Final Exam Fina 4321

- Buying on margin: Margin Call may occur when price depreciates You make money if the stock price increases -Short sale: Margin Call may occur when price appreciates You make money if the stock price decreases

Difference Between Short Sale and Buying on Margin

High Book-to-Market stocks (aka value stocks) have much higher average returns than Low Book-to-Market stocks (aka growth stocks).

DO value firms or growth firms have higher returns?

nominal rate

The amount of money generated by an investment before expenses such as taxes, investment fees and inflation are factored in.

Real rate

The annual percentage return realized on an investment, which is adjusted for changes in prices due to inflation or other external effects.

False

True or False:If the correlation between Yt and Xt is equal to 1, then the coefficient β in the above regression must be 1

risk-neutral

- If A=0, we say that the investor is - investor is someone that is indifferent between the risk-free and the risky project if the risk-premium on the risky project is zero

1. The short sale proceeds must be kept with the broker (to serve as collateral) 2. An Initial Margin Requirement (IMR) is specified: This means that in addition to the short sale proceeds, the investor must put a percentage of the amount of the short sale proceeds in the account (50%) from its own funds to serve as collateral. Makes sense to you? 3. The account must also satisfy a Maintenance Margin Requirement (MMR) i.e. the value of equity relative to the loan cannot decrease below a certain level (the MMR)

3 procedures to protect broker from credit risk:

1) The expected return of a portfolio is a weighted average of the expected returns of the securities in the portfolio 2) sum of weights = 1 3) variance is = the formula

3 rules of portfolios

1) get inputs 2) obtain optimal cal 3) obtain optimal global portfolio

3 steps of investments

1) obtain one the key inputs (expected returns) 2) find under priced and overpriced securities in the market 3) benchmark for portfolio performance evaluation

3 things one should do with capm

Efficient portfolio

: is a portfolio that has the highest possible expected return for each level of risk. Only portfolios on the frontier and above the MVEP are efficient.

portfolios sorted on book to market

: the CAPM was unable to explain the average returns of ___________

Fill-or-kill (FOK) orders

A type of time-in-force designation used in securities trading that instructs a brokerage to execute a transaction immediately and completely or not at all.

The two fund separation theorem:

All portfolios on the Minimum Variance Frontier can be found by combining ANY two distinct portfolios that are also on the Minimum Variance Frontier

Open order (aka good-till-canceled (GTC) orders)

An order to buy or sell a security at a set price that is active until the investor decides to cancel it or the trade is executed.

Day Order

An order to buy or sell a security that automatically expires if not executed on the day the order was placed

1- Returns are generated by an unknown k-common factor model. 2-The number of assets in the economy is very large (so that we can create many well diversified portfolios) 3- "Perfect markets" (as in the CAPM). So we have unrestricted short selling 4- "Homogeneous Expectations" (as in the CAPM) 5- KEY ASSUMPTION: NO ARBITRAGE OPPORTUNITIES

Assumptions of the APT:

CAPM

Based on the mean-variance analysis, we will develop an equilibrium model that will tell us what the equilibrium expected return (and hence prices) of each security SHOULD be.

Market Order:

Broker is instructed to buy or sell a stated number of shares immediately (most common)

No, only if the average covariance is zero

Can the risk of a portfolio be totally eliminated in a LARGE portfolio?

1- A small number of common factors which proxy for economic events that affect a large number of assets: aka systematic risk 2- A risk component that is unique to the asset aka non systematic risk

Factor model assumes that returns of assets can be broken down into two sources:

yes

Has correlation across international stock markets increased?

High Book-to-Market stocks (aka value stocks) have much higher alphas than Low Book-to-Market stocks (aka growth stocks).

How about the value strategies alphas?

1) Historical returns on various assets classes differ considerably 2) Long-Term gains from the stock market have been astounding 3) The variability in returns differs, too

How security returns behave across asset classes?

1) Relation between average returns and dispersion is not trivial 2) For a single asset class, like stocks, there is almost no relationship

How security returns behave compared with their "risk" ?

Even a naïve mix of just a few stocks reduces risk considerably

How security returns behave once they are grouped into "baskets"?

One short sells by (i.e. sell something that don't own) First borrow a security from the broker and sell the security Later, deliver the security back to the broker.

How short sells work?

risk-loving(seeking)

If A<0, we say that the investor is - investor is someone that prefers the risky project to the risk-free project if the risk-premium on the risky project is zero

risk-averse

If A>0, we say that the investor is _____ - investor is someone that will prefer the risk-free project to the risky project if the risk-premium on the risky project is zer

undermargined

If AM<MMR the account is said to be _______ The investor receives a margin call and will need to increase the equity (e.g. put cash in the account with the broker)

If M2p<aRm then p is bellow CML, and hence lost to the market

If M2p<aRm then p ______

M2p>aRm then p is above CML, and hence beat the market

If M2p>aRm then p _______

1) Investing in both securities generates SMALL gains from diversification 2) Investment opportunities set will curve left only slightly.

If correlation between returns is HIGH:

1) Investing in both securities generates HIGH gains from diversification 2) Investment opportunities set will curve sharply to the left.

If correlation between returns is LOW:

If αp <0 then manager lost to the market

If αp <0 using jensen's alpha

If αp >0 then manager beat the market

If αp >0 using jensen's alpha

If αp<0 short sale grand portfolio and buy Treasury Bills: make profit!

If αp<0 under apt

If 0 then the market returns don't explain anything of the returns of Belo Fund If 1 then the market returns explain all the movements in the returns of Belo Fund

It is a value of R^2 is between 0 and 1:

1) No security except the market portfolio and the Rf asset lies on CML 2) Every security has to be on SML

KEY DIFFERENCES BETWEEN SML and CML

1) The APT applies to well diversified portfolios and NOT necessarily to individual stocks. The CAPM applies to ALL securities Thus with APT it is possible for some individual stocks to be mispriced - i.e. not lie on the SML 2) APT is more general than the CAPM in that it gets to an expected return and beta relationship without the assumption that investors only care about the mean and the variance of the returns 3) APT can use multiple factors. The CAPM uses only one factor (the market return) 4) APT does not tell what the factor is (i.e. in applying the APT you need to make subjective decisions); the CAPM says that the market portfolio should be the only relevant factor (less subjective)

Key differences between the APT and the CAPM:

beta

Portfolio's systematic risk, measured by its

standard deviation

Portfolio's total risk, measured by its

SML: market (systematic) risk CML: total (systematic + unsystematic) risk

SML and CML expresses return as a function of different measures of risk:

the minimum variance frontier

The set of expected returns and return standard deviations is called the______________ defined as the set of portfolios with the lowest variance for a given return.

Buying on Margin: An Initial Margin Requirement (IMR)

This means that a percentage _____of the total investment must come from the investor's own funds (currently 50%, set by the Federal Reserve Board) E.g. If you want to invest $1000, then you can only borrow at most $500 and thus you will have to put the other $500 from your own funds.

Maintenance Margin Requirement (MMR):

This means that every day, the amount of equity relative to the market value of the stocks purchase cannot decrease below a certain amount. Why? To guarantee that there is enough collateral in the broker account to repay the loan

(1) Create a ZERO-beta well diversified portfolio (2) Define a STRATEGY

To show that an arbitrage opportunity exist you always follow two steps:

1) Portfolio's systematic risk, measured by its beta 2) Portfolio's total risk, measured by its standard deviation

Two different types of risk, and what are they measured by?

1) INDIVIDUAL STOCKS ARE BECOMING MORE VOLATILE: gains from diversification are higher! 2) INDIVIDUAL STOCKS ARE BECOMING LESS CORRELATED: gains from diversification are higher!

What 2 things are happening to the possible gains from diversification over time?

CONCLUSION: Small stocks have higher average returns than large firms. Consistent with the CAPM small stocks have higher betas. BUT, for the very small stocks the average returns are much higher than predicted by its beta! Why do I say this? Let's look at the alphas. ALSO So small stocks have higher CAPM alphas (and statistically significant). That is even after adjusting for risk via the CAPM, small stocks have earned higher average returns than large stocks...

What are the average returns and the betas of SIZE strategy?

CONCLUSION: The betas of the different portfolios are very DIFFERENT, but the average returns of these portfolios are almost all the SAME!

What are the average returns and the betas of the "BETA strategy"?

CONCLUSION: A portfolio of stocks with low past sales growth has on average much higher returns than a portfolio of stocks with high past sales growth. But they have almost the SAME (or even smaller) BETA!

What are the average returns and the betas of the sales growth strategy?

CONCLUSION: High Book-to-Market stocks (aka value stocks) have much higher average returns than Low Book-to-Market stocks (aka Growth stocks) but they have almost the same BETA!

What are the average returns and the betas of the value strategy?

it doesn't explain why some assets have higher expected returns than other assets

What doesn't CAPM explain very well?

borrow

What to do if Xs>1 or Xf<0 in regards to CAL

... because they pay up just when you need the money least, i.e. when the overall market is doing well

Why are high beta stocks risky?

(because they want maximum return with the least amount of risk possible)

Why do risk averse agents want to go as much as possible to the northwest region of the mean standard-deviation diagram?

market model

_____ assumes that there is one common factor: a stock market index

co variance is positive:

_______: if it tends to be that if one variable is unusually high (or low), then the other variable is also high (or low)

Margin call occurs when:

____________occurs when the price of the security decreases and that buying on margin is profitable when the price of the security increases

Buying on Margin

________means that the investor borrows part of the purchase price of the stock from a broker

mvep = market potfolio

according to capm: Since everybody holds the SAME MVEP of risky assets what must the MVEP be?

homogeneous expectations

all investors have the SAME perceptions regarding expected returns and the covariance of all the securities.

arbitrage

an arbitrage arises if an investor can construct a risk free portfolio that provides a risk free return different from the risk free rate. Thus an arbitrage is like a money-maker machine

perfect market, and investors prefer more return/ less variance

assumptions of capm

capital gain(or loss)

change in security price

income yield

dividends received by the investor

Small stocks have higher average returns than large firms.

do small or large stocks have higher average returns?

yes, everybody chooses the SAME portfolio of risky assets (the MVEP) but then each investor leverages this portfolio in different ways depending on its degree of risk aversion.

does everyone chose the same portfolio of risky assets?

no, real estate, human capital, bonds

does market refer to just the stock market?

no only covariance

does the variance matter for large portfolios?

Co variance is negative:

if it tends to be that if one variable is unusually high when the other variable is low, and vice versa

If αp>0 buy grand portfolio and short sell Treasury Bills (i.e. borrow): make profit!

if αp>0 under apt

portfolio

is a list of securities indicating the amount invested in each one

Perfectly Hedged Portfolio

is a portfolio of risky assets with zero risk (σ(Rp)=0)

well diversified portfolio

is a portfolio with ZERO firm-specific risk (i.e. no error term).

growth stock

is a stock with a high market price relative to the book value of assets

value stock

is a stock with a low market price relative to the book value of assets

indifference curve

is all the combinations of risk -σR- and expected return -E(R)- that provide an investor with an equal amount of utility.

Minimum Variance Portfolio

is the portfolio of risky assets which has the lowest standard deviation

Mean Variance Efficient Portfolio

is the portfolio of risky stocks with the highest Sharpe ratio

Diversification

is the process of combining risky securities into a portfolio in order to reduce total portfolio risk

CONCLUSION: Loser stocks, i.e. stocks that had the lowest returns in the past 12 month, tend to also have low returns in the subsequent years (the opposite is true for winner stocks (momentum). But the have SAME beta

momentum strategy?

NW (top left)

on the graph where would the graph go if utility is increasing

upward sloping

risk averse on the indifference curve is what___

Cal(capital allocation line)

shows all the risk-return combinations that are possible from a portfolio of one risky-asset and the risk-free return

true

t or f If the coefficient of determination R2 in the above regression is equal to 0 then the coefficient β in this above regression must also be 0

false

t or f If the coefficient of determination R2 in the above regression is equal to 1 then the coefficient β in the above regression must also be 1

false

t or f If the coefficient of determination R2 in the above regression is equal to 1 then the correlation between Yt and Xt must also be 1

true

t or f If the correlation between Yt and Xt is equal to 0, then the coefficient β in the above regression must be 0

If absolute value of t-statistic is >1.96 the coefficient IS statistically significant If absolute value of t-statistic is <1.96, the coefficient IS NOT statistically significant

t-stat rules

Market, SMB and HML

the Fama-French three factors are:

APT (arbitrage pricing theory)

the ___ tells us what the expected returns of well diversified portfolios should be based on one Major assumption: there are no arbitrage opportunities in the market

non-systematic risk

the risk that can be diversified away

systematic risk

the risk that cannot be diversified away

market model

the simplest factor model

financial leverage

use of debt to fund part of purchase price

find undervalued and overprice securities in the market

what can a capm model do?

make it so you only have to concentrate on forecasting one variable, the expected return of the market return

what does the market model essential do?

XValue = 592 (or 592%) XGrowth = (1-592) = -492 (or -492%)

what happens when Xvalue = 592

CML

what is the benchmark for sr and m2

SML

what is the benchmark in alpha and treynor?

sharpe ratio

what is the call ratio slope = to

Short sale

what to do if the stock is equivalent to allow for Xf>1 or Xs<0 in regards to CAL

Limit Order:

you specify a price at which you are willing to buy or sell a security

an immediate arbitrage opportunity opens up

αp must be ZERO! in the APT or what?