Portfolio

Weight on the exam = 5%

Number of formulas = 12

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.

E(R) - expected rate of return

P_{i} - probability that state of ecomony i will occur

R_{i} - 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

σ^{2} - variance of returns

P_{i} - probability that state of ecomony i will occur

R_{i} - asset return if the economy is in state i

Standard deviation of returns

σ - standard deviation of returns

σ^{2} - variance of returns

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

E(R) - expected rate of return

R_{i,1} - return on asset 1 in state of economy i

R_{i,2} - return on asset 2 in state of economy i

P_{i} - probability that state of ecomony i will occur

E(R_{1} ) - expected return on asset 1

E(R_{2} ) - 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.

E(R) - expected rate of return

R_{t,1} - return on asset 1 in period t

R_{t,2} - return on asset 2 in in period t

R _{1} - mean return on asset 1

R _{2} - mean return on asset 2

n - number of returns

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Correlation coefficient

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(R_{i} ,R_{j} ) - correlation coefficient between R_{i} and R_{j}

Cov(R_{i} ,R_{j} ) - covariation coefficient between R_{i} and R_{j}

σ(R_{i} ) - standard deviation of R_{i}

σ(R_{j} ) - standard deviation of R_{j}

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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

E(R_{p} ) - expected portfolio return

w_{i} - percentage of the total portfolio value invested in asset i

E(R_{i} ) - expected return on asset i

Expected return for a 2-assets portfolio

E(R_{p} ) - expected portfolio return

w_{1} - percentage of the total portfolio value invested in asset 1

w_{2} - percentage of the total portfolio value invested in asset 2

E(R_{1} ) - expected return on asset 1

E(R_{2} ) - 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.

or

σ_{p} - standard deviation for a portfolio

w_{1} - percentage of the total portfolio value invested in asset 1

w_{2} - percentage of the total portfolio value invested in asset 2

σ_{1} - standard deviation of returns of asset 1

σ_{2} - standard deviation of returns of asset 2

COR_{1,2} - correlation of returns of assets 1 and 2

Cov_{1,2} - 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.

E(R_{p} ) - expected return of a portfolio

r_{f} - risk free rate

σ_{p} - standard deviation of portfolio returns

E(R_{M} ) - expected return of a market portfolio

σ_{M} - 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).

Risk_{tot} - total risk

Risk_{sys} - systematic risk

Risk_{unsys} - 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.

β_{i} - beta of asset i

Cov_{i,mkt} - covariance of returns of market and asset i

σ_{mkt} ^{2} - 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.

E(R_{i} ) - expected return of asset i

r_{f} - risk free rate

β_{i} - beta of asset i

E(R_{mkt} ) - 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

E(R_{s} ) - expected return of a stock

E(R_{zbp} ) - expected return of zero beta portfolio

β_{s} - beta of the stock

E(R_{mkt} ) - expected market return

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