Q2 Flashcards
for 1 asset dominate other what needed
Er1>Er2 and sigma1<sigma 2 with one strict
when is indiffernce curve convex and when flat
risk adverse so more risk need more return
risk neutral
CAL is
how much to invest into risky and risk free portfolio sharpe ratio
sharpe ratio is
risky-rf/sigma p
issue with sharpe is
sigma punish all shocks the same and in reality happy see positve shocks and kurtosis and skew not accounted for
where is best place on CAl and how to find
depend on risk aversion, solve for Y*
SML vs CML VS CAL
The CML shows the risk-return tradeoff for efficient portfolios based on total risk
the SML depicts the relationship between expected return and systematic risk (beta) for individual securities or portfolios
and the CAL represents the risk-return combinations of any risky portfolio and a risk-free asset.
what is diversification
small amount of wealth in each asset to reduce risk, when asset not perfectly correlated reduces risk
correlation levels mean
+1 = perfect corr, move tog no risk reduced
0= random reduce some risk
-1= perfect hedge move oppo
in total diversification what important
covariance especially with more assets
correlation between same stock is and cov is
1 and cov is just variance
how does correlation effect portfolio risk if corr = -1,0.3 and 1
-1= 0 risk with proper weights frontier connects graph staright to left side
0.3= some diversification
1= weighted avergae of 2 asset = risk and becomes straight line frontier
portfolio varince contains how many terms and covariance how many terms
variance = N terms, covariance = N^2-N–> shows why covarinace imporatnt with high N bc more terms
what does variance approx too in large portfolio
For portfolios with large n, the variance is essentially the
average covariance
what risk does covariance capture and what does this mean
systemic and cannot diversify away avg covar
As N oncreases what 3 things happen
1- effect sec own variance decreases
2-effect of the sec covariance with other sec increase importance
3- risk of portfolio become avergae covariance of sec in portfolio
explain 2 types of risk
idiosyncratic: unique to firm related to issues they face can diversify away
Systemic: common with all sec related to general econ condition we demand compensation for this risk
what is systemic risk made of
average covariance cannot drop below with diversification
as n increase what is effect of idiosyncratic risk
neglible effet on portfolio risk and return, if no systemic risk then add no risk to diversified portfolio
what makes portfolio effeceint
highest returns for level of risk, CAL steepest, or lowest risk for given level of return
what is GMVP
minimize risk, start point of effeceint frontier, left most point, lowest sigma
ineffeceint frontier made up of:
low return, high risk or poor diversification
frontier is what capital markets offerso Cal reflects
combo fo risky and risk free
without rf asset how find portfolio
go along frontier and look risk prefrence, focusing soley on risky aset combo–> utlity max
with rf rate how to fin portfolio
use steepest CAL, choose combo of p and rf tangent to the forntier
what is orp
max sharpe ratio with combo of assest
issue with solving orp
1- covar/var change with time
2- past dat not equal optimal future
3- ppl use index fund as orp
steps find orp
1- find effeceitn frontier
2- establish orp and its retruna dn sigma
3- choose optimal $ to invest in with P,A Rf
what is mean variance optimize
hold combo of optimal p and rf, with weights that offer highest CAL slope
what is portfolio theory
how construct risky/rf in terms of mean variance trade off
what is CAPM
predicts expected/fair returns on risky asset –> world where investors follow mean variance
CAPM assumptions not improtant
investors risk adverse utility max and rational
frictionless markets
borrow at rf
simple same HPR
homogenous expecattions= same frotnier
investments highly liquid and infitnely divisble
price taker investors
investors solve for Y* in CAPM and invest what would market look like
all hold market portfolio and CAL = CML bc hold market portfolio which is also ORP
what is market portfolio
large diversified idiosynccratic risk not important, risk prem indv sec reflect market portfolio risk, risky asse = high covariance
how to decide if add sec to portfolio
determine sec contribution to portfolio in terms of reward to risk ratio and compare to market if greater add
due to s&d sec risk reward = market risk reward why?
sec with higher risk reward attract invetsors which increase prive lowering er till equil
what is mpr
extra return market portfolio provide over rf / market price of risk and is equal for all sec
In CAPM sec er depends on
A security’s expected return depends on the market risk premium and its exposure to market risk (beta)
er sec in capm described
fair ret7urns sec varies as a function of market risk prem
what is beta
contributuion of this sec to sigma or mp, how sensitive sec return is to market, asset systemic rick
market beta =
1
SML uses what vs stnd
beta
what is beta
A high-beta security has greater exposure to market risk (systematic risk), which cannot be diversified away.
beta of portfolio
SUM (weight of each security * beta of each security)
what is alpha
abnormal ror above or below capm, regression point from sml diff, excess risk adjusted return
3 factor capm model incl
beta excess return market, smb size beta, hml beta for value vs growth
limits capm
only beta captured, single period, not testable
total risk in capm sec =
beta * market stnd+ idiosyncratic
market effeceint when
all avil info reflected in pruce right away, asset refelct value so price = value no alpha
if there is an alpha in EMH then
people tarde on it pushing price to actual so no alpha in equil
for EMH what assumption req 1 of 3
everyone rational, some irrational but not systemic so cancel out, sometime irrational systemically and arb tarders make price right
what is weak effeceincy
Price reflects all information contained in market trading data
(past prices, volume, dividends, interest rates, etc.)
what cannot work to ID mispriced sec in weak effeceiency
past prices and technical analysis
what is technical analsyis
Refers to the practice of using past patterns in stock prices (and
trades) to identify future patterns in prices.
* Is not profitable in a market which is at least weak form (i.e.,
weakly) efficien
how to test market effeceincy
can yesterday predict today, how fast stock price change when info released, stock picking ability possibel or not, stcok prices should be random and stock return all info known so price only change when new info arrive = random
eveidience stock pikcing ability not work bc EMH
performance mutual funds, mean reversion
what is medium form in EMH
Price reflects all publicly available information.
2. So, an investor can not use publicly available information to identify
mispriced securities. If a market is semi-strong form efficient, then it is also weak form
efficient since past prices and other past trading data are publicly
available
what doesnt work in medium form EMH
Fundamental analysis:
* Refers to the practice of using financial statements, announcements,
and other publicly available information about firms to pick stocks.
* Is not profitable in a market which is at least semi-strong form (i.e.,
semi-strongly) efficient.
what is strong form EMH
Price reflects all available (public & private) information.
2. If a market is strong form efficient, then it is also semi-strong and weak form
efficient since all available information includes past prices and publicly
available information
what is private info and 2 types
What is “private” information?
* Information that you hold that is not reflected in the market price
* Two types of private information:
a) “Inside information” – info known to company management but not
yet made public – knowledge of an impending takeover bid –
knowledge that earnings are going to be lower than the street expects.
b) A private assessment based on public information – an analyst’s
report based on public accounting statements.
test with random walk is
stock price random past dont predict future, if ebeliev random = nbo pattern to trade on inbstant reflection in price
how else tets market effecenicy
how fast prices change when new info arrive
test market effeciency how with mujtual funds
consistent return above average but 50% investor above average so need LR test
fund manager not generate consistent alpha what proof
revert mean after 5 years, slight skew to negative alpha after fees,
Jan effect, size effect, BM, momentum, post earning drift, SEO
Jan: invest in jan close pos end of month average gen alpha
Size: small outperform large
BM: Low BM = growth and high BM gen alpha
momentum: shouldnt exist in effecient market, under 1 year winners win– 2-5 years reverse
post earn driftL take time reflect earnings bc markets slow
SEO: after SEO unerperform for 5 years drifting down
Publicvation effect
people learn alpha startand trade in it making market more effeceint
market effeceint if sec price = value how this happenb
people are rational in capm or arb correct mispring
what does BF suggest
contends EMH, investor irrational when make invest decesion so prices not right observe mispricng
can we exploit mis pricing in BF
no bc fricition so not able act mispring start bc arb costly
2 main point of BF
[yschology and costly arb
what does BF pyschology suggest
investor irrational in systemic way, people make mistake from capm
3 pyschological effect BF
conservatism, repreentativness and overconfidence
what is conservatism
- Slow updating when facing new information that contradicts current
beliefs;
not incrop new inf right away but defend
Conservatism and Post-earnings Drif
under react to news suggest change in firm bc concservatism take time to acknowledge vs EMH
what is represativness
Representativeness involves the tendency of humans to generalize
about a population of future outcomes after observing only a small
sample
what is representivness and return anomlies
look at growing stocks and use past performance into expected returns like high price to book = lower returns nut long term reversals
Representativeness and Mutual Funds
Representativeness could explain how investors choose investment
managers:
overconfidence
Overconfidence is a bias in which people demonstrate unwarranted faith
in their own intuitive reasoning, judgment, and cognitive abilities
what is self attrition bias
Events that confirm a person’s ability are because of the person’s high ability Events that disconfirm a person’s ability are due to bad luck or sabotage
why
don’t other people just capitalize on mispricing and keep markets efficient?
arb is costly, costly risky and hardmight nto be money made
2 types cost with arb
transaction like comission and spread
holding like noise and fundemental
what is noise trading
irrational investor trade on noise if was info,risk of mispricing worse befor ebetter, continue trade wrong direction lossess get worse
why timing market so difficult
aggregatley noise trader could be stronger than rational investor
what is fundemntal risk
intrisnic value changes after you buy = fundemntal volatility
this can cause arb to lose $ so reduce arb in volatiale investments
arb prefer less volaitale costs what cost arb
idiosyncratic risk more of it = less effeciency more mispricing in high idiosyncratic assets no one fix issue and hard make alpga
