fnce101-wk09

Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved

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Finance (FNCE 101)

Risk and ReturnChapters 12,13

Professor WANG Rong


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Today’s Agenda Historical Returns Measuring Risk and Return Risk and Diversification CAPM and Security Market Line Capital Market Efficiency Theories


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Historical Returns on Singapore Common Stocks (Based on Straits Times Index) from 1988-2007

Returns %

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

80.0%


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Historical Returns on US Common Stocks from 1900-2004

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Ret

urn

(%)

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Year

2004


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Average Annual Returns (1926-2005) in US

Question: Does this mean that small-company stocks are better investments?

Ave. RetSmall-company stocks 17.4%

Large-company stocks 12.3%

Long-term corporate bonds 6.2%

Long-term government bonds 5.8%

U.S. Treasury bills 3.8%


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Risk Premium Risk premium: The “extra” return earned for taking on the

risk. Stock market return = interest rate on Treasury bills +

Market risk premium Treasury bills are considered to be risk-free.

Average annual rate

of return Nominal

Average risk premium (excess return over treasury bills

Treasury bills 4.1 0 Common stocks 11.7 7.6 (≈11.7-4.1)


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Country Risk Premia (%)

0

2

4

6

8

10

12Italy

Japan

France

Germany (ex 1922/3)

Australia

South Africa

Sweden

USA

Average

UK

Ireland

Canada

Spain

Switzerland

Belgium

Denmark

Norway


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Ave. Ret Risk PremiumSmall-company stocks 17.4% ?

Large-company stocks 12.3%

Long-term corporate bonds 6.2%

Long-term government bonds 5.8%

U.S. Treasury bills 3.8%


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The greater the potential reward, the greater is the risk.

Ave. Ret Std. DevSmall-company stocks 17.4% 32.9%

Large-company stocks 12.3% 20.2%

Long-term corporate bonds 6.2% 8.5%

Long-term government bonds 5.8% 9.2%

U.S. Treasury bills 3.8% 3.1%


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Average return and Standard Deviation of Past Returns

Example: Calculate the average return and standard deviation of the following returns over the period of 2002 to 2004.

year Return2002 -20.9%2003 31.6%2004 12.6%


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Arithmetic vs. Geometric Mean

Arithmetic average – return earned in an average period over multiple periods

Geometric average – average compound return per period over multiple periods

Geometric average return=[(1+R1)x(1+R2)x…x(1+RT)]1/T - 1

The geometric average will be less than the arithmetic average unless all the returns are equal


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Example: Computing Averages

What is the arithmetic and geometric average for the following returns? Year 1 5% Year 2 -3% Year 3 12% Arithmetic average = Geometric average =


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Measuring Risk and Return We need statistics to summarize the range of outcomes.

Measures of location and dispersion.

Measures of location describe the most likely outcome given a range of possible outcomes (e.g. mean)

Measures of dispersion describe some average deviation of outcomes from the most likely outcome (e.g. variance)


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Expected Returns Expected returns (Mean) are based on the

probabilities of possible outcomes in the future.

The “expected” return does not even have to be a possible return

n

iiirprE

1

)(


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Expected ReturnsExample: Suppose you have predicted the

following returns for stock C in three possible states of nature. What is the expected return? State Probability C Boom 0.3 0.15 Normal 0.5 0.10 Recession ? 0.02


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Variance and Standard Deviation

They are measures of risk. It measures how spread out the possible return is around

its mean or expectation. Variance is the average of squared deviations from

mean, weighted by the probabilities.

Standard deviation is the square root of the variance. It has the same units of measure as the return.

n

iii RERp

1

22 ))((σ


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Example: Variance and Standard Deviation

Consider the previous example. What is the variance and standard deviation of stock C? State Probability C Boom 0.3 0.15 Normal 0.5 0.10 Recession 0.2 0.02


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Portfolios A portfolio is a collection of assets.Examples: Standard & Poor’s Composite Index (The S&P 500)

500 Large-Cap (American) Corporations. Holdings are proportional to the number of shares in the issues.

Straits Times Index (STI) a market value-weighted stock market index based on the

stocks of 30 representative companies listed on the Singapore Exchange, ranked by market capitalisation. (For example, SingTel, UOB, OCBC…)

http://en.wikipedia.org/w/index.php?title=Value-weighted&action=edit&redlink=1

http://en.wikipedia.org/wiki/Stock_market_index

http://en.wikipedia.org/wiki/Singapore_Exchange


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Portfolio Expected ReturnsTwo ways to calculate a portfolio’s expected return: Method 1: Find the portfolio return in each possible

state and computing the expected value as we do with an individual security.

Method 2: Find the weighted average of the expected returns for each asset in the portfolio.

m

jjjP rEwrE

1

)()(


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Expected Portfolio Returns Example: Consider the following information: Invest

50% of your money in Asset A and 50% in Asset B. What is the expected portfolio return? Do it in two different approaches. State Pr A B Boom .4 30% -5% recession .6 -10% 25%


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Expected Portfolio ReturnsMethod 1:

(1)Calculate rp in the Boom and Recession.

(2)E(rp)=Pr(B) rp(B) + Pr(R) rp(R)

Method 2:(1)Calculate E(rA), E(rB)

(2) E(rp)=wA E(rA)+wB E(rB)


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Portfolio VarianceMethod 1:

Compute the portfolio return for each state:rP = w1r1 + w2r2 + … + wmrm

Compute the expected portfolio return Compute the portfolio variance and standard

deviation using the same formulas as for an individual asset.

Note:Method 2: use the correlation among the returns

of each asset to calculate variance.

m

jjjP rwr

1

22 )()(

m

jjjP rwr

1

)()(


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Portfolio VariancePrevious Example: Invest 50% of your money in

Asset A and 50% in Asset B State Pr A B Boom .4 30% -5% recession .6 -10% 25%

What is the portfolio variance and standard deviation?


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Diversification Portfolio diversification is a strategy designed to

reduce risk by spreading the portfolio across many investments.

Why does diversification work? Stock price changes are not perfectly correlated

Diversification is not just holding a lot of assets. If you own 50 internet stocks, you are not well diversified. However, if you own 50 stocks that span 20 different

industries, then you are diversified.


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Diversification – Example Below are standard deviations for individual stocks (84-89)

AT&T 24.2% Bristol Meyers 19.8% Capital Holdings 26.4% Digital Equipment38.4% Exxon 19.8% Ford Motor 28.7% Genentech 51.8% McDonalds 21.7% McGraw Hill29.3% Tandem Computer 50.7%Equally weighted portfolio 20.0%


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Diversification

05 10 15

Number of Securities

Port

folio

sta

ndar

d de

viat

ion


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Market Risk vs. Unique Risk Not all risks can be diversified away Diversifiable risk

Unique risk or idiosyncratic risk Stems from firm-specific factors

Un-diversifiable risk Market risk or systematic risk

Stems from economy-wide factors: changes in GDP, inflation, interest rates, etc.

Total risk = Unique risk+ Market risk


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05 10 15

Number of Securities

Port

folio

sta

ndar

d de

viat

ion

Market risk

Uniquerisk

Risk and Diversification


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The Principle of Diversification

The contribution of a security to the risk of the portfolio depends on how the security’s returns vary with the returns of other securities.

The more two stocks move together, the less risk is being wiped out by holding a portfolio.

The more two stocks move apart, the more risk is being wiped out by holding a portfolio.

The greatest reduction in risk is achieved when two stocks are perfect negative correlated. However, the perfect negative correlation do not really happen among common stocks.


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ExerciseDiversification An investor is fully invested in gold mining

stocks. Which action would do more to reduce portfolio risk: diversification into silver mining stocks or into automotive stocks? Why?


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Exercise Imagine a laboratory at IBM, late at night. One

scientist speaks to another.“ You’re right, Watson, I admit this experiment will consume all the rest of this year’s budget. I don’t know what we’ll do if it fails. But if this yttrium-magnoosium alloy superconducts, the patents will be worth millions.”

Would this be a good or bad investment for IBM?

Can’t say. But from the ultimate investors’ viewpoint this is not a risky investment. Explain Why.


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Risk / Return Principle There is a reward for bearing risk. However,

there is not a reward for bearing risk unnecessarily.

Question: Is there a reward for bearing market risk?

Is there a reward for bearing unique risk?


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Market portfolio Market portfolio

Portfolio of all assets, including stocks, bonds, options, futures, commodities, real estates, etc

Practically, we use some comprehensive stock portfolio as a substitute for market portfolio.

For example: S&P500 Market portfolio only has market risk.


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Beta – Market Risk A stock’s market risk is measured by how sensitive

the stock’s returns are to the fluctuations in returns of the market portfolio.

This sensitivity is called the stock’s β. Examples: over the five-year period from 1999

to 2003, Dell has a beta of 1.77 and Coca-cola has a beta of 0.28

Question: What is the β of the market portfolio?


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Beta – Market Risk What does the stock’s β tell us?

The change in a stock’s return on average given a 1% change in the market return

Stock’s market riskAn Example Suppose a fully diversified portfolio has a beta

of 2.0. If the standard deviation of the market is 20% per year, what is the standard deviation of the portfolio return?


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Beta - Market Risk A beta of 1 implies the asset has the same

market risk as the overall market. Stock market portfolio has a beta of 1.

A beta < 1 implies the asset has less market risk than the overall market. What is the beta of treasury bills (T-bills)?

A beta > 1 implies the asset has more market risk than the overall market


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How to Estimate a Stock’s Beta in real life?

Three Steps: 1. Observe (monthly) rates of return for the stock and

the market. 2. Regress the stock’s return on the market return.

(Linear regression) 3. The coefficient on the market return is the estimated

beta. (Beta is the slope of the fitted line. You can use the “slope” function in excel.)

An example: the beta of General Motors (GM) (based on the monthly returns from 2002 to 2006)


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How to Estimate a Stock’s Beta in Real Life? – GM Beta

GM's Beta = 1.14

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.3 -0.1 0.1 0.3

S&P 500

GM

Ret

urn


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Stock Betas

.30Heinz.H.J

.41ExxonMobil

.46Pfizer

.51Mart-Wal

.76Boeing

.90sMcDonald'

.97GE1.34Ford1.64erDellComput2.49AmazonBetaStock

Betas calculated with price data from January 2001 thru December 2004


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Portfolio Betas The beta of your portfolio will be a weighted

average of the betas of the securities in the portfolio.

For example, a portfolio with two stocks has a beta as follows: Beta of portfolio=(fraction of portfolio in 1st

stock × beta of 1st stock) + (fraction of portfolio in 2nd stock × beta of 2nd stock)


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Exercise - Risk and ReturnExample: We assume that a treasury bill of 4% (beta=0)

and a market return of 13% (beta=1.0). Calculate the beta and expected return for the following portfolios.

Portfolio Treasury Market Beta Return1 100% 0%2 80% 20%3 60% 40%4 0% 100%


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Risk and Return

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Beta

Expe

cted

Ret

urn

(%) .

Market Portfolio

What is the interception of the line? What is the slope of the line?


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Capital Asset Pricing Model (CAPM)

CAPM - Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium.

The CAPM assumes that the stock market is dominated by well-diversified investors.

fm

f

r-r=premiumrisk Market r-E(r)=assetany on premiumRisk

E(r) = rf + β ( rm - rf )


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Total versus Market Risk Consider the following information:

Standard Deviation Beta Security C 20% 1.25 Security K 30% 0.95

Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected

return according to CAPM?


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In-Class Practice Problem Example: A share of stock with a beta of 0.75 now sells

for $50. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year?


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Problem – cont. Reconsider the stock in the preceding problem.

Suppose investors actually believe the stock will sell for $52 at year-ends.

(a) Is the stock a good or bad buy?(b) What will happen?


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Security Market LineSecurity Market Line - The graphic

representation of the CAPM.

Beta

Expe

cted

Ret

urn

(%) .

Rf

Rm

Security Market Line

1.0


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Security Market LineExample: The manager of StarPerformer Mutual Fund

expects the fund to earn a rate of return of 12% this year. The beta of the fund’s portfolio is .8. The return on risk-free assets is 5% and the expected return on the market portfolio is 15%.

(a) What is the required rate of return on this mutual fund according to CAPM?

(b) Can you create a portfolio with the same beta as StarPerformer Mutual Fund, but with a higher expected rate of return?


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Security Market LineExample-cont. © Draw the SML and depict the positions of risk-free

asset, market portfolio, StarPerformer Mutual fund and your portfolio.


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How Well Does the CAPM Work in US?Avg Risk Premium 1931-1965

Portfolio Beta1.0

SML30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium


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How Well Does the CAPM Work in US?

Avg Risk Premium 1966-2002

Portfolio Beta1.0

SML

30

20

10

0

Investors

Market Portfolio

Beta vs. Average Risk Premium


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Capital Market Efficiency Why does stock prices fluctuate widely from year to

year?

A market is said to be efficient if prices adjust quickly and correctly when new information arrives, or, in other words, prices fully reflect “available information”.


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Reaction of Stock Price to New Information in Efficient and Inefficient Market

-8 -6 -4 -2 0 +2 +4 +6 +8

100

140

180

220

Price ($)

Days relativeto announcement day(Day 0)

Overreactionand correction

Delayedreaction

Efficient marketreaction

Efficient market reaction:

Delayed reaction:

Overreaction and correction:


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Fundamental Analysis and Technical Analysis

Fundamental Analysis: Research the value of stocks using NPV and other measurements of cash flow.

Technical Analysis: Forecast stock prices based on watching the fluctuations in historical prices.


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Three Forms of Market Efficiency Strong Form Efficiency

Market prices reflect all information, both public and private

Semi-Strong Form Efficiency Market prices reflect all public information SFE implies that fundamental analysis will not lead to

abnormal returns. Weak Form Efficiency

Market prices reflect all historical information. WFE Implies that technical analysis will not lead to

abnormal returns.


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Homework Assignment Problems are posted at eLearn.

Next Week Quiz 2 – week 7&9 Chapters 14, 15

fnce101-wk09

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