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Portfolio

 

Weight on the exam = 5%

Number of formulas = 12

CFA formulas

quantitative economics financials

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fixedincome derivatives alternative

 

Expected rate of return

Expected rate of return is the return that analyst's calculations suggest a security should provide. Here the expected rate of return is based on the probabilities of different states of economy occurs and the respective returns for these states.

exprr

E(R) - expected rate of return

Pi - probability that state of ecomony i will occur

Ri - asset return if the economy is in state i

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Variance of returns

Variance of returns is a measure of the risk (volatility) of an asset

varr

σ2 - variance of returns

Pi - probability that state of ecomony i will occur

Ri - asset return if the economy is in state i

Standard deviation of returns

varr2

σ - standard deviation of returns

σ2 - variance of returns

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Covariance

Covariance is a measure of the co-movement (linear association) between the returns of two assets.

covar

E(R) - expected rate of return

Ri,1 - return on asset 1 in state of economy i

Ri,2 - return on asset 2 in state of economy i

Pi - probability that state of ecomony i will occur

E(R1) - expected return on asset 1

E(R2) - expected return on asset 2

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Sample covariance

Sample covariance is focused on the calculation of the covariance between two asset returns using historical data.

scovar

E(R) - expected rate of return

Rt,1 - return on asset 1 in period t

Rt,2 - return on asset 2 in in period t

R1 - mean return on asset 1

R2 - mean return on asset 2

n - number of returns

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Correlation coefficient

correlation

Correlation coefficient measures the strength and the direction of a linear relationship between two variables. The correlation coefficient can range from -1 to +1

COR(Ri,Rj) - correlation coefficient between Ri and Rj

Cov(Ri,Rj) - covariation coefficient between Ri and Rj

σ(Ri) - standard deviation of Ri

σ(Rj) - standard deviation of Rj

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Expected return for a portfolio

Expected return for a portfolio is the weighted average of the returns on the individual assets, using their portfolio weights

exprp1

E(Rp) - expected portfolio return

wi - percentage of the total portfolio value invested in asset i

E(Ri) - expected return on asset i

Expected return for a 2-assets portfolio

exprp2

E(Rp) - expected portfolio return

w1 - percentage of the total portfolio value invested in asset 1

w2 - percentage of the total portfolio value invested in asset 2

E(R1) - expected return on asset 1

E(R2) - expected return on asset 2

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Standard deviation for 2-asset portfolio

Standard deviation of returns is a measure of risk focused on the dispersion of returns from the mean.

stdp1

or

stdp2

σp - standard deviation for a portfolio

w1 - percentage of the total portfolio value invested in asset 1

w2 - percentage of the total portfolio value invested in asset 2

σ1 - standard deviation of returns of asset 1

σ2 - standard deviation of returns of asset 2

COR1,2 - correlation of returns of assets 1 and 2

Cov1,2 - covariance of returns of assets 1 and 2

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CML equation

Capital market line (CML) is the line with an intercept point equal to the risk-free rate that is tangent to the efficient frontier of risky assets. It represents the efficient frontier when a risk-free asset is available for investment.

cmle

E(Rp) - expected return of a portfolio

rf - risk free rate

σp - standard deviation of portfolio returns

E(RM) - expected return of a market portfolio

σM - standard deviation of a market portfolio returns

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Total risk

Total risk is the sum of systematic (the variability of returns that is due to macroeconomic factors that affect all risky assets) and unsystematic risk (risk that is unique to an asset, derived from its particular characteristics; it can be eliminated by a diversification).

totr

Risktot - total risk

Risksys - systematic risk

Riskunsys - unsystematic risk

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Beta

Beta is a standardized measure of systematic risk based upon an asset's covariance with the market portfolio.

beta

βi - beta of asset i

Covi,mkt - covariance of returns of market and asset i

σmkt2 - variance of market returns

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CAPM

Capital asset pricing model (CAPM) is an equation describing an expected return of any asset (or portfolio) as alinear function of its beta relative to the market portfolio.

capm

E(Ri) - expected return of asset i

rf - risk free rate

βi - beta of asset i

E(Rmkt) - expected market return

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Zero-beta CAPM

Zero-beta portfolio is a portfolio of securities with returns that are uncorrelated with market returns

zcapm

E(Rs) - expected return of a stock

E(Rzbp) - expected return of zero beta portfolio

βs - beta of the stock

E(Rmkt) - expected market return

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