equity and fixed income exam 1

ch 10-13

arbitrage

exploitation of security mispricing in such a way that risk free profits can be earned

asset returns have two sources of risk

systematic (market) and non systematic (firm specific)

E(Ri)= BiE(M)

E(Ri) = expected excess return on stock i

Bi= sensitivity of firm i to factor M

M = macroeconomic factor (inflation, interest rates, gdp)

Ri = E(Ri) + BiF + 𝑒𝑖

Ri= realized excess return on stock I

F=M-E(M); deviation of common factor from its expected value

ei = non-systematic components of returns (should be 0)

Two factor model

sources of risk are

1. uncertainties surrounding the state of the business cycle and changes in interest rates

Two factor model equation

Ri = E(Ri) + biGDPFGDP + biIRFIR + 𝑒𝑖

what can factor betas do?

provide a framework for a hedging strategy

what determines a security’s expected excess rate of return

APT (arbitrage pricing theory)

Arbitrage pricing theory (APT)

predicts a security market line (SML) by linking expected returns to risk, but that path is much different than the path predicted by the CAPM

What is a trivial example of arbitrage

when shares of the same stock sell at different prices on two different exchanges (siameses twin example)

what is the law of one price

if two assets are equivalent in all economically relevant respects, then they should have the same market price (if not then people will trade till this holds true)

APT formula

what does apt do

it separates the variance of the portfolio into its systematic and non-systematic sources

what happens as N goes to infinity

what kind of risk is negligible in well diversifies portfolios

non-systematic (firm-specific risk)

can stock with the same betas but different levels of returns exist?

no, this would be an arbitrage opportunity

are risk premiums proportional to portfolio betas?

yes, as in the simple capm, the risk premium is zero for beta o and rises in direct proportion to beta

What is the final step for sml of apt

for the sml relates the portfolio risk premium to its beta against a market index

as well diversified portfolios are perfectly correlated with the macro factor what?

there fore the market index port is weel diversified so its reutrn will perfectly refect the value of the macro factor

For any well diversified portfolio P

APT

Built on the foundation of well-diversified portfolios

does not assume investors are mean-variance optimizers

uses an observable market index

Cannot rule out a violation of the expected return beta relationship for any particular assets

CAPM

• Model is based on the inherently unobservable “market” portfolio

• Provides unequivocal statement on the expected return- beta relationship for all securities

Fama French Three Factor Model

SMB (Small Minus Big)

return of a portfolio of small stocks minus return of a portfolio of big stocks

HML (HIgh Minus Low)

return of a portfolio of stock with high book to market ratio minus return of a portfolio of stocks with low book to market ratio.

How Could you construct an arbitrage portfolio

Long position in a portfolio (P) composed of portfolios A and B will offer an

expected return-beta trade-off lying on a straight line between points A and B

• Choose weights such that bP = bC; expected return will be higher than that of C

but will have same beta

• Go long P, sell short C

Random Walks (drunk guy)

if prices are bid immediately to fair levels, it must be that they increase or decrease only in response to new information

Random walk assumptions

• new info must be unpredicatble

• stock prices that change in response to new info must also move unpredicatably

Efficient market hypothesis (EMH)

The notion that stocks already reflect all available information

What is the most precious commodity on wall street

Information

Weak EMH

Stock prices reflect all information contained in the history of past prices, returns, and trading volume

( in this form fundamental analysis still works)

Semi-strong EMH

Stock prices reflect all publicly available information

Strong EMH

Stock prices reflect all information, including insider information

if markets are efficient what should be the correlation between stock returns for two non overlapping time periods

zero

does 1 person beating the market mean it is ineffienct

no some investors will outpreform in the short term simple due to luck

What does all form of EMH imply for Technical analysis

it is worthless and will not work

Trading Away

once a useful technical rule is discovered traders will trade on it make the technical rule no long hold true

Fundamental analysis

use of earning prospects, dividend prospects, and risk evaluation of the firm to determine proper stock prices (looking for mispricings)

what is the fundamental trick

finding firms that are better than everyone else’s estimate

active management

• expensive strategy

• suitable for manager with very large portfolios

Passive management

• No attempt to outsmart the market

• Implicity accept EMH

• Low-cost strategy

what would happen to market efficiency if all investors folowed a passive strategy

• price will eventually fail to refect new infrormation

• profit oportunities fro active investors

• prices will again be driven to fair levels

if the market is efficient what is portfolio managemnts role?

• Diversification

• tax considerations

• risk profile of investor

In other words “ tailor the portfolio to investors individual needs, not to beat the market

what are some examples of systematic resource misallocation due to inefficient markets

• Overvalued securities can raise capital too cheaply

• Corporations with undervalued securities may pass up profitable opportunities because the cost of raising capital is too high

what does it mean if prices reflect all available information

then price changes must reflect new developments so you can back out the economic impact of those events

Event study

Methodological approach designed to measure the impact of a certain things on stock returns

Expected return

Realized return

Abnormal return

Leakage

occurs when information regarding the relevant event is released to a small group of investors before its official public release

selection bias issue

only unsuccessful investment schemes are public, if it acutally works then they are kept private so the compnay can make money

magnitude issue

only managers of large portfolios can earn enough trading profits to make the exploitation of minor mispricing worth it

Lucky event issue

for every big winner, there is a big loser, but we rarely hear about these losers

momentum effect (short horizons)

tendency of poorly performing stocks and well performing stock in one period to continue that abnormal performance in following periods

reversal effect (long horizons)

tendency of poorly performing stocks and well performing stocks in one period to experience reversals in following periods

what are the two weak form test

• momentum effect

• reversal effect

Semi strong form test

low p/e stocks outperform high p/e stocks

low market cap stocks outperform

high btm stock outperform

firm with large postive earning surprises earn higher returns for weeks after

firm with higher gross profitability earn higher returns

Small firm effect

low market cap stocks outperform

Book to market effect

High book to market firms tend to outperform low vaule outperforms growth

Post earnings announcement drift

firm with large postive earning surprises earn higher returns for weeks after

Strong form test

SEC requites all insiders to register their trading activity

What does Fama and French argue can explain these effects?

Risk Premium

Fama and French ( risk premium argument)

book to market and size are not risk factors but they may proxy for risk factors

what do lakonishok, shleifer, and vishny argue

they think that these are example of inefficient markets cause by behavioral biases

Anomalies or data mining

simple chance will cause some variable to appear to predict returns

anomalies over time

they should self destruct in well functiong markets (trading away)

stock market analysts properties

• tend to be overwhelmingly positive

• difficult to separate effects of new reco form changes in investor demand

hard to tell if recommendation drive price changes or if investor demand resulting from the recommendation drives price changes.

does casual evidence support the claim that professionally managed portfolios can consistently beat the market

No

are some markets less efficient than others

yes , emerging markets, illiquid markets (real estate), market with limits to arbitrage

Behavioral critique

conventional theory ignore how real people make decisions and that people make a difference

Limited attention, under- and overreaction

individuals have limited time and attention so they use rule of thumb (heurisitcs)

intuitive decision making procedures (rules of thumb)

heuristics

limited analytic processing capacity may cause what

over or underreact to less salient information

ex recent events are typically more salient

overconfidence

people tend to overestimate the precision of their beliefs or forecasts (trade activity is negatively associated with portfolio performance)

Conservatism

Investors are too slow in updating their beliefs in response to new information

leads to underreaction

Confirmation bias

tendency to interpret new information in a way that confirm or support one’s prior beliefs

this can lead to short term momentum

Extrapolation and pattern recognition

people are adept at discerning patterns and prone to believe that these patterns are likely to characterize an etire popultion

may infer a pattern too quickly from small sample and extrapolate apparent trends too far into the future

when people think that a small sample pattern characterize an entire popultion

represnetativeness bias

Framing

decision are affected by how choices are described

(remeber the coin toss vs gift gamble)

Mental accounting

Specific form of framing in which people segregate certain decisions

ex saving money but carrying a credit card balance

what is a reluctance to realize losses called

disposition effect

Regret avoidance

individuals who make decision that turn out badly have more regret when that decision was more unconventional

ex. losing money on a blue chip stock is less painful than losing money on a startups

If a company is socially responsible what is it said to have

good affect- this may drive price up as investors feel good about buying this company

Prospect theory

conventional view- curve concave

behaviorla view- more sensitive to losses than to equivalent gains ( losses convex and gains concave)

Conventional view

utility depends on total welath with marginal utility typically declining as wealth increases

Behavioral view

individuals evaluate gains and losses relative to a reference point and are more sensitive to losses than to equivalent gains

fundamental risk and limits to arbitrage

mispricing can widen before price eventually converges to intrinic value

markets can remain irrational longer than you can remain solvent

what does , “ markets can remain irrational longer than you can remain solvent”

markets can hold arbitrage long enough for you to go bankrupt

implementation costs as a limit to arbitrage

transaction costs and restrictions on short selling can limit arbitrage activity

ex cost money to borrow and short stocks, may have to return borrowed security at lower price

Model risk as a limit to arbitrage

the apparent mispricing may refelct an incorrect valuation model rather than a ineffieciency. you could just be wrong

Law of one price

identical assets should have identical prices

Siamese Twin companies (violation of LOP)

royal dutch petroleum and sheel transport operated under a dual listed structure in which royal dutch had 60 economic interest and sheel had the other 40. in theory royal dutch should trade for 1.5 times the price of shell. this was not the case

equity carveouts violate LOP

company spins of into another in a 1-1.5 split so in theory the orginal share should be worth 1.5 the new but this does not hold for months

Closed end funds violate LOP

funds may trade at a premium or discount to nav discount due to fund exp preium due to risk adjusted alpha

When are bubbles the easiest to spot

after they end lol

what do you estimate during the first pass regression

beta

average risk premia

idiosyncratic risks

estimate beta (first pass)

Estimate average risk premia first pass

Estimate idiosyncratic risk

shouldn’t matter for pricing as it can be diversified away