Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
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=
R
+ 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=
R
+ U = =
R
+ 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.
