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37 Cards in this Set
 Front
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Correlation formula 
p1,2 = Cov1,2  σ1 σ2 

Variance of a two asset portfolio 
with covariance: σ2 = w1^2 *σ1^2 + w2^2*σ2^2 + 2*w1*w2*covariance(1,2)
with correlation: σ2 = w1^2 *σ1^2 + w2^2*σ2^2 + 2*w1*w2*p1,2σ1σ2 

Expected return on a 2 asset portfolio 
E(Rp) = w1E(R1) + w2E(R2)
where E(Rp) is the expected return on portfolio P w = weighting of that asset E(R) expected return on that asset


Capital allocation line (CAL) 
describes the combinations of expected return and standard deviation of return available by combining an optimal portfolio of risky assets with the riskfree asset; the graph of this starts at the intersection of the RFR return and is tangent to the efficient frontier of risky assets – the line itself represents an optimal portfolio of risky assets
Y = a +bX E(Rc) = [E(Rt)  Rfr] RfR +  x σc σt


Capital market line (CML) 
when investors share identical expectations about mean returns, variance of returns, and correlations of risky assets; when the CAL is the same for all investors E(RA) = [E(RM)  Rfr] x σA RfR +  σM


Relationship between CAL and CML 
CML is when the CAL is the same for all investors 

Equally weighted portfolio risk 


CML and CAPM 
CML represents the efficient frontier when the assumptions of the CAPM hold 

Security market line (SML) 
is the graph of the CAPM model, or the CAPM equation
CAPM = E(Ri) = RFR + Beta * (E(R of Market) – RFR) 

Beta definition as it relates to the market 
Beta is a measure of the asset’s sensitivity to movements in the market Covi,m  σm^2 σi pi,m x  σm pi,mσiσm  σm^2 

Market risk premium 
E(Rm)  RFR 

Sharpe Ratio 
the ratio of mean return in excess of the RFR to the standard deviation of return (E(Ri) – RFR)  sd of Asset i 

Adding assets to the portfolio and the Sharpe Ratio 
Adding a new asset to your portfolio is optimal if the following condition holds: 

Market Model 
describes a regression relationship between the returns on an asset and the returns on the market portfolio 

Market Model assumptions 
The expected value of the error term is 0 

Adjusted beta 
if historical beta is not deemed to be the best predictor, can use adjusted beta 

Historical beta 
assumes that beta for each stock is a random walk from one period to the next, and the error term mean is “0” – so Beta t+1 = Beta t + error (or 0) 

Multifactor model 
multifactor models could also address: interest rate movements, inflation, or industryspecific returns 

Active return 
return on portfolio – return on the benchmark (comparable to the portfolio) 

Active risk 
the standard deviation of active returns 

Active factor risk 
the contribution to active risk squared resulting from the portfolio’s differentthanbenchmark exposures relative to factors specified in the risk model 

Active selection risk or Active specific risk 
the contribution to active risk square resulting from the portfolio’s active weights on individual assets as those weights interact with assets’ residual risk = sum of weight differences and variances of the asset’s returns unexplained by factors 

Tracking error 
synonym with active risk, but the term “error” is confusing as it is meant to represent “difference” here 

Tracking risk 
also a synonym of active risk = 

Separation theorem 
everyone holds the same portfolio of risky assets and individual investor’s determine the weight of that portfolio with their domestic RFR “separately” 

Real exchange rate movements 
are defined as movements in the exchange rates that are not explained by the inflation differential between the two countries 

Foreign currency risk premium working in concert with interest rate parity 
E(R) – RFR, or the expected movement in the exchange rate less the interest rate differential (domestic RFR – foreign RFR), and after factoring in appreciation/depreciation for the period 

Information ratio 
a tool for evaluating mean active returns per unit of active risk  =  annualized residual risk w
IR = IC x √BR 

Information Coefficient 
measures managers forecasting accuracy if a manager makes N bets on the direction of the market and Nc are correct, the IC is the covariance between forecast and actual direction of the market
IC = 2x (Ncorrect/Ntotal guesses)  1
when we add another source of information that is correlated, the skill (IC) of the manager does not increase proportionately. ICcom represents the new info. ICcom = ICorig x √(2/1+r)
where r = correlation


expost information ratio 
related to the tstat one obtains for alpha in the regression of portfolio excess returns against benchmark excess returns: tα t statistic of alpha  √n number of years of data 

Value added 
Objective of active management is to maximize value added
VA = α  (λ x ω^2)
λ = risk aversion ω = residual risk 

Highest achievable value added * 
function of optimal level of residual risk and the portfolio managers IR
VA* = ω* x IR  or 2
VA* = IR^2  or 4λ
VA* = IC^2 x√BR  4λ 

Breadth 
# of forecasts made in a year
IR = IC x √BR 

Optimal level of residual risk
ω* 
ω* = IR IC x √BR  =  2λ 2λ
λ = risk aversion 

Systematic Risk 
reflects factors that have general effect on the securities market as a whole and cannot be diversified away
for example macroeconomic risk represented by Beta 

Unsystematic risk 
can be reduced through diversification 

The single factor market model covariance calculation 
One of the predictions of the singlefactor market model is that Cov(Ri,Rj) = bibjsM2. In other words, the covariance between two assets is related to the betas of the two assets and the variance of the market portfolio. 