CH 13- Textbook

Question 1

to a diversified investor what sort of risks matter

Answer 1

systematic risk

Question 1

what are the two types of risks associated with individual assets

Answer 1

systematic risk: affects all asssets in economy
unsystematic risk: affects small number of assets

Question 2

what is the SML high level

Answer 2

realtionship between risk and return; it is a representation of market equilbrium

Question 3

what are the states of the eocnomy

Answer 3

boom, recession, etc.

Question 4

how do you calcualte expected reurn from a stock?

Answer 4

Let the stock be Stock C

E(Rc)= (prob of boom)( stock c returns in boom)+(prob of recession)(stock c return in recession)

or E(R) = sumj Rj x Pj (R=Value of jth outcome, P= prob of jth outcome)

its the sum of the possible returns
multiplied by their probabilities

Question 5

How do you calculate regular riskpremium?

how do you calc projected/ expected risk preiium?

Answer 5

risky investment- risk free investment

expected return on a risky investment- certain return on a risk free investment

Question 6

How to calculate the vriance

Answer 6

1. get expected return
2. return-expected return
3. square #2
4. ultiply by Probability

and then if you want SD then sqrt #4

Var= Sumj[ Rj - E(R)]^2 x Pj
SD= sqrt(var)

Question 7

how to do analysis with sd, var and mean?

Answer 7

1. which has the higher expected return?
2. does this also have higher volatility? (remember you can cover 2/3 probability by adding / subtracitng one standard deviation)

Question 8

what is a portfolio?

Answer 8

owning several stocks/bonds/assets

Question 9

Portfolio weights

Answer 9

the amount of the total portfolio value that is invested in each portfolio asset

if you have $50 in asset A and $150 in asset B, portfolio is worht $200, and A has 25% weight and B has 75%

PORTFOLIO WEIGHT MUST ADD UP TO 1

Question 10

How to calcualte portfolio returns in each state of economy

hwo to calcualte expected return of the portfolio from this?

Answer 10

FOR BOOM= (portfolio weight x return of asset A)+ (portfolio weight x return of Asset B)

FOR RECESSION= (portfolio weight x return of asset A)+ (portfolio weight x return of Asset B)

E(Rp)= Sum FOR BOOM + FOR RECESSION

Question 11

IS Standard deviaiton of a portfolio the sum of standard deviation of all individual assets?

Answer 11

NO! diversifiying portoflio reduces risk!!!

this is because of correlation

Question 12

positive correlation
negative correlation
0 correlation

Answer 12

assets A and b move together

aseets a and b move in opp directions

unrelated

Question 13

what does it mean when portfolios are dominated b the min var portfolio

Answer 13

like a curve on the grpah, there is apoint with min variance and higher expected retunr

though you could invest 100% in these portfolios it wouldr educe the expected return and require greater variance so no one would od it

Question 14

When the returns on the two assets are perfectly correlated, the portfolio standard
deviation is simply the weighted average of the individual standard deviations. In this
special case:
Page 481
With perfect correlation, all possible portfolios lie on a straight line between U and L in
expected return/standard deviation space as shown in Figure 13.4. In this polar case,
there is no benefit from diversification. But, as soon as correlation is less than perfectly
positive (CORR , < +1.0), diversification reduces risk.
As long as CORR is less than +1.0, the standard deviation of a portfolio of two securities is
less than the weighted average of the standard deviations of the individual securities.
Figure 13.4 shows this important result by graphing all possible portfolios of U and L
for the four cases for CORR given in Table 13.7. The portfolios marked 1, 2, 3, and 4
in Figure 13.4 all have an expected return of 20.91%, as calculated in Table 13.7.
*
COVL,U = CORRL,U × σL × σU
TABLE 13.7
Portfolio standard deviation and correlation
Stock L x = 2/11 σ = 45% E(R ) = 25%
Stock U x = 9/11 σ = 10% E(R ) = 20%
E(R ) = (2/11) × 25% + 9/11 × 20% = 20.91%
CORR Portfolio Standard Deviation of Portfolio σ
1. −1.0 0.0000%
2. 0.0 11.5708%
3. +0.7 15.0865%
4. +1.0 16.3636%
L L L
U U U
P
L,U P
(
2
11
× 45%) + (
9
11
× 10%) = 16. 3636%
L U
L,U
Their standard deviations also come from Table 13.7. The other points on the respective
lines or curves are derived by varying the portfolio weights for each value of CORR .
Each line or curve represents all the possible portfolios of U and L for a given correlation.
Each is called an opportunity set or feasible set. The lowest opportunity set representing
CORR = 1.0 always has the largest standard deviation for any return level. Once again,
this shows how diversification reduces risk as long as correlation is less than perfectly
positive.

Question 15

While higher correlations reduce its advantages, doubts about
diversification were overstated for two reasons. First, although correlations undoubtedly increased during
the crisis, they later returned to more normal levels. Second, even with relatively high positive correlation
between assets, diversification still reduces risk as long as the correlation coefficient is less than 1.0
(perfect positive correlation).

Question 16

What is total return?

Answer 16

expected return + unexpected return

R= E(R) +U

Question 17

Announcement = expected part + surpruse

Answer 17

expected part= what we use to form expectation (E(r)

SURPRISE = UNEXPECTED PART

market generally already discounts for the expected part

Question 18

Systematic risk:

Answer 18

affects lots of assets, market-wide, market risks

Question 19

unsystematic risk

Answer 19

surprise risk, affects a single asset or a small group, unique/asset speciifc,

Question 20

break down the return using systematic and unsytsematic risk

Answer 20

Return= exp return + systematic portion + unsystematic portion

R= E(R) + SYSTEMATIC + UNSYSTEMATIC

Systematic = m
USYSTEMATIC= e

Question 21

the more stocks you have in your pprootfolio

Answer 21

the less risk you face in terms of standard deviation

Question 22

Principle of diversificaiton

Answer 22

spreading an investment across many assetss elimiates some of the risk!

Question 23

diversifiabel risk is

Answer 23

the part hta t can be elimiated by diveristiofication

Question 24

Can a minimum level of risk be elimated?

Answer 24

not possibel simply by diversifying, min level= non diversificable risk

Question 25

DIVERSIFICATION REDUCES RISK BUT ONLY TO A CERTAIN POINT

Question 26

Unsystematic risk is essentially eliminated by diversification, so a
relatively large portfolio has almost no unsystematic risk. In fact, the terms diversifiable risk and unsystematic
risk are often used interchangeably.

Answer 26

basically if you hold a large enough portfolio you do not face unsystematic risk since they cancel out

Question 27

can you elimiate systematic risk by diversificaton

Answer 27

NO! SYSTEMATIC RISK= NON DIVERSIFIABLE

Question 28

Total risk= systematic risk + usnystematic risk

Answer 28

Systematic risk is also called nondiversifiable risk or market risk. Unsystematic risk is also called
diversifiable risk, unique risk, or asset-specific risk

Question 29

for a well diversified portoofio what is the type of risk you have

Answer 29

mostly all systematic risk

Question 30

systematic risk principle

MAIN TEACHING

Answer 30

reward for bearing risk depends only on the systematic risk of an investent

(since you can eliminate all unsystematic risk by diversifying, you dont get rewardsed for this risk)

the expected return on an
asset depends only on that asset’s systematic risk

Question 31

WHAT DOES BETA TELL US

Answer 31

how much systematic risk a particular asset has relative to an average asset representing the market portfolio

an avg asset has a beta of 1.0 itself
an asset with beta 0.5 has half as much systematic risk as an avg asset

Question 32

is high or low beta better

Answer 32

LOW!! high=high volatilyty

Question 33

if you have two assets, one has high sd and low beta and other has high beta low sd what do you know?

Answer 33

low beta one has low systematic risk, so it has greater unsystematic irsk

high beta= high systematic risk so higher premiums, low unsystematic risk

Question 34

how to calculate portfolio beta

Answer 34

just like expected return

Port Beta= (weight invested in stock A x stock A beta) + (Weight invested in stock B x stock B beta)

multiply each asset’s beta by its
portfolio weight and then add the results to get the portfolio’s beta

Question 35

what does risk free rate mean
-what does it imply for beta?

Answer 35

no systematic risk

beta=0

Question 36

for assets that are risk free, they do not have an expected return they have a

Answer 36

risk free rate (no risk so this is the guaranteed return)

Question 37

lets say you have portfolio w ASSET A and a risk free asset

you invest 25% into asset a and 75% into b

what is your expected return?
what is your portfolio beta?

Answer 37

Exp return= (inv into asset a x exp return asset a) + (1- inv into A x risk free rate)

Beta Portfolio= (inv into asset a x Beta A)+(1- inv into A x 0)

==X 0 BECAUSE THERE IS NO BETA ON RISK FREE ASSETS
==Why do you do 1- inv into A and not just inv into B ? because often you can borrow money at risk free rate and then invest it backk

Question 38

If you plot portfolioe xpected return (E(rp)) along y axis and Portoflio beta( Bp) along x axis

describe the graph

Answer 38

the y int is the risk free rate

the line itself is the combinations of different %’s being invested into each asset (SECURITY MARKET LINE)

slope is the reward to risk ratio
(E(R(A)) - Rf)/Beta A

The reard to risk ratio tells us the premium per uunit of systematic risk on Asset A

Question 39

The reard to risk ratio tells us the premium per uunit of systematic risk on Asset A

Answer 39

The reard to risk ratio tells us the premium per uunit of systematic risk on Asset A

Question 40

1How can we compare if asset investments are better given that we know the reward to risk ratio?

Answer 40

PLOT THE LINES ON GRAPH, the higher reward risk ratio (slope is steeper) means its a bettter investment!!!!

Question 40

how to know if stocks are correctly priced?

Answer 40

1. plug in values to CAPM
2. COMPARE to given expected returns (is it higher or lower)?

or use reward to risk ratio
-> calculate it
-> compare to market risk premium! is it too high or too low

Question 41

What happens if for Asset A the reward to risk is higher than B?

Answer 41

PRICE AND RETURN MOVE IN OPP DIRECTIONS, so Price of A would rise since its better and return would fall; this would create vice versa effect

UNTIL the reard to risk ratio for both is equal (this is what happens in an active market, the reward risk ration on all securtiies is equal)

if one asset has twice as much
systematic risk as another asset, its risk premium is simply twice as large; meaning that the return is lower

Question 42

visualize market equilbirum of assets returns and asset prices on return and beta chart

Answer 42

If you have an asset above the market equilbrium (meaning that it has higher return) the price will rise until the return falls to the equilbrium, beocming one with the main line again

Question 43

An asset is said to be overvalued if its expected return is too low given its risk.

Question 44

how to determine if an assset is overvalued or undervaluesd?

Answer 44

1. compute reward to risk ratio for al l idnividual assets
2. the higher ratio will be what investors want to go for, and the price of the other would drop, the lower ratios return would rise until market equilbrium

so if prices are going to fall then it is overvalued

Question 45

How to calcualte beta

Answer 45

Draw a line relating expected return to diff returns in the market, it is the characteristic line of security, and slope= stocks beta

Question 46

low R^2 means that most of the risk of a firm is unsystematic

Question 47

What is SML
- equation

Answer 47

(E(Rm)-Rf/BetaM), WHERE E(Rm)= expected return on the market portfolio [portfolio of all the assets in the market], and the beta is 1

SO

E(Rm)-Rf = SML Slope

THIS IS CALLED THE MARKET RISK PREMIUM

Question 48

Capital asset pricing model CAPM

if you are given a beta of a stock, expected return on the market, and risk free rate, how to calc expceted retunron on this stock?

FORMULA CAVEAT!!

Answer 48

E(Ri) = Rf + [ERm -Rf] x Bi

Expected Return on Stock i= Risk free rate +(Expected return on market - risk free rate) x Stock Beta

CAVEAT!! IF YOU ARE GIVEN MARKET RISK PREMIUM- > that is equal to (ERm-Rf)

ExP RETURN ON asset i is risk free rate + exp return on market portfolio = risk free rate x beta of i

Question 49

WHAT DOES CAPM SHOW

Answer 49

exp return on an asset depends on 3 things:

1. The pure time value of money. As measured by the risk-free rate, R , this is the reward for merely waiting
   for your money, without taking any risk.
   f
2. The reward for bearing systematic risk. As measured by the market risk premium [E(R ) − R ], this
   component is the reward the market offers for bearing an average amount of systematic risk in addition to
   waiting.
   M f
3. The amount of systematic risk. As measured by β, this is the amount of systematic risk present in a
   particular asset, relative to an average asset.

Question 50

arbitrage pricing theory APT

Answer 50

handles multiple factors CAPM ignore,

The three factors F , F , and F represent systematic risk because these factors affect many securities.
The term ε is considered unsystematic risk because it is unique to each individual security.
Under this multifactor APT, we can generalize from three to K factors to express the relationship between
risk and return as:

beta with respect to the second factor, and so on. For example, if the first factor is inflation, β is the
security’s inflation beta. The term E(R ) is the expected return on a security (or portfolio) whose beta with
respect to the first factor is one and whose beta with respect to all other factors is zero. Because the market
compensates for risk, E[(R ) − R )] is positive in the normal case. (An analogous interpretation can be
given to E(R ), E(R ), and so on.)
The equation states that the security’s expected return is related to its factor betas. The argument is that each
factor represents risk that cannot be diversified away. The higher a security’s beta is with regard to a
particular factor, the higher the risk that security bears. In a rational world, the expected return on the
security should compensate for this risk. The preceding equation states that the expected return is a
summation of the risk-free rate plus the compensation for each type of risk the security bears.
As an example, consider a Canadian study where the factors were:
Total return = Expected return + Unexpected return
R = E(R) + U
R = E(R) + βIFI + βGNPFGNP + βrFr + ε
I GNP r
E(R) = RF + E[(R1) − RF]β1 + E[(R2) − RF]β2 + E[(R3) − RF]β3 + … + E[(RK) − RF]βK
1 2
1
1
1 f
12
2 3
1. The rate of growth in industrial production (INDUS).
2. The changes in the slope of the term structure of interest rates (the difference between the yield on longterm and short-term Canada bonds) (TERMS).

Using the period 1970–84, the empirical results of the study indicated that expected monthly returns on a
sample of 100 TSX stocks could be described as a function of the risk premiums associated with these five
factors.
Because many factors appear on the right side of the APT equation, the APT formulation explained
expected returns in this Canadian sample more accurately than did the CAPM. However, as we mentioned
earlier, one cannot easily determine which are the appropriate factors. The factors in this study were
included for reasons of both common sense and convenience. They were not derived from theory, and the
choice of factors varies from study to study. A more recent Canadian study, for example, includes changes
in a U.S. stock index and in exchange rates as factors.
The CAPM and the APT by no means exhaust the models and techniques used in practice to measure the
expected return on risky assets. Both the CAPM and the APT are risk based. They each measure the risk of a
security by its beta(s) on some systematic factor(s), and they each argue that the expected excess return
must be proportional to the beta(s). As we have seen, this is intuitively appealing and has a strong basis in
theory, but there are alternative approaches.
One popular alternative is a multifactor empirical model developed by Fama and French and based less on a
theory of how financial markets work and more on simply looking for regularities and relations in the past
history of market data. In such an approach, the researcher specifies some parameters or attributes
associated with the securities in question and then examines the data directly for a relation between these
attributes and expected returns. Fama and French examine whether the expected return on a firm is related to
its size and market to book ratio in addition to its beta. Is it true that small firms have higher average
returns than large firms? Do growth companies with high market to book ratios have higher average returns
than value companies with low market to book ratios? A well-known extension of the Fama-French
model includes a fourth, momentum, factor measured by last year’s stock return.
Although multifactor models are commonly used in investment performance analysis, they have not become
standard practice in estimating the cost of capital. Surveys of corporate executives show that only one in
three employ multifactor models for this purpose while over 70% rely on the CAPM.
Concept Questions
3

Question 51

The best thing is when we find that two stocks have a negative correlation; then we can start to
make a portfolio out of them where one goes up and another goes down

Answer 51

diversificaiton can reduce our risk as long as our stocks arent perfectly corealted
p<1

Question 52

Does expected return have to be a possible return?

Answer 52

NO! it can be an imagined rturn

Question 53

what is the feasible set

Answer 53

the opportuntiy set/ or the curve that comprises all of the possible portoflio combos

Question 54

what is the efficient st

Answer 54

the protion of the feasible set that only includes efficient protoflio (max return for x amount of risk or min risk for x amount of return)\

That’s what efficient means: no other portfolio ties on risk and wins on return,
or ties on return and wins on risk, or wins on both

Question 55

WHAT IS THE MVP on the graph

Answer 55

minimum variance portfolio the posible pportfolio with the least amount of risk

NOT SYAING ITS THE BEST, BUT IF YOU WANT TO AVOID RISK THIS IS THE ONE TO GO WITH

Question 56

OVERTIME WHAT is the averagge of the unexpected component

Answer 56

it is zero

Question 57

Efficient markets are a result of investors trading
on the unexpected portion of announcements.

Answer 57

they also involve random price changes bc we cant predict surpirses

Question 58

what is the slope of the SML

Answer 58

reward to risk ratio

E(Rm)-(Rf)

Question 59

What is the CAPM

Answer 59

capital asset pricing model

E(ra) = Rf + BetaA(E(Rm)-Rf)

relates risk and return

tells us what return woudld make us happy iwth a fiven stock

Question 60

capm, if we have a specialc ase when portfolio is equally weighted betwene risk free asset and a stock

Answer 60

sum the returns of each asseet and divide by number of assets

Question 61

If you are given an assets expected return, beta and the risk free rate, told to make a table for portfolios of asset and a risk free asset, how do you calc portfolio expected return and protfolio beta?

Answer 61

1. We know beta of risk free asset is 0, and weight of a risk free asset (with 2 assets in the porftolio only) is 1- weight of stock
2. Solve for Beta:
   Beta = Weight of stock(Beta of stock) + (1-Weight of stock)(Beta of risk free)

-> note that the second term is 0, now you have to solve using the CAPM

3. Use CAPM to solve for the Market Risk Premium=
   E(Rm) = Rf +(ERm - Rf)(Beta)

**MRP= (Erm-Rf)

4. Now you have created an equation that is a slope, with the x being Beta (plug in the various weights to caluclate the beta), and then fill the chart

Question 62

if given two stocks and asked to give a risk free rate where the stocks are correctly priced what do you do

Answer 62

1, set each stocks reward to risk ratio = to each other
2. cross mulitply and solve for the risk free rate