Copyright © 2006 McGraw Hill Ryerson Limited10-1 prepared by: Sujata Madan McGill University Fundamentals of Corporate Finance Third Canadian Edition.

Copyright © 2006 McGraw Hill Ryerson Limited 10-1

prepared by:Sujata Madan

McGill University

Fundamentals

of Corporate

Finance

Third Canadian Edition


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


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


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


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.


79 Years of Capital Market HistoryValue of a $1 investment made in 1925:


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


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


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.


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


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%


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%


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.


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.


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%



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

( )( )



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%



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.


Risk and DiversificationCorrelation Coefficient

A measure of how closely two variables move together.

The correlation coefficient is always a number between -1 and +1.


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


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?


Risk and Diversification

Diversification Reduces Risk

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Market Risk

Unique Risk


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.


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


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.


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.

Copyright © 2006 McGraw Hill Ryerson Limited10-1 prepared by: Sujata Madan McGill University Fundamentals of Corporate Finance Third Canadian Edition.

Documents

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risk slide

rate market risk

measuring risk variance

review slide

pitals slide

lowest average rate

standard deviation variance