risk Premium Deviation

Treasury Bills 4.8% - 4.3%

Gov’t Bonds 6.4% 1.6%capitals9.2%

Common Stocks 11.8% 7.0%capitals18.6%


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Measuring Risk

• Standard Deviation for Various Securities You should see the risk-return trade-off:

T-bills have the lowest average rate of return, and the lowest level of volatility. The standard deviation of a t-bill is only 4.3%

Stocks have the highest average rate of return and the highest level of volatility. The standard deviation for a common stock

portfolio is 18.6%.Bonds are in the middle, offering a “mid-level”

return with a “mid-level” risk.


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Risk and Diversification• Diversification

If you look at Table 9.6 on page 286, you will see the standard deviation for some representative Canadian common stocks.

Remember, a market portfolio of Canadian common stocks has a standard deviation of about 19%.

Do you see anything peculiarabout the list in Table 9.6?


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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 component parts?


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Risk and Diversification•Diversification

The answer to this question is:“diversification”

You will discover that diversification reduces variability.


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Suppose you are looking at investing in either a gold stock or an auto stock.

You have the following information about the two investments:

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%


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You have to ask yourself:Why would anyone buy the gold stock?

It’s significantly more risky than the auto stock, yet it gives a smaller return.

The gold stock looks like a lousy investment, by itself.

But, what do you think would happen if you were to put some of the gold stock in a portfolio with the auto stock?


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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.


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That is for two assets:

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

( )( )


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Under the recession scenario you would calculate the portfolio rate of return as:

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

( )( )

= (0.75 x -8%) + (0.25 x 20%)

= -1.0%


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Below we see the return table expanded to include the portfolio (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%


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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.


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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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Key Question:Can we quantify how much two assets move in

lock step with each other? Yes!

The correlation coefficient is a measure of the degree to which any two variables move together.

Thus, it is a useful concept for understanding how stocks move relative to each other.


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Risk and Diversification•Correlation Coefficient

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.


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If the correlation coefficient 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.


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If the correlation coefficient 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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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 = x2

x + y2

y

+ 2xyxy

x

y

2 2


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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.


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If you calculate the standard deviation of a portfolio,

p, you will find the following:

-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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Risk and Diversification• 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 as in the graph on the next slide.


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Risk and DiversificationDiversification Reduces Risk

0

2

4

6

8

10

12

14

16

0 5 10 15 20 25 30

Number of Securities

Po

rtfo

lio S

tan

dar

d D

evia

tio

n

Market Risk

Unique Risk


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If you look at the graph, you should note: 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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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.


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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 market risk.


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Risk and Diversification• Thinking About Risk

There are 3 messages which you want to take from this chapter:Message1: 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.


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Message2: 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 favourable, investors do well and vice versa when they go the other way.


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Message3: 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.

This measure will be developed in the next chapter.


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Summary of Chapter 9 You can estimate the opportunity cost of capital for a

zero risk and an “average risk” project. A project with zero risk should be discounted at the t-bill rate. A project with average risk should be discounted at the return

expected on a market portfolio of common stocks. The market rate of return can be estimated by adding

7% to the t-bill rate. You can measure the risk, or volatility, of a security by

measuring the standard deviation, or variance, of its price over a period of time.


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Summary of Chapter 9 Standard deviation and variance are measures

of the volatility of a security’s price. The standard deviation on a market portfolio of

common stocks has averaged 19% per year. 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.

Risk which can be eliminated by diversification is known as unique risk.


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Summary of Chapter 9Risk which can’t be eliminated by diversification is called market risk. Even a well diversified portfolio can’t eliminate all risk.

When we talk about a risky stock, we are not talking about a stock held in isolation. We mean a stock which makes an above average

contribution to the risk of a diversified portfolio. Investors do not have to worry about risk they can

diversify away, but they do have to worry about risk that cannot be diversified.

This non-diversifiable risk depends on a security’s sensitivity to macroeconomic factors.

copyright © 2003 mcgraw hill ryerson limited 9-1 prepared by: carol edwards ba, mba, cfa...

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