978-1259709685 Chapter 11 Lecture Note Part 2

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Slide 11.15 –

Slide 11.16 Portfolios

11.4. The Efficient Set for Two Assets

With two assets, you can form portfolios composed of different

percentages of each asset.

The possible portfolios are referred to as the opportunity set, and

the set of portfolios with the highest return for a given level of risk

is referred to as the efficient frontier.

Slide 11.17 –

Slide 11.18 The Efficient Set for Two Assets

The shape of the set is determined by the correlation between the

two assets.

Slide 11.19 Portfolios with Various Correlations

11.5. The Efficient Set for Many Securities

With more than two assets, the outcome is essentially the same,

except the opportunity set is “filled in” with many more possible

portfolios.

.A Variance and Standard Deviation in a Portfolio of Many Assets

The variance can be calculated using the extended form of the

equation for the two asset portfolio. Specifically, the variance of

each asset’s returns would be included, as well as the covariance

between each possible pair of assets, all adjusted by their relative

proportions in the portfolio.

Slide 11.20 –

Slide 11.21 The Efficient Set for Many Securities

11.6. Diversification

.A The Anticipated and Unanticipated Components of News

Slide 11.22 –

Slide 11.23 Announcements, Surprises, and Expected Return

Any announcement, such as an earnings or dividend

announcement, will have a part that is expected and a part that is

unexpected (called the “innovation” or “surprise”). Security prices

react to new information, i.e., the surprise.

Current security prices already reflect the expected part of an

announcement, and there will not be any reaction to this part.

Ri=



+ U = Expected return + Unexpected return

Therefore, risk depends only on the surprise. In a well-diversified

portfolio, part of the risk of an individual security can be

diversified away and only systematic risk is relevant.

.B Risk: Systematic and Unsystematic

Slide 11.24 Risk: Systematic and Unsystematic

Systematic (or market) risk is that which affects a large number of assets,

although at varying degrees. It is sometimes called market risk.

Unsystematic (or diversifiable) risk is that which affects a small number of

assets (or one). It is sometimes called unique or asset-specific risk.

Changes in GDP, interest rates and inflation are examples of systematic risk.

Strikes, accidents, and takeovers are examples of unsystematic

risk.

Lecture Tip: You can expand the discussion of the difference between

systematic and unsystematic risk by using the example of a strike

by employees. Students will generally agree that this is unique or

unsystematic risk for one company. However, what if the UAW

stages the strike against the entire auto industry. Will this action

impact other industries or the entire economy? If the answer to

this question is yes, then this becomes a systematic risk factor. The

important point is that it is not the event that determines whether it

is systematic or unsystematic risk; it is the impact of the event.

.C The Essence of Diversification

When securities are combined into portfolios, their unique or unsystematic

risks tend to cancel out, leaving only the variability that affects all

securities to some degree. Thus, diversifiable risk is synonymous

with unsystematic risk. Large, diversified portfolios have little or

no unsystematic risk.

Systematic risk cannot be eliminated by diversification since it

represents the variability due to influences that affect all securities

to some degree. Therefore, systematic risk and nondiversifiable

risk are the same.

Thus,

Ri=



+ U = =



+ m + 

where m is the systematic risk and  is the unsystematic (unique)

risk

Portfolio variability can be quite different from the variability of individual

securities. For example, a typical single stock on the NYSE has a

standard deviation of annual returns around 50%, while the typical

large portfolio of NYSE stocks has a standard deviation of around

20%.

Lecture Note: Common sense suggests that, to the extent that national

economies are less than perfectly positively correlated, there may

be diversification benefits to be had by investing in foreign

securities. Empirical research bears this notion out. For example,

Solnik (Financial Analysts Journal, 1974) and Harvey (Journal of

Finance, 1991) find that the returns on U.S. stocks are

significantly less than perfectly positively correlated with returns

on stocks in other industrialized countries. As a result, the

potential for risk reduction is greater when you include

international stocks in your portfolio. However, other findings

suggest that these correlations increase during bear markets (take

2008 and 2009 for example).

Slide 11.27 Total Risk

The principle – The reward for bearing risk depends only on the systematic

risk of the investment.

The implication – The expected return on an asset depends only on that asset’s

systematic risk.

A corollary – No matter how much total risk an asset has, its expected return

depends only on its systematic risk.

11.7. Riskless Borrowing and Lending

The risk-free asset plots on the y-axis (zero risk).

Slide 11.28 Optimal Portfolio with a Risk-Free Asset

.A The Optimal Portfolio

Now, investors can form portfolios of the risk free asset with any

of the portfolios from the opportunity set. Choose to combine the

risk free asset with the portfolio that gives the highest sloped

capital market line.

Slide 11.29 –

Slide 11.30 Riskless Borrowing and Lending

11.8. Market Equilibrium

.A Definition of the Market Equilibrium Portfolio

If all investors face the same set of assets, then all will choose the

same risky portfolio since it provides the highest possible returns

for every level of risk.

Differences will occur in what percentage of the final portfolio is

composed of the risky fund and what percentage is composed of

the risk free asset.

Slide 11.31 –

Slide 11.32 Market Equilibrium

.B Definition of Risk When Investors Hold the Market Portfolio

A riskless asset has a beta of 0. When a risky asset with >0 is combined with

a riskless asset, the resulting expected return and beta are weighted

sums. By varying the amount invested in each asset, we can get an

idea of the relation between portfolio expected returns and betas.

All of the risk-return combinations lie on a straight line. Remind

the students that the equation for a line is:

y = mx + b

where: y = security return

x = market return

m = slope (beta)

b = y-intercept

Introducing this equation now prepares the students for the SML and the

CAPM.

Slide 11.33 Risk When Holding the Market Portfolio

Lecture Tip: It is possible to have greater than 100% invested in an asset.

This means that the investor has borrowed money on margin

(technically at the risk-free rate) and used that money to purchase

additional shares of asset A. This can increase the potential

returns, but it also increases the risk. The maximum amount that

an investor can borrow on margin is 50% of the total value of the

position. If the value of the portfolio drops such that the loan

amount is greater than 50% of the value of the portfolio (or some

other amount established by the broker), then the investor will

receive a margin call and will have to add additional cash to the

brokerage account. Also, students may have heard about margin

accounts in relation to futures contracts – buying stock on margin

and posting margin for futures trades are different types of trades

and have different mechanics involved with how margin calls are

issued.

.C The Formula for Beta

A beta coefficient measures the amount of systematic risk present

in a particular risky asset relative to the average risky asset. (The

market portfolio will serve as an appropriate proxy for the average

risky asset.) Since risk is a function of the changes in, or

“movement of,” an asset’s price, systematic risk must be

attributable to the movement in a risky asset’s price relative to the

movement in the price of the average risky asset (or the market

portfolio).

Given the above, we should not be surprised to find that the beta

coefficient is nothing more than a statistical measure of the

relationship between the returns on asset j and the market portfolio.

This relationship is most often quantified via the use of simple

linear regression. Specifically, we estimate the following model:

Rjt = j + jRMt + j

Where:Rjt = the return on stock j in period t,

RMt = the return on the market portfolio in period t,

j, j = the intercept and the slope coefficients, respectively,

and

j = the random error term.

The model above is called the “market model” and is usually

estimated using daily, weekly, or monthly historical returns.

(Although there are no universally accepted guidelines, most

people use approximately 250 daily returns, 104 weekly returns, or

60 monthly returns to estimate the model.) The estimated 

coefficient in the model above is the beta referred to in the chapter.

It is also possible to show that, given certain assumptions about the

distribution of returns, the beta coefficient is equal to the

correlation between returns on stock j and the market portfolio,

times the ratio of the standard deviation of the returns on stock j to

the standard deviation of the market portfolio. In equation form,

j = j,M(j/ M)

j = Cov (j,m) / 2M

Notice that the beta equation also suggests that beta has the

following properties.

1. The beta of the market portfolio, M, must equal one.

2. The beta of the risk-free asset must equal zero.

Finally, it should be noted that most people need not bother to

calculate betas for stocks they are interested in. Beta coefficients

are computed by several firms (for example, Merrill Lynch,

Standard and Poor’s Corporation, Value Line, and Moody’s) and

appear in various publications, as well as at various sites on the

Internet.

Slide 11.34 Estimating β with Regression

Slide 11.35 The Formula for Beta

.D A Test

11.9. Relationship between Risk and Expected Return (CAPM)

.A Expected Return on Market

The expected return is equal to the risk free rate plus a market risk

premium.

Slide 11.36 Relationship between Risk and Expected Return (CAPM)

.B Expected Return on Individual Security

For an individual security, the premium depends on the level of

systematic risk, i.e., beta.

The line that gives the expected return/systematic risk combinations of assets

in a well functioning, active financial market is called the security

market line.

Lecture Tip: Although the realized market risk premium has on average been

approximately 8 %, the historical average should not be confused

with the anticipated risk premium for any particular future period.

There is abundant evidence that the realized market return has

varied greatly over time. The historical average value should be

treated accordingly. On the other hand, there is currently no

universally accepted means of coming up with a good ex ante

estimate of the market risk premium, so the historical average

might be as good a guess as any. In the late 1990’s, there was

evidence that the risk premium had been shrinking. In fact, Alan

Greenspan was concerned with the reduction in the risk premium

because he was afraid that investors had lost sight of how risky

stocks actually are. Investors had a wake-up call in late 2000 and

2001, then again in late 2008 and 2009.

Market Portfolios: Consider a portfolio of all the assets in the market and call

it the market portfolio. This portfolio, by definition, has “average”

systematic risk with a beta of 1. Since all assets must lie on the

SML when appropriately priced, the market portfolio must also lie

on the SML. Let the expected return on the

market portfolio = E(RM). Then, the slope of the SML = reward-to-risk ratio =

[E(RM) – Rf] / M = [E(RM) – Rf] / 1 = E(RM) – Rf

The Capital Asset Pricing Model: Go back to the discussion of the equation of

a line:

E(Rj) = Rf + slope(j)

E(Rj) = Rf + (E(RM) – Rf)(j)

The CAPM states that the expected return for an asset depends on:

-The time value of money, as measured by Rf

-The reward per unit risk, as measured by E(RM) – Rf

-The asset’s systematic risk, as measured by 

Slide 11.37 Expected Return on a Security

Slide 11.38 –

Slide 11.39 Relationship Between Risk & Return

Slide 11.40 Quick Quiz

To access Appendix 11A (Is Beta Dead?), go to www.mhhe.com/rwj.