investments!!! L1-8

3 different measures of return:

holding period return (total return on an asset or portfolio over a period during which it is held. HPR for a stock= dividend yield plus capital gains yield
expected return ER / average return: value of a random variable one could expect if the process of

holding period return

rate of return over a given investment period.
the HPR of a share of stock depends on the increase/decerase in the price of the share over the investment period as well as any dividend income the share has provided.
HPR= (ending price - beginning price +

arithmetic average return

sum of returns in each period divided by the number of periods.

geometric average return

single per-period return that gives the same cumulative performance as the sequence of actual returns
terminal value (TV) of 1/n - 1

variance

the expected value of the squared deviation from the mean.
=stdev^2 = (sum(r- r mean)/n

value at risk
=
equation: Mean of 10%, investment 100$, 1 year VaR=

measure of downside risk. worst loss that will be suffered with a given probability often of 5%
the 5% VaR is the 5th percentile rate of return. for a sample of 100 returns with rates ordered from high to low, found the 5th observation from the bottom.
Va

VaR and CTE are complements or substitutes?

complements.
VaR is a threshold measure- very popular with new Basel rules. Content is different for CTE.

you have option to take a bet on the toss of a coin. 50% H or T.
head you win 1 euro, tail 0 euro.
what are you willing to pay if you are risk averse? and what is this called?
gambler?
fair game?

up to 50 cents, bc there is an expected payoff of 50 cents. risk averse student won't spend over 50.
we call this a speculation0 you want to receive a risk premium for taking on this risk.
gambler: willing to spend over 50 cents. they expect a negative ri

does low medium or high risk portfolio generate highest utility?

medium risk.

how are systematic risk and firm specific risk correlated?

uncorrelated to each other

If two investments have the same expected return, but one has a lower variance, which once is the better choice?

the one with the lower variance is the better choice.
Different levels of diversification can be achieved in a portfolio by combining stocks with different variances and expected returns.

ranking portfolios by their sharpe ratios is called

mean-variance analysis

is it enough to just know averages?

no- you need more info than just averages.
this is why we use VaR value at risk.

3 measures of dispersion

variance: how much a set of observations differ from each other. represents how spread out the data set numbers are.
bias-corrected variance:
volatility: degree of variation of a trading price series over time as measured by the standard deviation of loga

two measures to describe the shape of return distributions

skewness: measure of the asymmetry of a probability distribution.
averaged cubed deviation from the mean divided by the stdev cubed. negatively skewed distributions have a long left tail, meaning greater chance of extremely negative outcomes
kurtosis: aka

as investor going long for an asset, would you prefer an investment skewed to left or right?

skewed right bc higher chance for positive return

fat tailed distribution

exhibits large skewness or kurtosis.
important bc fatness of tails shows a riskier investment- higher probability for a negative return. this is bad to investors.
kurtosis is actually a measure of excess kurtosis.
In finance, fat tails are considered unde

two measures of comovement

covariance: measure of the degree to which returns on two risky assets move in tandem. positive moves together, negative move inversely. (covariance=correlation coefficient x stdev stock A x stdev stock B) =
=*
betaA
betaB*stdevOfMarket^2=
=sum probaiilit

serial correlation

correlation between return of yesterday and today.
high correlation means there was high distribution today and yesterday.
why does correlation fall close to zero? efficiency-markets tend to be efficient. so if there are high returns, everyone will find o

risk premium

expected excess return over the risk free rate (risk-free interest rate is the theoretical rate of return of an investment with no risk of financial loss, over a given period of time)
minimum amount of money by which the expected return on a risky asset m

sharpe ratio

excess return per unit of risk*
useful in understanding how returns increase relative to risk increases
examines performance of an investment by adjusting for its risk.
calculates risk-adjusted return
a dimensionless score to compare similar investments t

normal distribution and why is it useful?

68, 95, 99
its symmetric. mix of normally distributed variables is also normal.
its entire shape can be defined with only two parameters (mean and st dev)
dependence of normally distributed variables can fully be characterized by correlation

serial correlation of daily returns is close to what? returns are therefore easy/hard to predict from the past.
on the other hand, variance has what correlation for small horizons?

close to zero. hard to predict
positive autocorrelation. variance aka squared returns

variance vs volatility

Variance is a measure of distribution of returns and is not neccesarily bound by any time period. Volatility (R^2) is a measure of the standard deviation (square root of the variance) over a certain time interval. In finance, variance and volatility both

is VaR ir CTE a more conservative measure of downside risk?

CTE because it takes an average return of worst cases, while VaR takes the highest return from the worst cases

R squared

percent of variance explained by the model.
squared returns
represents the percentage of a fund or securitys movements that can be explained by movements in a benchmark index.
r-squared values range from 0 to 1 and are commonly stated as percentages from

the distribution of daily returns has smaller/fatter tails than the normal

fatter. higher probability of large losses. increasing the holding horizon (month, year) brings the distribution closer to normal

the distribution of daily returns is what?

asymmetric, typically negatively skewed. there are more large drops in returns that upward moves

value-at-risk

aka VaR: a measure of downside risk.
It measures the potential loss over a specified horizon such that
there is a (low) probability ? that the actual loss will be larger
� VaR as a quantile of the projected distribution of returns
� The 5% VaR, commonly e

the most popular and traditional measure of risk is ____. the main problem with _______ however is that :

The most popular and traditional measure of risk is volatility. The main problem with volatility, however, is that it does not care about the direction of an investment's movement: a stock can be volatile because it suddenly jumps higher. Of course, inves

VAR using normal distribution for mean (u) and st dev (o)

VaR of alpha (a) = u - Fa^-1o
= mean - inverse N(0,1) CDF for probability a
compose the "left tail" of the histogram. These are the lowest 5% of daily returns (since the returns are ordered from left to right, the worst are always the "left tail"). The re

for an investment of $100 in a stock with annual mean of 10% and stdev of 15%, the 5% 1-year VaR is:
(stdevs from the mean for 95% confidence: 1.645)

VaR of alpha (a) = u - Fa^-1o
= mean - inverse N(0,1) CDF for probability a
5% 1 year var means 95% confidence level.
VaR(0.95)= -100 x (0.10-1.645x0.15) = $14.675
= -$ x (mean-(stdevZscore x stdev))

if we increase the time horizon, does VaR increase or decrease?

increase

the variance of a T-day return :

T times the variance of a 1-day return

if returns are independent and identically distributed:
VaR(95%,T periods)=
VaR(95%, 10 days)=

0

assumption of var using historical returns?

distribution of tomorrows returns( R(t+1) ) is well approximated by the empirical distribution of past observations (m)

expected shortfall aka...

aka conditional tail expectation CTE, conditional VAR (CVAR), mean excess loss, mean shortfall, average value at risk
risk measure- a concept used to evaluate the market risk or credit risk of a portfolio.
the "expected shortfall at q% level" is the expec

VaR measures ....
CTE measures....

number of losses. VaR takes the highest return for the worst cases.
magnitude of losses. CTE takes an average return of the worst cases. more conservative measure of downside risk than VaR
The VaR model allows managers to limit the likelihood of incurring

is the absolute value of CTE or VaR greater?

CTE always greater, because it is always located more negatively on the timeline

risk averse investor

averse=dislike/opposition to risk.
accepts risk free or speculative prospects with positive risk-premiums
rejects portfolios that are fair games (or worse)

how to rank portfolios based on investors preferences over their risk-return trade-off?

Utility is enhanced by higher expected returns and diminished by higher risk
assign a utility (welfare) score.**
utility function is an important concept that measures preferences over a set of goods and services. Utility is measured in units called utils

mean variance utility=

U= Er - .5Ao^2
U=utility.
A is risk-aversion coefficient.
investors are ... risk averse if A>0.
risk-neutral if A=0 (decisions are only based on Er).
risk loving if A<0.
process of weighing risk (variance) against expected return. By looking at the expect

choice of your portfolio depends on...

risk aversion

Consider the case when the investor has to allocate her
portfolio between risk-free money-market securities (with
return rf) and a risky one (with return rE).
� The return of the portfolio is:

Rp= wxRe + (1-w)Rf
w=weight on the risky asset

portfolio of one risky and a risk-free asset.
the expected rate of return of the portfolio:
standard dev of the portfolio:

E(Rp)= wE(Re)+(1-w)Rf = Rf+w(E(Re)-Rf)
op=w(oe)
o=sigma=stdev
oe=stdev of the risky asset

optimal portfolio allocation with one risky asset
In order to find the optimal allocation to the risky asset,
the investor solves the following utility maximization
problem:

optimal portfolio of risky assets is found in the weights that result in the steepest CAL
The optimal CAL is the one that is tangent to the efficient frontier. This CAL offers the highest reward-to- variability ratio (sharpe), which is the slope of the CA

Solving for "w" gives the following expression for the
optimal portfolio weights invested in the risky asset:

w*= E(Re)-Rf / Ao^2

Find the optimal portfolio weights of a mean-variance investor with risk aversion coefficient of 6 who chooses
between a risk-free and a risky asset. Assume a risk free rate of 0.001
� Using monthly Heineken data between 2006 and 2015:
� Applying the form

w*= 0.014-0.001 / (6 x (0.062)^2 ) = 0.56
w*= (mean - risk free rate) / (risk aversion coefficient x (stdev)^2))

optimal portfolio allocation with one risky asset.
how will the graph look?

utility as a function of the allocation to the risky assets.
so x axis: weight in risky asset.
y axis: utility
line is like an umbrella. optimal portfolio at highest relative max on umbrella line.
The optimal CAL is the one that is tangent to the efficien

what are the required portfolio returns for varying op levels, such that utility remains constant (the investor is indifferent between the risk-return combos)
recall that: E(Rp)=U+.5Ao^2

thus, we can find the required expected portfolio return for different levels of risk (through op) and for a given utility score

indifference curves

the higher the indifference curve, the higher the utility level.**
the steeper the indifference curve, the higher the risk aversion **(ex: higher compensation required for the same level of risk).
represents a series of combinations between two different

what is the highest attainable utility level given the investment opportunity set?

fix the level of risk aversion of the investor.
the tangent indifference curve to the CAL gives the highest possible utility.
the tangent point gives the optimal portfolio.

markowitz portfolio selection model

we can generalize the two asset case to many risky assets. solving for optimal portfolio involves following steps:
identify the risk-return opportunities available to the investor.
find the optimal risky portfolio on the efficient frontier which provides

markowitz portfolio selection model:
mean-variance frontier.
optimal risky portfolio.
risky-riskless asset mix.

minimize variance for each target level of expected return. draw efficient frontier.
search for the CAL with the highest reward-to-variability ratio. locate point P.
solve for the optimal mix btwn the risk-free and the risky assets, which depends on indid

challenges in applying markowitz portfolio selection model

Challenges in applying the model
A large number of parameters. For n stocks
N estimates of expected return
N estimates of variance
(n^2 - n)/2 estimates of covariances
Errors in estimating correlation coefficients

the single index model

accounts in a tractable way for the sources of risk- due to common factors (business cycle, IRs).
decomposes uncertainty to: systematic risk and firm-specific risk.
Ri=excess return = Ri-Rf= BiRm + Ei
BiRm=return due to movement in overall market
Bi=respo

single factor model

decomposes the risky assets return into the sum of an expected and unexpected components
Ri=E(Ri)+BiM+Ei
m=common factor. captures the uncertainty about the economy.
Ei=unexpected return. captures the uncertainty about the particular firm.
Bi: exposure to

decomposition of risk: the variance of the risky asset has how many components?

2: systematic and firm specific

the Information Ratio

*measures the extra return we obtain from security analysis per unit of firm specific risk we are exposed to if we under or over weight securities relative to the market index.
abnormal return (alpha) per unit of non-systematic risk (tracking error).
alph

assumptions behind the CAPM

investors are price takers: individual trades don't affect prices.
single period investment horizon.
investments are limited to traded assets.
no taxes or transaction costs.
all investors are rational mean0variance optimizers.
info is costless and availab

capital market line

its the CAL using the market index portfolio as the risky asset.
CML. it is the best attainable CAL capital allocation line
the CAL:investment opportunity set formed with a risky asset and a risk-free asset. The CAL has an intercept equal to the risk-free

why do all investors hold the market portfolio?

passive strategy: investing in the market index is efficient.
mutual fund theorem (separation property): all investors choose to hold a market index mutual fund. the allocation btwn the mutual fund and the risk free asset depends on individual investors r

CAPM

Tests of the CAPM that use regression techniques are subject to inaccuracies because the slope coefficient of the regression equation is biased downward. This would be a problem even if it were possible to use the returns on the true market portfolio in t

zero-beta model of Black

extension of CAPM.
Absence of a risk-free asset (i.e. restrictions on borrowing or investing in the risk-free asset)
Combinations of portfolios on the efficient frontier are also efficient
Any portfolio on the efficient frontier has a companion (zero-beta

ICAPM

intertemporal capital asset pricing model.
linear factor model with wealth and state variable that forecast changes in the distribution of future returns or income.
value stocks typically ha
ve higher returns than growth stocks.
relaxes assumptions that w

CCAPM

consumption CAPM
Allocate current wealth between current consumption and savings and investments (i.e. future consumption)
Assets are riskier if they co-vary positively with consumption growth -> they have higher equilibrium risk premiums
Risk premium of

with CCAPM, what kind of premium would you require for assets that comove highly with consumption in order to buy them?

require a high premium.

security market line.
an overpriced security will plot where on the SML?

representation of CAPM. displays the expected rate of return of an individual security as a function of systematic, non diversifiable risk.
x axis represents risk (beta) and y axis reps expected return. market risk premium is determined from slope of the

difference of CAPM and index model?

index model: model that relates stock returns to returns on both a broad market index and firm-specific factors.
capital asset pricing model is expected returns, index model is realized returns

low beta securities generally have negative/positive alphas

positive

weak emh vs semi-strong vs strong

Weak: stock prices reflect all information that can be derived by examining market trading data (e.g. prices, volume, etc.).
Semi-strong: stock prices reflect all publicly available information regarding past performance and prospects of the firm (i.e. in

types of stock analysis

technical analysis: using past trading info (price and volume) to predict future prices. the weak form of EMH rules out its benefits. focuses on stock price patterns and on proxies for buy or sell pressure in the market.
fundamental analysis: uses economi

response of stocks to new info over time

at -1 time, already some effects- from selected set of investors, possibly inside trading. then effects boom either positively or negatively, then flatten out.

active vs passive management

Active management
Involves security analysis, timing
Large vs. small investors
The EMH: no benefit from pursuing active management
Passive management
Involves the creation of an index fund, buy and hold Supported by the EMH

even if the market is efficient, there is still these roles for portfolio management:

selecting a well-diversified portfolio.
selecting investment policies with tax considerations.
matching a portfolio policy with the risk profile of the investor.

weak form tests of the EMH

Weak form tests (patterns in stock returns)
Momentum over short horizons: market indices have low serial correlation, but portfolios of best/worst recent performers display a momentum effect
Reversals over long horizons: overreaction to news, which is cor

cumulative abnormal return

CAR: sum of all abnormal returns in the event window

predictors of broad market returns:

fama and french (aggregate returns are higher with higher dividend/price ratios.
campbell and shiller: earnings yield can predict market returns.
keim and stambaugh (bond spreads can predict market returns)
Is asset return predictability In violation of t

test of EMH: strong form tests.

inside information.
The ability of insiders to trade profitability in their own stock
Regulators usually require all insiders to register their trading activity
Evidence that following insider transactions (after they become public) generates no abnormal

interpreting evidence of EMH:

Inefficiencies or risk premiums?
� On one hand these effects could be due to risk premiums associated with risk factors (e.g. Fama and French)
� Alternatively, they may be evidence of inefficient markets (e.g. systematic errors in the analysts' forecasts)

beta

measure of market risk.
smeasure of volatility, or systematic risk, of a security or portfolio in comparison to the market as a whole. it gives a sense of a stocks market risk compared to the greater market.
ensitivity of the expected excess asset returns

In a well-diversified portfolio, what risk is present?

Market, systematic, or nondiversifiable, risk is present in a diversified portfolio; the unsystematic risk has been eliminated.
unsystematic risk is negligible (so small it isn't worth being considered)

Company XYZ just announced yesterday that its first quarter sales were 35% higher than last year's first quarter. You observe that XYZ had an abnormal return of -2% yesterday. This suggests that

investors expected the sales increase to be larger than what was actually announced.

According to proponents of the efficient market hypothesis, the best strategy for a small investor with a portfolio worth �10,000 is probably to

invest in mutual funds. Individual investors tend to have relatively small portfolios and are usually unable to realize economies of size. The best strategy is to pool funds with other small investors and allow professional managers to invest the funds.

framing

a person may reject an investment when it is posed in terms of risk surrounding potential gains but may accept the same investment if it is posed in terms of risk surrounding potential losses

multifactor models

can be motivated by APT or CAPM extensions.
allow for more than one factor-thus introduce different sensitivities of assets to the separate sources of systematic risk.
factors may include unanticipated changes in GDP, IRs, inflation, etc.
estimate the loa

correlation coefficient

the covariance divided by the product of the standard deviations of the returns on each fund. denoted by greek letter Rho (p)
p(SB)= Cov(Rs,Rb)/ (stdevS*stdevB)
correlation can range from -1 to 1.
-1 = one assets returns varies perfectly inversely with th

Consider the regression equation:
ri- rf= g0+ g1bi+ g2s2(ei) + eit
where: ri- rt= the average difference between the monthly return on stock i and the monthly risk-free rate; bi= the beta of stock I; s2(ei) = a measure of the nonsystematic variance of the

0. If the CAPM is valid, the excess return on the stock is predicted by the systematic risk of the stock and the excess return on the market, not by the nonsystematic risk of the stock.
g1 would be the market risk premium which equals the avg difference b

If an investor has a portfolio that has constant proportions in T-bills and the market portfolio, the portfolio's characteristic line will plot as a line with ___________; if the investor can time bull markets, the characteristic line will plot as a line

constant slope, positive slope.
These characteristics are shown in Figure 24.5. If the proportions are constant the beta of the portfolio stays constant. If the investor switches the proportions in favor of the market portfolio to take advantage of bull m

Hedge fund performance may reflect significant compensation for ________ risk.

liquidity. Hedge fund performance may reflect significant compensation for liquidity risk - recall the LTCM example

A zero-coupon bond has a yield to maturity of 11% and a par value of $1,000. If the bond matures in 27 years, the bond should sell for a price of _______ today.

59.74
1000/1.11^27
FV/(1+i)^N

straight bond
callable bond

straight: has a coupon that is paid to bondholders periodically. issuer repays principal at maturity.
callable: debt security / bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its

forward rates
short rates
spot rate
Which of these are observable today?

forward: future yield on a bond. calculated using yield curve. imperfect forecasts.The forward rate for period n is the short rate that would satisfy a "break-even condition" equating the total returns on two n-period investment strategies. forward IR is

duration of bond

duration of a bond normally increases with an increase in A. term to maturity.
The relationship between duration and term to maturity is a direct one; the relationship between duration and yield to maturity and to coupon rate is negative.
Duration (and th

. Holding other factors constant, the interest-rate risk of a coupon bond is lower when the bond's: A. term-to-maturity is higher.
B. coupon rate is lower.
C. yield to maturity is higher.
D. term-to-maturity is higher and coupon rate is lower. E. All of t

yield to maturity is higher.
greater.
The longer the maturity, the greater the interest-rate risk. The lower the coupon rate, the greater the interest-rate risk. The lower the yield to maturity, the greater the interest-rate risk. These concepts are refle

Before expiration, the time value of a call option is equal to A. zero.
B. the actual call price minus the intrinsic value of the call.
C. the intrinsic value of the call.
D. the actual call price plus the intrinsic value of the call. E. None of these is

actual call price minus the intrinsic value of the call.
The difference between the actual call price and the intrinsic value is the time value of the option, which should not be confused with the time value of money. The option's time value is the differ

put option
call option

put: option to SELL assets at an agreed price on or before a particular date.
the holder will not exercise unless the asset price is less than the exercise price.
ex: if Fin Corp shares were to fall from 80 to 70, a put option with exercise price of 80 co

hedge ratio of an option

aka delta.
compares the value of a position protected through the use of a hedge with the size of the entire position itself. A hedge ratio may also be a comparison of the value of futures contracts purchased or sold to the value of the cash commodity bei

clearinghouse

guarantees that a future contract will be fulfilled.
once two parties have agreed to enter the transaction, the clearinghouse becomes the buyer and seller of the contract and guarantees its completion.
� Clearing house says if somebody has obligation, suc

sharpe ratio=
treynors measure=
jensons alpha=

0

1. Which of the following statements is (are) true regarding the variance of a portfolio of two risky
securities?
A. The higher the coefficient of correlation between securities, the greater the reduction in the portfolio
variance.
B. There is a linear re

C. The degree to which the portfolio variance is reduced depends on the degree of correlation between
securities.
the lower the correlation between the returns of the securities, the more portfolio risk is reduced

An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the
Capital Allocation Line must:
A. lend some of her money at the risk-free rate and invest the remainder in the optimal risky portfolio.
B. borrow some m

B and C. the only way that an investor can create portfolios to the right of the capital allocation line is to create a borrowing portfolio (buying stocks on margin). in this case, the investor will not hold any of the risk-free security, but will hold on

to find beta, using stdevs..

stdev squared of portfolio / stdev squared of market = beta squared

beta and returns equation =
The risk-free rate is 7 percent. The expected market rate of return is 15 percent. If you expect a stock
with a beta of 1.3 to offer a rate of return of 12 percent, you should

Rate of return < Rf rate + beta (Market rate of return - Rf rate)
sell short the stock because it is overpriced.
12% < 7% + 1.3 (15% - 7%)= 17.4%, therefore stock is overpriced and should be shorted.

systematic vs nonsystematic risk

nonsystematic=unsystematic=diversifiable risk.
uncertainty that comes with company you invest in. it can be reduced through diversification.ex: news specific to small number of stocks, like a sudden strike by employees of a company you have shares in.
sys

multifactor SML

if risk exposures are measured by a multi factor model, the expected rate of return of a security will be a sum of:
Rf rate, sensitivity to F1 risk (its beta) times the risk premium for bearing this risk.......
....the sensitivity of Fn risk (its beta) ti

APT.
how to solve an APT for expected return of a portfolio:
calculate variance for a well-diversified portfolio:

arbitrage pricing theory. law of one price.
an arbitrage opportunity is a portfolio with zero volatility and positive return. no arbitrage in an efficient market. if theres an arbitrage opportunity, everyone will slightly shift their portfolios towards th

CAPM vs APT

APT applies to well diversified portfolios and not
necessarily to individual stocks
� With APT it is possible for some individual stocks to be
mispriced - not lie on the SML
� APT is more general in that it gets to an expected return
and beta relationship

fama-french 3 factor model

asset pricing model that expands on CAPM by adding size and value factors to the market risk factor.
value and small-cap stocks outperform markets on a regular basis.

CAPM vs fama french

CAPM uses one factor (market portfolio) to estimate expected return for an individual stock as compared to the returns of the market as a shoe.
fama french: three factors
1: market risk (market index),
2: company price-to-book ratio, aka book to market ra

how to find variance in a stock model

variance = stdev^2.
so.... stdev^2 = B^2 x stdev^2

what is the volatility and risk premium of a risk free asset?

0

speculation
gamble
fair game

a positive risk premium distinguishes speculation from gambling.
investors taking on risk to earn a risk premium are **speculating.
speculation is undertaken despite the risk bc of a favorable risk return tradeoff.
in contrast, gamblers take on risk even

consider case when investor has to allocate her portfolio btwn risk free money market securities and a risky one. return of the portfolio is:

risk free money market securities have return of Rf, risky one has return of Re
Rp= w*Re + (1-w)Rf
where "w" is the weight on the risky asset

markowitz portfolio selection models

mean variance frontier: minimize variance for each target level of expected return. draw efficient frontier.
optimal risky portfolio: search for the CAL with the highest reward-to-variabliity ratio. locate point P.
risk-riskless asset mix: solve for optim

active management vs passive management

active: security analysis, timing. EMH says no benefit from pursuit active management.
passive: creation of an index fund, buy and hold. supported by EMH.
regardless, its important to select a well-diversified portfolio. select investment policies with ta

jagannathan and wang:

added human capital and cyclical variations in betas

glamour firms

characterized by recent good performance, high prices, and lower book-to-market ratios

jensens measure:
treynors measure:

average return above predicted from the CAPM
aP= Rp-(Rf+Bp(Rm-Rf))
treynor: excess return per unit of systematic risk.
Tp= Rp-Rf / Bp
= avg portfolio return - avg rf rate / portfolio beta

a more easily interpretable measure than the sharpe ratio

developed by modigliani and modigliani.
equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio. then performance can be compared by comparing returns:
M^2= Rp*-Rm

which measure to use? treynor, sharpe, or jensen?
if portfolio represents the entire investment for an individual:
if many alternatives are possible:
if allocating between an active portfolio and an index:

It depends on the investment assumptions
If the portfolio represents the entire investment for an individual: Sharpe Index compared to the Sharpe Index for the market
If many alternatives are possible, use the Jensen's alpha or the Treynor measure. The Tr

bull markets
bear markets

market in which share prices are rising, encouraging buying.
a market in which share prices are falling, encouraging selling

market timing. if weights on the risky assets change: shift to market portfolio in bear/bull markets.
shift to the risk-free asset in bear/bull markets.

market portfolio-bull.
risk-free asset-bear

betas of the portfolio: large in bull or bear markets? small in which?

large in bull markets.
small in bear markets.

style analysis

Returns-based style analysis is a statistical technique used in finance to deconstruct the returns of investment strategies using a variety of explanatory variables. The model results in a strategy's exposures to asset classes or other factors, interprete

effective asset mix

style of the investor's overall portfolio (especially for multiple-managed portfolios

performance evaluation has two main problems:

many observations are needed for significant results.
shifting parameters when portfolios are actively managed makes accurate performance evaluation elusive

bogey portfolio

aka benchmark portfolio: used to evaluate a funds performance. the benchmark is an index that reflects the investment scope of the funds investment.

hedge funds strategies

directional:
bets that one sector or another will outperform other sectors.
nondirectional:
exploits temporary misalignments in security valuations. buys one type of security and sells another. strives to be market neutral. convergence vs relative value.

hedge funds vs mutual funds

...

hedge fund performance

hedge funds tend to outperform the market:
signifcant positive alphas. higher sharpe ratios.
reason?
liquidity (lock up periods, serial correlation of hedge fund returns as an indication of illiquid holdings).
survivorship bias.
changing factor loadings
m

LTCM

long term capital management- a large hedge fund led by nobel prize winning economists and renowned wall street traders that nearly collapsed the global financial system in 1998 as a result of high risk arbitrage trading strategies
big hedge fund due to h

Consider a bond with a coupon rate of 6% paid semi- annually, face value of $1000, maturity of 10 years. Suppose that the interest rate is 5% annually

Then F=$1000, r=2.5% semi-annually, T=20 periods, coupon per 6-month period = 3% of $1000 face value, i.e. $30
� The price of the bond:
Pb= 30/0.025 x (1- (1/(1+0.025)^20) + 1000/(1+0.025^20) = 1077.95

accrued interest

The quoted price does not include the interest that has accrued since the last coupon payment date
� For bonds traded between coupon dates: the buyer pays the accrued interest
� E.g. for a bond with semi-annual coupon payments:
accrued interest = annual c

YTM

realized yield if coupons are reinvested at an IR that is equal to the yield of the bond. if the reinvestment rate is above/below the yield of the bond, then the realized compound return will exceed/fall below it.
the IR that makes the PV of the bonds pay

premium bonds vs dissent bonds. which have higher IRs? higher FV? higher coupon? higher maturity? higher price?

premium bonds have higher price and lower IR.
FV and coupon stay the same for both.

relationship btwn bond prices and yields?

inverse relationship

what is a bonds current yield?

bonds annual coupon pmt divided by the bond price.
the YTM is the bonds internal rate of return.
for bonds selling at a premium, coupon rate > current yield >YTM.
reversed for discount bonds

yield curve

graphic representation of the relationship btwn yield and maturity.
investors can form expectations of future IRs using the yield curve.
a line that plots the IRs, at a set point in time, of bonds having equal credit quality but differing maturity dates.

nelson-siegel function

...

theories of term structure

expecation hypothesis: zerio liquidity premium. upward sloping yield curve means that investors anticipate increase in IRs.
liquidity preference: investors demand a premium to hold long term bonds. liquidity premium is positive, which implies an upward sl

an upward sloping yield curve is associated with the fact that the ___ rate for the coming period is lower/higher than the ___ yield.

forward rate higher than current yield

capital allocation line slope equation?

slope= (Er - Rf)/ stdev

A company whose stock is selling at a P/E ratio greater than the P/E ratio of a market index most likely
has ________.

a dividend yield less than that of the average firm.
profit per earnings ratio.
firms lower than avg dividend yields are usually growth firms, having higher P/E ratio than avg
P/E= (1-B)/(Er-BxROE)

A bond will sell at a discount when __________.
A. the coupon rate is greater than the current yield and the current yield is greater than yield to maturity
B. the coupon rate is greater than yield to maturity
C. the coupon rate is less than the current y

D: coupon rate is less than current yield is less tha YTM.
In order for the investor to earn more than the current yield the bond must be selling for a discount.
Yield to maturity will be greater than current yield as investor will have purchased the bond

how to calculate a forward rate?

forward rate= (1 + i)^N / (1+FwdRateYr1 x 1+FwdRateYr2 )

greater duration is made up what?

longer maturity and lower coupon percent

what factors effect the price of a stock option?

Rf rate, riskiness of stock, and time to expiration. all 3 directly related to price of the option. the expected rate of return on the stock does not affect the price of the option.

the intrinsic value of an at-the-money put option is equal to:

An option is at the money (ATM) if the strike price (the price at which a put or call option can be exercised) is the same as the current spot price of the underlying security. An at-the-money option has no intrinsic value, only time value. For example, w

. To hedge a short position in Treasury bonds, an investor most likely would

buy IR futures.
By taking the long position, the hedger is obligated to accept delivery of T-bonds at the contract
maturity date for the current futures price, which locks in the sales price for the bonds and guarantees
that the total value of the bond-pl

Suppose that the risk-free rates in the United States and in Japan are 5.25% and 4.5%, respectively.
The spot exchange rate between the dollar and the yen is $0.008828/yen. What should the futures price
of the yen for a one-year contract be to prevent arb

.008891dollars per yen.
0.008828 (1.0525/1.045)

give an expression for the systematic risk variance of two stocks:
nonsystematic risk component?

stdev of investment = (B^2 x stdev of market ^2) + (HML coeff^2 x stdev of hml^2)
stdev^2= 0.5 x stdev^2

Construct a portfolio out of the two stocks that has exposure of 1 to the HML factor. Give an
analytical expression of its weights.

W1+W2=1.
Coeff1xW1 + Coeff2xW2=1.

performance attribution procedures.

The portfolio management decision process typically involves three choices: (1) allocation of funds
across broad asset categories, such as stocks, bonds, and the money market; (2) industry (sector) choice
within each category; and (3) security selection w

how to calculate expected return for two stocks, given 3 different states of probability (1,2,3) each with a probability and return amount.
how to calc stdev?
calculate correlation coefficient between two stocks?
If you invest 35% in stock A, and 65% in s

Er= P1xR1 + P2xR2 + P3xR3
stdev^2= P1x((R1-Er1)^2) + P2x(R2-Er2)^2 + P3x(R3-Er3)^2
Cov= ?corr?
ERp- WaxERa + WbxERb
stdev^2= (Wa^2 x stdeva^2 + Wb^2xstdevb^2 + 2 x Wa x Wb x stdeva x stdevb x corra,b

Discuss the differences in risk-taking behavior between investors who are risk averse, risk neutral, and
risk loving

The investor who is risk averse will take additional risk only if that risk-taking is likely to be rewarded
with a risk premium. This investor examines the potential risk-return trade-offs of investment
alternatives. The investor who is risk neutral looks

Discuss duration. Include in your discussion what duration measures, how duration relates to maturity,
what variables affect duration, and how duration is used as a portfolio management tool (include some
of the problems associated with the use of duratio

Duration is a measure of the time it takes to recoup one's investment in a bond, assuming that one
purchased the bond for, say, 1000 euro. Duration is shorter than term to maturity on coupon bonds as
cash flows are received prior to maturity. Duration equ

formula for zero rate coupon bonds

...

protective put.
advantages?

consists of investing in stock and simultaneously purchasing a put option on the stock.
regardless of what happens to the price of the stock, you are guaranteed a payoff equal to the put option exercise price.

You are pricing a European call option using a binomial tree and the Black-Scholes formula. What is the
relationship between the two valuations when you increase/decrease the number of steps in the
binomial tree?

The Black-Scholes formula can be thought of the limiting case of a binomial tree. Increasing the number
of nods in the binomial tree brings the value of the option closer to that of the Black-Scholes formula.
This document is property of Vrije Universitei

an upward sloping yield curve is associated with fact that ........ (forward rate, short rate, current yield)
what explains this?

forward rate for coming period is higher than current yield
increase in forward rate is explained by:
Fn- ERn + liquidity premium

macaulays duration

weighted avg time until CFs are received, and is measured in years for bond duration

duration=
modified duration=

0

dollar duration:

measure price change for a given change in the yield
change in Price / change in Y = -D x P

the duration of a zero coupon bond is what?
for bonds with the same maturity, duration increase/decreases for higher coupons
for bonds with the same coupon rate, duration usually increases/decreases with time to maturity
the duration of a coupon bond is l

equal to its maturity
decreases
increases
higher
: 1+y / y

pros and cons of duration?

pros: key measure of IR sensitivity. easy to compute and interpret.
cons: gives good approximations only for small yields. assumes parallel yield shifts.
applicable only for securities with fixed cash flows.

passive bond management strategies:

aim is to control the risk of a bond portfolio.
bond market indexing and immunization

bond index funds

contains thousands of issues many of which are infrequently traded. bond indexed turn over more than stock indexed as the bonds mature.
therefore, bond index funds only hold a representative sample of the bonds in the actual index.
bond indexed contain th

immunization. limits?

Immunization, also known as "multiperiod immunization," is a strategy that matches the durations of assets and liabilities, thereby minimizing the impact of interest rates on the net worth.
targeting net worth: matching duration of assets and liabilities.

active bond management strategies

swapping strategies:
substitution swap
intermarket swap
rate anticipation swap
pure yield pickup
tax swap
horizon analysis:
Select a particular holding period and predict the yield curve at end
of period.
� Given a bond's time to maturity at the end of th

leverage ratio:

helps determine bond ratings.
assets/equity.
debt to equity ratio.

liquidity ratios:

helps determine bond ratings.
current ratio (current assets/current liabilities)
quick ratio (current assets without inventories/current liabilities)

derivative contract

aka contingent claims, bc their payoffs depend on the value of other securities.
financial contract whose value is derived from the value of an underlying asset
main types of contracts: forwards, futures, options, swaps.
standardized contracts traded on e

key ingredients of an options contract:

call option(BUY at specified price),
put option (SELL at specified price)
underlying asset, exercise/strike price, premium (price of the option), maturity (expiration of the option)
maturity of the option: right to exercise option within 1 year, 2 years,

there are different types of options depending on the time the option can be exercised:

European: can be exercised only at expiration.
American: can be exercised at any time before expiration
Bermudan: exercise is restricted to certain periods during the life of the option

types of options in terms of the underlying.
which option is most liquid and most majority of trade volume?

SIFFI
stock options
index options (buy an option on an index such as AJAX-you don't buy al the stocks, but you buy an ETF share)
futures options (option to enter into a future contract such as entering future contract three months from now to buy oil thre

what is the largest exchange for trading derivatives?

CBOE chicago board of exchange

the clearing house

options clearing corporation (OCC):
effective buyer/writer of the option.
guaranteed contract performance.
margin required from the option writers to guarantee that they will fulfill contract obligations. (depends on the likelihood that the option will be

moneyness of an option

In the money:
� Call option: Market price > Exercise price (you want to exercise your right in this case bc you can buy the underlying for this amount and sell it fro exercise price)
� Put option: Exercise price > Market price
Out of the money:
� Call opt

payoff and profit of a call option=
payoff and profit of a put option=

for the holder:
payoff= max(0,spot price at expiration-strike price)
profit=pay off - option premium
for the holder:
payoff=max(0,strike price-spot price at expiration)
profit=pay off - option premium

covered call

invest in a stock and at the same time write a call option on the stock

straddle

a bet on volatility*
buying both a call and a put on a stock, with the same exercise price and expiration date.
Long call plus long put on a stock with the same strike
price and the same expiration date
� Used by investors who expect that the stock will m

spread
bullish spread

A combination of several calls or puts on the same stock with differing exercise prices of times to expiration
with different exercise prices or times to maturity
� Money spread: exercise prices differ
� Time spread: expiration dates differ
Bullish spread

collar

A strategy designed to keep the value of the portfolio
between two bounds
� Limits upside potential
� Provides downside protection
� Good for targeting some wealth goal
A collar with a net outlay of approximately zero is an options strategy that combines

intrinsic value of an option?
time value of an option?

Intrinsic value of an option: the pay-off if immediate
exercise
� Call: stock price - exercise price
� Put: exercise price - stock price
� Intrinsic value adjustment: PV of the exercise price
Time value of an option = option price - intrinsic value

what determines the value of an option? how does it drive the value of a call option?

-Stock price
� Exercise price
� Volatility
� Time to expiration
� Interest rate
� Dividends
if you hold a call on a stock with exercise price of $80, and the stock is now selling at 90, you can exercise your option to purchase the stock at 80 and simultan

two ways to price options:

binomial tree approach
black and scholes formula

how to construct the replicating portfolio?
how to determine the weights of the replicating portfolio constituents?

A replicating portfolio is a portfolio that replicates the payoff
of the derivative
How to determine the weights of the replicating portfolio
constituents?
� Buy H shares of the underlying stock and invest B in the risk-free
asset (rate rf)
� Solve for H

the price of the call option is the:

risk-free discounted expected payoff using risk-neutral probabilities
the price of the option is the same as the one that we obtain using the replicating portfolio or the perfectly hedged portfolio

start solving a price tree how?

solve for the last nodes first

instead of calculating the replicating portfolio using the hedge ratio H, we can compute what instead?

the risk-neutral probabilities Q at each node, starting from the ones ta time T, and then use those to obtain the call price. this should yield the same result.

Whether we price options using the replicating portfolio or
risk-neutral probabilities, the same general rules apply:

Start by calculating the option pay-offs at expiration for all spot
price scenarios
� Move iteratively backwards one step at a time, calculating option
prices on each node
� Ultimately, you obtain the price today
The time discretization of the tree can be

assumptions underlying the black-scholes formula?

The stock pays no dividends
� Adjust the stock price downwards: S0 - PV(dividends)
� The interest rate and the variance of the stock are
constant
� Stock prices are continuous (no jumps)
I) the risk-free interest rate is constant over the life of the opti

option greeks: measurements of the risk involved in options:

all measurements of sensitivity of the call or the call's greeks.
Delta - aka hedge ratio. the sensitivity to the underlying instrument's price
� Gamma - the sensitivity of delta in response to price changes in the
underlying instrument. how much delta ch

option delta

sensitivity of the price of the option towards changes in the underlying stock price

delta hedging

A portfolio of stocks and options that is hedged against
fluctuations of the price of the underlying
� Recall that:
� Assume that we buy ? shares of the stock and we write
one call option
� If the stock goes up/down by $1, then the option goes
up/down by

the option's gamma

rate of change of delta with respect to the price of the underlying asset (sensitivity with respect to S)

the option's vega:

Volatility risk: the risk from unpredictable changes in
volatility
� While delta-neutral strategies eliminate the risk exposure
from fluctuations in the price of the underlying, the
volatility risk remains
� The option's vega: the sensitivity of an option

when a distribution is negatively skewed...

standard deviation underestimates risk.

When borrowing and lending at a risk-free rate are allowed, which Capital Allocation Line (CAL) should the investor choose to combine with the efficient frontier?

I) The one with the highest reward-to-variability ratio.
II) The one that will maximize his utility.
III) The one with the steepest slope.
all three.
The optimal CAL is the one that is tangent to the efficient frontier. This CAL offers the highest reward-

The standard deviation of a two-asset portfolio is a linear function of the assets' weights when

the assets have a correlation coefficient equal to one.
When there is a perfect positive correlation (or a perfect negative correlation), the equation for the portfolio variance simplifies to a perfect square. The result is that the portfolio's standard d

statistical arbitrage

uses quantitative techniques and often automated trading systems to seek out many temporary misalignments among securities

the YTM on a bond is...

the discount rate that will set the PV of the payments equal to the bond price

Consider a 5-year bond with a 10% coupon that has a present yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be _______

lower.
bond is a premium bond as IRs have declined since the bond was issued. if IRs remain constant, the price of a premium bond declines as the bond approached maturity.
YTM is lower than coupon rate, so it is a premium bond.

given the bond described above, if interest were paid semi-annually (rather than annually), and the bond continued to be priced at $917.99, the resulting effective annual yield to maturity would be:

more than 10%.
if coupon frequencies increase, then duration decreases and we discount over a short time period (on average). Hence, to keep the same price, the yield has to go up.

inverted yield curve

occurs when short term rates are higher than long term rates.
it slopes downward.

The duration of a 20-year zero-coupon bond is

equal to 20.
duration of zero coupon bond equals bonds maturity

Speculators buying put options anticipate the value of the underlying asset will __________ and speculators selling call options anticipate the value of the underlying asset will _______.

decrease, decrease.
The buyer of the put option hopes the price will fall in order to exercise the option and sell the stock at a price higher than the market price. Likewise, the seller of the call option hopes the price will decrease so the option will

future contracts

profits from future contract:The amount that the holder of the long position gains must equal the amount that the holder of the short position loses.
the net profit on the contract is zero- it s a zero-sum game.
A futures contract is a legal agreement, ge

Credit risk in the swap market

is limited to the difference between the values of the fixed rate and floating rate obligations.
Swaps obligate two counterparties to exchange cash flows at one or more future dates. Swaps allow firms to restructure balance sheets, and the firm is obligat

w
=ERe-Rf / A
stdevE^2 weight for portfolio with risky and risk free assets. you've found the optimal risk.
discuss each variable and relationship. assume investor is risk averse.

The optimal proportion in the risky portfolio (the one containing the optimal mix of risky assets) is the one that maximizes the investor's utility. Utility is positively related to the risk premium [E(re)-rf]. This makes sense because the more expected r

How would you define an ideal situation of perfect foresight, (using a graphical interpretation). Hint: think of a derivative instrument.

perfect foresight is equivalent to holding a call option on the index portfolio.

Consider two perfectly negatively correlated risky securities X and Z. X has an expected rate of return of 10% and a standard deviation of 15%, and Z has an expected return of 5% and a standard deviation of 7%. You want to construct a portfolio out of the

What is the formula for the variance of the portfolio?
stdev^2= (WeightE
stdevE - WeightD
StdevD)^2
ii. What is the variance of the portfolio?
It is 0, since the two assets are perfectly negatively correlated.
iii. What proportions of X and Z should you h

What does credit risk mean in the context of bond pricing? Which agencies assess the credit risk of bond issuers? Explain briefly the rating scheme employed by those agencies.

A credit risk is the risk of default on a debt that may arise from a borrower failing to make required payments. Credit risk is measured by credit rating agencies, most important of which are Moody's, Standard & Poor's, and Fitch. Each credit rating agenc

State the put-call parity. Why is it called in such a way? **Derive the put-call parity, using two options strategies that provide the same payoffs.

The put-call parity represents the proper relationship between put and call prices. More specifically,
C + (x/(1+Rf)^T) = S0 +P
call price + purchase price of the ZC bond = purchase price of the stock + put price
To derive the parity, consider two strateg

You hold a portfolio of 56 million euro with a beta of 0.75 on the AEX. You expect that the AEX will drop by 2.5% over the next one year. You decide to hedge the AEX exposure of your portfolio with index futures with expiration of one year. The contract m

Do you buy or sell index futures in order to hedge your position?
You sell index futures
ii. What is the projected loss on your portfolio (in euro), if you do not hedge?
Beta
projected loss (in %)
portfolio value=0.75
0.025
56*10^6=1.05 mil
iii. How much

what is the optimal portfolio for an investor?

along the CAL if there is one risky and one risk free asset. if there is no risk free asset, there is no tangency portfolio that is best for all investors. so investors then choose from the efficient frontier aka indifference curve of risky assets.

portfolio of two risky assets:
(a stock fund and bond fund).
Expected return of portfolio:
Variance of portfolio:
Cov(Re,Rd)=

Erp= We
Ere + Wd
Erd
stdev^2= (We^2)
(stdeve^2) + (Wd^2)
(Stdevd^2) + 2
We
Wd*Cov(Re,Rd)
Cov= stdevE
stdevD
CorrelationDE

in case of perfect positive correlation, what are the diversification benefits?

no diversification benefits (correlationDE=1)

correlation for perfect negative correlation?

correlationD,E = -1

sharpe ratio is shown how on graph?

sharpe ratio= reward to volatility = CAL

passive strategy

investment policy that avoids security analysis.
choose a broad index fund or ETF and divide your savings between it and a money market fund.

simplest way to reduce risk in the risky portfolio?

shift funds from the risky portfolio to the risk-free asset. another method involved diversification of the risky portfolio

a risky investment portfolio (referred to as what?) can be characterized by its what ratio?
this ratio is the slope of what?
what lies on this slope/line?
investors prefer a steepless or steeper slopoing CAL, because of what?

aka the risky asset.
characterized by reward to volatility / sharpe ratio.
its the slope of the CAL, the line connecting the Rf asset to the risky asset.
all combos of risky and risk free asset lie on this line.
steep CAL is preferred bc it means higher e

represents a set of portfolios that maximized expected return at each level of portfolio risk

efficient frontier aka indifference curve

book to market effect

tendency for investments in shares of firms with high ratios of book value to market value to generate abnormal returns

random walk

notion that stock price changes are random and unpredictable.
stock prices should follow a random walk. price changes should be random and unpredictable.
statistical research has shown that to a close approximation stock prices seem to follow a random wal

durbin watson test

examines if there is correlation in residuals.
a number that tests for autocorrelation in the residuals from a statistical regression analysis. always between 0 and 4. 2=no autocorrelation in the sample. approaching 0=positive autocorrelation, approaching

how to assess if markets are informational efficient?

use an event study- measure normal returns over estimated period.
run CAPM model for estimated period to find estimates at time T for a alpha and beta.
run the model and calculate normal return.
NR=AR-ER

TomTom

July 2013: company isn't doing as poorly as people thought. so you expect price of this stock to go up.
step 1: estimate market model.
estimate a and b.
A=0, b=1.23.
then calculate normal returns and compare them to actual returns.
at time 0, there had be

stocks with low book ratio have high or low returns?
inefficiencies?

low book ratio is low returns.
high book ratio have high returns.
inefficiencies?
why would high BTM stocks have low returns if marketers are inefficient? investors may be overoptimistic about some stocks. so market value of stocks go up more than fundame

f you have one source of systematic risk, what will happen when you start aggregating assets in a big portfolio?

systematic component will remain.
if you have a well diversified portfolio, sensitivity will start decreasing.

is there covariance between systematic and nonsystematic risk?

no

how to test CAPM?

o Testing CAPM
� Capm is relationship about expected returns
� First, select a sample from 1 to T
� We want to get the returns of n stocks (a large number of stocks)
� CAPM must hold for all stocks, not just one stock
� We need to find out systematic sour

what does it mean if you reject CAPM?

it means exposed portfolio you used is not efficient.
every test is a test on the efficient scale. so even if we don't find very strong evidence, the CAPM might still hold. this is the reason this is the most popular theoretical model***

if there is a dividend tomorrow and we buy stock today, do we get full divined? or only a fraction?

buy gets full dividend.

for premiums, which are greater than which? current yield, YTM, coupon rate

coupon rate > current yield > YTM.
current yield exceeds YTM bc YTm accounts for the built in capital loss on the bond. the bond bought at premium of 1276 will eventually fall in value to 1000 at maturity.
current yield: investments annual income (interes

price path of premium bond. premium increases or decreases over time. why?

decreases.
eventually at maturity, the bond will be at par. as you approach maturity date, there are less and less coupon payments. closer to maturity, fewer coupon payments. so over time, there is a convergence of premium and discount bonds to the par va

are HPR and YTM always the same?

no, can be very different. HPR is the rate of return over given interval. YTM is an average return if bond is held until maturity and theres no reinvestment.

why are yield curves useful?

we can get info about future IRs from yield curves.
why do we want to know what IRs will be in the future? matters for market risk premium. and for what investors will do.

why do we have different rates? (forward, short, spot)

there is uncertainty in the future. forward rate gives an expectation.

**if you're a risk averse investor, would you like forward rates to be slightly higher or lower than expected rate in order to take account risk that IR might be different than your expectation?

...

when something is risky, what do you expect to get with it?

some sort of risk premium (liquidity premium)

three good ratios for determinants of ratings:

coverage ratio (comparing earnings to fixed costs. you expect company with high coverage ratio to have high rating).
leverage ratio.
liquidity ratio: compare assets to liabilities (assets/liabilitiyes). if you have more assets on your balance sheet, you a

sinking funds

a fund formed by periodically setting aside money for the gradual repayment of a debt or replacement of a wasting asset.
when you issue a fixed income security, you pay a coupon payment. at end you pay the larger FV. at time of maturity there is a very la

if you are worried issuer won't pay back everything, in case of default, the bond you had will be bought back first.
if you are worried that issuer won't pay back debt, you can impose this covenant saying that you have a max on amount of divined you can p

subordination of further debt
dividend restrictions

collateral

issuer pledges some assets to the bondholder, in case the issuer defaults on their obligation (equipment, building, etc)

promised YTM vs expected YTM

� YTM is not the actual yield that you get
� Promised YTM: what we infer from current prices
� Expected YTM: takes into account probabilitiy/likelihood that issuer might default on their obligation

what means " to hold the broader market

indexing

this is specific for fixing securities. try to completely eliminate any IR risk in our portfolio

immunization.
Suppose you are managing APP fund. What is your biggest risk (for a pension fund)? Interest- IR risk bc you have huge liabilities with very long duration (30-40 years). Your assets cant match this duration. If theres a decrease in IR, presen

price risk
reinvestment risk

� Technique that targets net worth, matching duration of assets and liabilities
o When you invest in fixed income securities- problem with price risk (change in value of fixed income security), and problem with reinvestment risk (refer to fact that you re

swapping strategies

benefit from projected or real changes in IRs. A bond swap consists of selling one debt instrument in order to use the proceeds to purchase another debt instrument. Investors engage in bond swapping with the goal of improving their financial positions. Bo

bond swapping strategies

substitution swap: long in some undervalued asset and short in overvalued asset with similar risk profile. An exchange that is carried out by trading a fixed-income security for a higher yielding bond with similar features. A substitution swap involves th

horizon analysis

The analysis of a security or portfolio's total returns over a period of time, referred to as the investment horizon. Horizon analysis allows an investor to assess performance under different levels of risk, market yields and return expectations. This is

what is good/special about derivatives?

their payoffs can be higher and nonlinear to underlying asset.
very bad payoffs if things are bad.

contingent claims

aga derivatives.

is a call option an obligation?

no, it is an option. if it was an obligation, it would be called a future.

exercise price

aka strike price.
pay a premium to get this asset.
price at which you agree to give that option to the holder. give holder right to buy the underlying asset at pre specified exercised/strike price

investing in options versus the stock market: 3 options:

invest entirely in stock. this is risky. using no derivatives. it stock goes below 100, your rate of return -100. you will get nothing.
call options with 6 month to maturity. strike price of 100.
1000 in call option and rest in T bills. safest option.

what is a perfectly hedged position?

value is independent of value of stock price at year end

two ways to calculate value of our call right now:

1) calculate replicating portfolio where we had a fraction invested in stock and in riskless bonds
2) discounting payoffs in two stages of world using risk neutral probabilities. when apply binomial tree approach, we don't know actual/true probabilities.

in case of call, do we want underlying to have high or low value?

high, in case of call. for higher returns.

why do we buy future contract instead of buying underlying today? why postpone?

benefit if there was a price increase (speculation)

three options for pricing of options:

replication portfolio, risk neutral probabilities, black scholes formula

what is the yield to maturity on a bond

the discount rate that will set the present value of the payments equal to the bond price.
NOT based on assumption that any payments received are reinvested at the coupon rate.

the intrinsic value of an out of the money call option is equal to what?

zero- the fact that the owner of the option can buy the stock at a price greater than the market price gives the contract an intrinsic value of zero, and the holder will not exercise

stdev in APT model?

stdev^2= (1/n)*(stdev^2)

how to calculate interest rate for a bond?

(Face Value / Price ) ^1/N

graph of a call option?
graph of a put option?

horizontal line shows the cost of the option (if it costed $14, then the horizontal line is at -$14, and then slopes diagonally for a profit
downward sloping line from 0 to the exercise price of 80. then horizontal flat line from 80 to the right

how to make a binomial tree and definition:

an option valuation model predicated on the assumption that stock prices can move to only two values over any short time period. binomial model requires a computer to be useful in actual trading.
start with stock price. you buy the stock at 100. then the

when to use binomial model vs black-scholes

both are option valuations.
while binomial model we have described is extremely flexible, it requires a computer to be useful in actual trading.
an option-pricing formula would be far easier to use than the tedious algorithm involved in the binomial mode.

black scholes formula

values an option that uses the stock price, risk free interest rate, the time to expiration, and the standard decimation of the stock return.
used to price european-style call options

standard deviation of portfolio with one risky and one risk free asset?

stdevP=W*stdevRisky asset
weight of whole portfolio = the weight of the risky asset * stdev risky asset

you took a short position in three S&P 500 futures contracts at a price of 90 (the contract multiplier is 250) and closed the position when the index futures was 885, you incurred:

a gain of $11,250
900-885=15 x250 x3

one reason swaps are desirable is that

they offer participants easy ways to restructure their balance sheets.
for example, a firm can change a floating rate obligation into a fixed rate obligation and vice versa

. The buyer of an American call option on a non-dividend paying stock will
A. always exercise the call as soon as it is in the money.
B. only exercise the call when the stock price exceeds the previous high.
C. never exercise the call early.
D. buy an off

C: an american call option buyer will not exercise early if the stock does not pay dividends; exercising forfeits the time value. rather, the option buyer will sell the option to collect both the intrinsic value and the time value

Construct a portfolio out of the three stocks that has exposure of 1 to the Size factor
and an exposure of 0.5 to the Value factor. Provide the system of equations to be used
to solve for the weights. You do not need to find the explicit solution for the

The weights solve the following system of equations:
??1+??2+??3 =1
??1??1+??2??2+??3??3 =1
??1??1+??2??2+??3??3 =0.5

how to compute the prices, duration, and the modified duration of bonds.
Consider the data on the following three coupon bonds:
Bond Maturity Coupon Yield Face Value
A 2 0.07 0.02 100
B 3 0.06 0.03 100
C 4 0.04 0.04 100
i. Compute the prices, duration and

P= coupon/(1+YTM) + (FV+YTM)/(1+YTM)^N
For bond A:
PA = 7/1.02 + 107/1.02^2 =109.71
DA = 1
7/1.02/109.71 + 2
107/1.02^2/109.71 = 1.94
DA* = 1.94/(1+0.02) = 1.90
You can easily follow the steps for the other two bonds
Price Duration Modified Duration
Bond

Discuss the relationship between option prices and a) volatility of the underlying stock, and b)
the exercise price

The greater the volatility of the underlying stock, the greater the option premium; the more
volatile the stock, the more likely it is that the option will become more valuable (e. g., move
from an out of the money to an in the money option, or become mor