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50 Cards in this Set
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Define Interest Rate with an equation of premiums.

r = Real riskfree rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium


Future Value equation

FV = PV(1+r)^n


Future Value from Stated Annual Interest Rate

SAR = Quoted Interest Rate; with more than one compounding period per year, FV = PV(1+r/m)^mn
where m = periodicity 

Future Value from Continuous Compounding

FVn = PVe^(r*N)


finding Effective Annual Rate (EAR) from Periodic interest rate

EAR = (1 + Periodic interest rate)^m  1


finding EAR from continuous compounding

EAR = e^r  1


define: Annuity, Ordinary Annuity, Annuity Due, and Perpetuity

Annuity  a finite set of level sequential CFs
Ordinary Annuity  first CF that occurs one period from now (t=1) Annuity Due  first CF occurs immediate (t=0) Perpetuity  set of level neverending sequential CFs, with first CF occuring at t=1 

Future Value of an Annuity

FV = A*[((1+r)^n  1)/r]


How does PV relate to discount rate and number of periods?

1. For a given discount rate, the farther in the future the amount to be received, the smaller that amount's present value
2. Holding time constant, the larger the discount rate, the smaller the present value of a future amount 

Present Value of a Perpetuity

PV = A/r as long as interest rates are positive


solve for interest Rates and Growth Rates

g = (FV/PV)^(1/n)  1


Cash Flow Additivity

dollar amounts indexed at the same point in time are additive. use when dealing with uneven cash flows


NPV Rule and equations

if the investment's NPV is positive, an investor should undertake it, if NPV is negative, investor should not take it.
NPV = sum(CFt/(1+r)^t) 

IRR rule

Accept projects for which the IRR is greater than the opportunity cost of capital or the hurdle rate. IFF is only correct if CFs are reinvested at IRR.


Problems with IRR rule

IRR and NPV rules project differently when:
1. size or scale of the projects differ 2. the timing of the projects' cash flows differ when IRR and NPV rules differ, follow NPV b/c NPV represents the expected addition to shareholder wealth from an investment. 

Holding Period Return (Holding Period Yield)

HPR = (P1  P0 + D1)/P0


MoneyWeighted vs. TimeWeighted Returns

MW accounts for the timing and amount of all dollar flows into and out of the portfolio. Generally, clients determine when money is given to the manager and how much money is given  which may influence the manager's moneyweighted ROR.
TW measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period. Not sensitive to additions and withdrawals of funds; returns are averaged over time. To compute TW; price portfolio, compute HPR for each subperiod, obtain annual ROR, and take geometric mean of annual ROR for average. 

define Money Market, Pure Discount Instrument, Discount, Bank Discount Basis

MM = market for shortterm debt instruments.
Pure Discount  pay interest as the difference b/w the amount that gives the price for the Tbill. Discount  reduction from the face amount that gives the price for the Tbill. Bank Discount Basis  used to quote Tbills, based on 360day year, a percentage of face value. 

equation for Yield on a Bank Discount Basis and why is it not a meaningful measure

r = D/F * 360/t
1. yield based on face value of bond, not purchase price 2. yield annualized on 360day year 3. bank discount yield annualized with simple interest ignores opportunity to earn interest on interest 

Effective Annual Yield (EAY)

EAY = (1 + NPY)^(365/t)  1
does account for interestoninterest. Generally more than the bank discount yield. 

Money Market Yield

r = 360(bank discount rate)/[360  (t * bank discount rate)]


define Descriptive Statistics and Statistical Inference

Descriptive  study of how data can be summarized effectively to describe the important aspects of large data sets.
Statistical  making forecasts, estimates, or judgements about a larger group from the smaller group actually observed. 

define Population, Parameter, Sample, Variance, Sample Statistic.

Population  all members of a specified group
Parameter  any descriptive measure of a population. Sample  a subset of a population Variance  range of investment returns. Sample Statistic  a quantity computed from or used to describe a sample. 

define Measurement Scales: Nominal, Ordinal, Interval, and Ratio Scales.

Nominal Scale  the weakest level of measurement, categorize data but do not rank them.
Ordinal  stronger level of measurement, categories that are ordered with respect to some characteristics Interval  ranks and assures that the differences b/w scale values are equal. Ratio  strongest level, interval scale plus a true zero point as the origin. 

Define Frequency Distribution and explain how to construct.
What is Absolute Frequency, Relative Frequency, and Cumulative Relative Frequency? 
Frequency Distribution  tabular display of data summarized into relatively small number of intervals.
determine range and number of intervals (k), Divide range/k for interval end points, count # points falling into each range, construct table to show observations. Absolute Frequency is the actual number of observations in a given interval. Relative Frequency is the absolute frequency of each interval divided by the total number of observations. Cumulative Relative Frequency adds the relative frequency as we move from the first to last interval. 

define Histogram and Frequency polygon

Histogram  bar chart of data that have been grouped into frequency distribution.
Frequency Polygon  plot midpoint of each interval on xaxis and absolute frequency for that interval on yaxis; connect points with straight line. 

define arithmetic mean, population mean, and sample mean, median, mode.
What is important about arithmetic means, drawbacks? 
Arithmetic  sum of observations divided by total number of observations
Population  arithmetic mean value of a population Sample  (average) arithmetic mean value of a sample. Median  value of the middle item of a set Mode  most frequently occurring value in a distribution. Deviations from arithmetic means indicate risk. A drawback is its sensitivity to extreme values. Can also compute a weighted mean. 

define Geometric Mean and what would it be used for? Formula for Geometric Mean Return?

the most frequently used to average rates of change over time or to compute the growth rate of a variable.
Compute by multiplying all rates, take the nth root of the product. Rg = [product(1+Rt)^t]^(1/t)1 

define Harmonic Mean and what is it used for?

the value obtained by summing the reciprocals of the observations  terms of the form 1/X  then averaging that sum by dividing it by the number of observations, n, then taking the reciprocal of the average.
X = n/sum(1/X) Special type of weighted mean in which the weight is inversely proportional to its magnitude. Most appropriate when averaging ratios when the ratios are repeatedly applied to a fixed quantity to yield a variable number of units (EX: cost averaging). 

define Quartiles, Quintiles, Deciles, Percentiles.
How can they be used in investment practice? 
QUARTILES divide the distribution into quarters, QUINTILES into fifths, DECILES into tenths, PERCENTILES into hundredths.
Used in portfolio performance evaluation, strategy development & research. characterize an investment in terms of quartiles in which they fall relative to the performance of peers. 

define Dispersion, Mean Absolute Deviation, Absolute Dispersion, Range, Variance, Standard Deviation, Population Variance, and Population Standard Deviation.

Dispersion  variability around central tendency
Mean Absolute Deviation  (MAD) variance & SD MAD = sum(abs(xxi))/n Absolute Dispersion  the amount of variability present without comparison to any reference point or benchmark. Range  the difference b/w the max and min values in a data set. Variance  average of the squared deviation around the mean. Standard Deviation  positive square root of the variance. Population Variance  σ^2 = sum(Xiu)^2/n where u=population mean Population SD = σ = sqrt(σ^2) 

define Semivariance, Semideviation, Chebyshev's Inequality

Semivariance  defined as the average squared deviation below the mean.
Semideviation  the positive square root of semivariance. Semivariance = (XiX)^2/(n1) Chebyshev's Inequality  the proportion of the observations within k standard deviations of the arithmetic mean is at least 1  1/k^2 for all k>1. 

define Relative Dispersion, Coefficient of Variation (and formula), Sharpe Ratio (and formula, and limitation)

Relative Dispersion  the amount of dispersion relative to a reference value or benchmark.
Coefficient of Variation  ratio of the SD of a set of observations to their mean value; CV = SD/X Sharpe Ratio  S = (RpRf)/SDp Rf risk free return Rp portfolio return SDp SD of portfolio measures excess return over risk taken, but Sharpe is limited to only considering one aspect of risk, the SD of return. 

Symmetry and Skewness in Return Distributions. Describe characteristics of Normal Distribution.
Define Skewness. 
Normal Distribution: 1. its mean and median are equal.
2. Completely described by its mean and variance 3. roughly 68% of observations b/t +/ 1 SD, 95% b/t +/ 2 SDs, 99% b/t +/ 3 SDs. Skewness  a nonsymmetrical distribution. Computed as the average cubed deviation from the mean standardized by dividing by the SD cubed to make the measure free of scale. Sk = [n/(n1)(n2)]*[sum(XiX)^3/SD^3] 

define Kurtosis, Leptokurtic, Platykurtic, Mesokurtic.
What do they describe. Write equation to compute excess kurtosis. 
Kurtosis  statistical measure that telss when a distribution is more or less peaked than a normal distribution.
Leptokurtic  more peaked than normal Platykurtic  less peaked than normal Mesokurtic  distribution identical to the normal distribution. Describe the depth and width of a normal distribution curve. Sample Excess Kurtosis Ke={n(n+1)/(n1)(n2)(n3)*(XiX)^4/SD^4}[3(n1)^2/(n1)(n2)] 

Contrast Variance with Semivariance and Target Semivariance

Variance  average of the squared deviation around the mean.
Semivariance  average squared deviation below the mean Target Variance  average squared deviation below a stated target. Variance is often used to measure an asset's risk, but since investors are only concerned with downside risk, use semivariance to determine the downside risk. Target semivariance can be used to determine the risk below a stated target. 

define Probability

the 2 defining properties are as follows:
1. the probability of any event E is a number b/t 0 and 1 2. the sum of the probabilities of any set of mutually exclusive and exhaustive events equals 1. mutually exclusive means that only one event can occur at a time, exhaustive means that the events cover all possible outcomes. 

Name and Define the 3 types of Probability.

Empirical  probability of an event as a relative frequency of occurrence based on historical data.
Subjective  probability drawing on personal or subjective judgment  of great importance to investors. A Priori  baed on logical analysis rather than on observation or personal judgment. A Priori and Empirical probabilities are usually referred to as Objective Probabilities. 

Probabilities stated as Odds of event E happening and not happening.

1. Odds of E = P(E)/[1P(E)]
2. Odds against E = [1P(E)]/P(E) the reciprocal of odds for E. 

define Unconditional, Conditional, and Joint probabilities. Show examples and equations of each.

Joint  answers "What is the probability of both A and B happening?"
Unconditional  answers straightforward questions such as "What is the probability of this event A?" Conditional  answers the question "What is the probability of A, given B has occurred?" This is equal to the joint probability of A and B divided by the probability of B. P(AǀB)=P(AB)/P(B),P(B)≠0 

define Multiplication Rule of Probability, and Addition Rule.

Multiplication  joint probability of A and B: P(AB) = P(AǀB)P(B)
Addition Rule  probability that A or B occurs, or both occur, is equal to the probability that A occurs, plus the prob that B occurs, plus the prob that B occurs minus prob that A and B occur. P(AorB) = P(A)+P(B)P(AB) 

Define Independent Events, and Multiplication Rule for Independent Events.

Independent Event  two events A and B are independent if and only if P(AǀB)=P(A) or P(BǀA)=P(B)
Multiplication Rule  when 2 events are independent, the joint prob of A and B equals the product of individual prob of A and B. P(AB)=P(A)P(B) 

define Total Probability Rule
define Expected Value, Variance, and Standard Deviation 
Total Probability Rule:
1. P(A)=P(AS)+P(ASc) =P(AǀS)P(S)+P(AǀSc)P(Sc) 2. P(A)=P(AS1)+P(AS2)+...+P(ASn) P(A)=P(AǀS1)P(S1)+P(AǀS2)P(S2)+...+P(AǀSn)P(Sn) where Sn are mutually exclusive and exhaustive scenarios. Expected Value of a random variable is the probweighted average of the possible outcomes of the random variable. Denoted as E(X) E(X)=P(X1)X1+P(X2)X2+...+P(Xn)Xn Variance of random variable is the expected value of squared deviations from the random variable's expected value. σ^2(X)=E[(XE(X))^2] Standard Deviation is the positive square root of variance. 

define Conditional Expected Values and Total Probability Rule for Expected Value.

Conditional E(X)=expected value of random variable X given an event or scenario S is denoted E(XǀS).
E(XǀS)=P(X1ǀS)X1+P(X2ǀS)X2+...+P(XnǀS)Xn Total Probability Rule for E(X): principle for stating unconditional expected values in terms of conditional expected values: 1. E(X)=E(XǀS)P(S)+E(XǀSc)P(Sc) 2. E(X)=E(XǀS1)P(S1)+...+E(XǀSn)P(Sn) 

Example: use Total Probability Rule for Expected Value to determine expected EPS when rates can decline or stay stable.

E(EPS) = E(EPSǀdeclining rates)* P(declining rates) + E(EPSǀstable rates)* P(stable rates)


Properties of Portfolio Expected Value

1. E(w1R1)=w1*E(R1)
2. E(w1R1+w2R2+...+wnRn) = w1*E(R1)+w2*E(R2)+...+wn*E(Rn) to calculate the Expected Return of a Portfolio: E(Rp) = sum(wn*E(Rn) 

define Covariance. What does a positive, negative, and 0 covariance mean.
define Correlation and its properties. 
Cov(Ri,Rj)=E[(RiE(Ri))(RjE(Rj))]
if Covariance is negative, return on one asset is above its expected value, return on the other is below expected value. Covariance is 0 if returns on assets are unrelated. Covariance is pos if returns on both assets tend to be on the same side (above or below) their expected values at the same time. Correlation b/t 2 random variables Ri and Rj defined as p(Ri,Rj)=Cov(Ri,Rj)/σ(Ri)σ(Rj). Properties of Correlation: 1. Corr is a number b/t 1 and 1 for 2 variables X and Y. 2. Corr of 0 indicates an absence of any linear relationship b/t the variables. Pos Corr indicates an increasingly strong pos. linear relationship, and neg corr indicates negative linear relationship. 

When are two random variables independent? What is the expected values of two random uncorrelated variables?

X and Y are independent if and only if P(X,Y)=P(X)P(Y).
EV of the product of uncorrelated random variables is the product of their expected values. E(XY) = E(X)E(Y) 

Bayes' Formula

given a set of prior probabilities for an event of interest, if you receive new information, the rule for updating your probability of the event is:
Updated probability of event given new info = (Prob of new info given event/Unconditional prob of new info)*Prior prob of event. OR P(EventǀInfo)=[P(infoǀEvent)/P(Info)]*P(Event 

define multiplication rule of counting.
Multinomial Formula Combination Formula Permutation Formula 
Multiplication: if one task can be done in n1 ways, and a second task, given the first, can be done in n2 ways...for k tasks, then the number of ways k tasks can be done is (n1)(n2)...(nk)
Multinomial: n!/(n1!n2!...nk!) Combination: C = (n!/(nr)!r!) Permutation: P = n!/(nr)! Multinomial: number of ways that n objects can be labeled with k different labels, with n1 of the first type... Combination: number of ways to choose r objects from a total of n objects, when order in which th r objects does not matter. Permulation  number of ways to choose r objects from a total of n objects, when the order in which the r objects are listed does matter. 