chapter 8 and 10 powerpoints

Question 1

two drawbacks of the Markowitz Procedure

Answer 1

Requires a huge number of estimates to fill the covariance matrix

Provides no guideline to the forecasting of the security risk premium to construct the efficient frontier of risky asset

Question 2

advantages of index models

Answer 2

simplify the estimation of the covariance matrix

Enhance the analysis of security risk premiums

Decompose risk into relevant sources of security risk called factors (like systematic risk) versus firm diversifiable risk

Are as accurate as the Markowitz algorithm

Simplify estimates to those common forces that affect most firms

Question 3

arbitrage opportunity

Answer 3

Whenever a wide set of securities is mispriced and investors can exploit this opportunity

Question 4

when has arbitrage happened

Answer 4

Whenever a wide set of securities is mispriced and investors earned a risk-free economic profit

Question 5

arbitrage

Answer 5

involves the simultaneous purchase and sale of equivalent securities in order to profit from discrepancies in their price relationship

Question 6

The basic principle of capital market theory

Answer 6

In equilibrium securities are properly priced

Question 7

why does the capital market theory not support arbitrage

Answer 7

If securities are mispriced then strong pressure on security prices will restore the equilibrium (proper equilibrium prices)

As a result, in equilibrium, capital markets satisfy the no arbitrage condition

Question 8

Arbitrage Pricing Theory or APT

Answer 8

when we want to capture countless economy wide affecting risk factors in a model that explains securities’ returns

we obtain a multifactor version of the security market line in which each factor is a separate source of risk with its own risk premium

Question 9

A single factor APT assumes

Answer 9

securities are affected by a single common risk factor

Question 10

what do index models assume

Answer 10

one risk factor, the market factor, affects all security prices

Question 11

how can we price the holding period return on a security using the single factor APT method?

the single factor model

Answer 11

ri = ERi + 𝛽𝑖 · mi + ei

ri: represents the holding period return that can be earned on the security

ERi: the expected return on the security as of the beginning of the holding period

mi: the unanticipated return achieved on the security caused by unanticipated movements (shocks) in the risk factor
ei: the unanticipated return achieved on the security caused by unanticipated movements (shocks) in the firm itself

Question 12

the single factor model: the mi and ei assumptions

Answer 12

The expected value of both mi and ei is zero because we cannot expect unanticipated events

The correlation between mi and ei is assumed to be zero: shocks to the risk factor are uncorrelated with firm specific shocks

If our risk factor is a good proxy for the whole economy (or capital market) then our risk factor is called the market factor

Question 13

in the single factor model, what is the risk when investing in security i

Answer 13

Shocks in the market (mi)

Shocks in the firm itself (ei)

Question 14

σ^2 for i in the single factor model

Answer 14

σ^2 (for i) = 𝛽^2𝑖 · σ^2m + σ^2ei

Question 15

the covariance between two securities using the single factor model

Answer 15

cov (ri, rj) = 𝛽^𝑖 · 𝛽^j · σ^2m

Question 16

the conclusion for the returns of firms with similar market exposure (betas) single factor model framework

Answer 16

should lead to the same expected return

not same realized return

Question 17

the regression equation

Answer 17

𝑅𝑖(𝑡) = 𝛼𝑖 + 𝛽𝑖𝑅𝑀(𝑡) + 𝑒𝑖(𝑡)

Ri(t): is called the dependent variable

RM(t): is called the independent variable

𝛼 and 𝑒 are called the coefficient of the regression

ei(t): is called the residual of the regression

𝑅𝑖(𝑡) with a hat above is the estimated dependent variable

Question 18

the single index model on a portfolio

Answer 18

𝑅p(𝑡) = 𝛼p + 𝛽p𝑅𝑀(𝑡) + 𝑒p(𝑡)

𝛽p = (E𝛽t) /n

𝛼p = (E𝛼t) /n

𝑒p = (E𝑒t) /n

𝜎^2𝑃 = 𝛽^2𝑃 · 𝜎^2𝑀 + 𝜎^2𝑒p

𝜎^2𝑒p = (𝜎^2𝑒_) / n

As n gets large, 𝜎^2𝑒p becomes negligible

Question 19

how do obtain the estimated dependent variable (𝑅𝑖(𝑡) with a hat above)

Answer 19

by evaluating our regression model for every observation of the independent variable

Question 20

Security Characteristic Line

Answer 20

𝑅𝑖(𝑡) = 𝛼𝑖 + 𝛽𝑖𝑅𝑀(𝑡) + 𝑒𝑖(𝑡)

Question 21

how do we estimate the Security Characteristic Line

Answer 21

1. we need to calculate the excess return of both our security “i” and the market “M”
2. we regress (on EXCEL for this course), the excess return of our security “i” on the excess market return “M”

–> The intercept of this line is 𝛼𝑖

–> The slope of this line (coefficient of RM(t) ) is our 𝛽𝑖

3. Check whether the intercept and the slope are significant
4. Check the explanatory power of our SCL for this particular security

We need to check whether the intercept and the slope are statistically significant

Question 22

how do we check whether the intercept and the slope are statistically significant in the
Security Characteristic Line

Answer 22

when we are saying that the slope and the intercept are statistically significant, it means that they are different from zero

we will rely on the t-statistics to measure the significance of our estimated alpha and beta

If the estimated t-statistics is greater than 1.96 then we can say that we are 95% confident that our estimated coefficient is different from zero

we are satisfied with a 95% confidence level

Question 23

How to obtain the t-statistics for our estimated slope (beta) and intercept
(alpha):

Answer 23

𝑡𝛽^ = (𝛽^ - 0) / Standard error 𝛽^

The standard error measures the level of imprecision in estimating our coefficient
(alpha, or beta

the the higher the standard error relative to the estimated coefficient, the more the likelihood that our result would be less than 1.96, the less we are confident that our estimated coefficient is statistically different from zero

Question 24

R-square

Answer 24

measures how much variation in the dependent variable (the stock in our case) is explained by independent variable (the market)

measured as the ratio of the total variation in the estimated dependent variable to the total variation in the actual observed dependent variable

Question 25

Adjusted-R-square

Answer 25

similar to R-Square but it adjusts R-Square for the fact that we are conducting our test on a subset of the data (sample) and not the whole entire data available

considered more reliable than R-Square in small sample regression estimation

Question 26

What are the crucial assumptions needed to build a M-V frontier relying on a single index model?

Answer 26

We have properly estimated the betas of our securities

We have properly estimated the next period market premium (RM –RF)

Question 27

Alpha Transpose

Answer 27

the process of building an investment strategy that has an expected return equal to alpha (like 𝛼P for having the 𝛼 of portfolio P) without being exposed to the market risk (systematic market risk)

The process of searching for alphas is one major role of hedge funds

we long portfolio P with a positive alpha, and short portfolio Q with no alpha (properly priced)

–> 𝐸(𝑟𝐶) = 𝛼𝑃 and 𝑟𝐶 = 𝛼𝑃 + 𝑒P

Question 28

when using the Alpha Transpose, if f portfolio “P” is well diversified, then why should eP be small?

what happens to portfolio Q

Answer 28

because it represents unsystematic risk

Portfolio “Q” should be well priced (alphaQ = 0) and having only market exposure, BetaQ

–> “Q” should also be well diversified

Question 29

how to create portfolio “Q”+

Alpha Transpose

Answer 29

We can create portfolio “Q” with BetaQ by investing in an Index Fund and RF

If BetaP = 1.5 then we should form a portfolio Q with BetaQ
= 1.5

We can invest 150% of the money we have in a market index fund and borrow 50% of our money from RF

–> The resulting portfolio has a beta = 1.5

Question 30

two factor index model

Answer 30

can be estimated using the same techniques used for the single factor index model

we rely on regression technique to evaluate our multifactor model

Question 31

Single vs. Multi- Factor Model

Answer 31

In the single index model, we assume that there is one systematic risk factor that is affecting our economy

–> All risk factors in the economy can be aggregated in one risk-factor (the market factor)

–> we are assuming that all
our securities have the same exposure (Beta) to all the risk factors forming our market factor

In multifactor models, we managed to find more than one systematic risk factor that is affecting our stocks’ returns

–> In multifactor models, we give our securities the flexibility to have different
sensitivities (betas) to every risk factors

–> it may be justified to have negative factor risk premium

Question 32

why may it be justified to have negative factor risk premium in the multi factor model?

Answer 32

if the exposure to this risk factor is considered a positive thing (good news) by investors and may accept a lower return for it

Question 33

who developed the Arbitrage Pricing Theory (APT) model?

Answer 33

Stephen Ross

Question 34

Propositions that lead to the derivation of APT models

Answer 34

Whenever an arbitrage opportunity exists, investors will invest a big amount of money in it (high volume) independent of their Risk Aversion

–> This implies that Arbitrage Opportunities, once found, will not last for long periods

There are sufficient securities to drive away idiosyncratic risk

Securities can be explained in a factor model

No market imperfections: no taxes, no transaction costs and no restrictions on short sales

whenever an Arbitrage Opportunity exists, investors, regardless of their risk aversion, will try to take infinite positions in them and this will quickly push prices up or down until this opportunity disappears

–> markets should satisfy
the no-arbitrage opportunities

Question 35

The Law of One Price

Answer 35

states that if two assets are equivalent in all economically relevant respects, then they should have the same market price

Question 36

what happens when the Law of One Price is not respected

Answer 36

an Arbitrage Opportunity exists and investors will buy the cheap asset and sell the expensive one until the law of one price is established

Question 37

the difference between the critical properties between APT and CAPM/ICAPM

Answer 37

in APT, whenever an Arbitrage Opportunity exists, investors, regardless of their risk aversion, will try to take infinite positions in them and this will quickly push prices up or down until this opportunity disappears

–> markets should satisfy
the no-arbitrage opportunities

–> prices will adjust quickly to their proper prices.

in CAPM/ICAPM, whenever there is a mispricing in securities, then investors, each according to his/her risk aversion, will adjust his/her own portfolio in order to include more of this mispriced security

–> This will push prices to gradually adjust to their proper values

Question 38

Uncertainty in asset returns has which two sources?

Answer 38

A common or systematic or macroeconomic factor

A firm-specific or idiosyncratic or microeconomic factor

–> In well diversified portfolios, the firm-specific factor is reduced to zero

Question 39

which risk is the only one that requires a risk premium?

Answer 39

market risk

Question 40

the APT and arbitrage opportunity implies that we bear zero risk, this basically means that firm specific risk is null even if we solely rely on on security only

does this mean that its better than diversification?

Answer 40

naaah booooooy

we cannot get rid of firm specific risk by APT strategy when have a single security

this means we will apply it to well diversified portfolios

–> If a portfolio is mispriced, then arbitrage opportunity exists and an arbitrage strategy can take place if economically profitable

–> If a one or very few securities are mispriced then the effect on well diversified portfolios is small, and an Arbitrage Opportunity will not be economically profitable

–> For this reason we conclude that in an APT world, we can face few securities that may violate the arbitrage pricing theory but we cannot find a lot of these mispriced security

Question 41

APT vs. CAPM

Answer 41

1. The APT stresses the fact that investors should require premium for non-diversifiable risk and nothing for diversifiable ones (that is why, we tolerate the existence of few securities that may violate the APT models)

The CAPM model requires that all securities follow the CAPM

2. The APT yields an SML where the factors can be any type of risk factors that investors deem important

CAPM is derived based on the unobserved market factor and what possible other factors may affect our investment opportunity set (ICAPM)

3. CAPM is based on the mean-variance efficiency
4. CAPM specifies that the relevant factor is the market factor

–> ICAPM adds factors affecting our opportunity set to the market factor

APT does not specify what are the factors! It does not provide any economic justification for the chosen factors! Consequently it leaves the door open for the selection and choice of the factors (that may be deemed to affect securities returns)!

Question 42

Fama and French three factor model

Answer 42

big ass formula

SMB (small minus big): the return of a portfolio of small stocks in excess of the return of a portfolio of large stocks

HML (high minus low): the return of a portfolio of stocks with a high book-to-market ratio in excess of the return of a portfolio of stocks with a low book-to-market ratio