CFP - Formulas Flashcards
Rp
Portfolio Return
Rm
Market or Benchmark Return
σp
standard deviation of portfolio returns (Variability)
σm
standard deviation of market returns
ρpm
Correlation of p to m
(ranges from -1 to +1)
R-Squared
Correlation Squared. AKA “Coefficient of Determination”
This number must be 80%. Otherwise risk-adjusted performance numbers are not valid.
Rf
Risk Free rate of return (90 day T-Bill)
βp
Portfolio Beta (systematic risk) (Volatility) = relative variability
Risk Premium of the Market
Rm – Rf
Market or Benchmark Return - Risk Free rate of return (90 day T-Bill)
Risk Premium of a portfolio
β(Rm – Rf)
Active Return
Rp – Rm
Portfolio Return - Market or Benchmark Return
“alpha” (be careful not to confuse this with Jensen’s alpha)
Active Risk
σ(Rp – Rm)
(Tracking Error (TE)) = standard deviation of active returns
Portfolio Beta
βp=ρpm×σp / σm
Portfolio Beta is the correlation of portfolio (p) to the market (m) times the standard deviation of p relative to (divided by) the market standard deviation. This is the risk which remains after diversification. Correlation (ρpm) must be high (0.85+) for Beta to be relevant
Portfolio required rate of return
Rp=Rf+(Rm–Rf)βp
The portfolio required rate of return (CAPM) is equal to the risk-free rate of return plus the risk premium of the market times the Beta (relative risk) of the portfolio.
The Sharpe Ratio
Sp=Rp−Rf / σp
=Risk Premium / Total Risk
The Sharpe Ratio measures return relative to total risk by dividing the return of the portfolio (above the risk free rate) by the total risk of the portfolio
The Treynor Ratio
Tp=Rp−Rf / βp
=Risk Premium / Systematic Risk
The Treynor Ratio is similar to the Sharp except Beta (systematic risk) is used as the proxy for risk.
The Jensen Ratio/The Jensen’s alpha
αp=Rp–(Rf+(Rm−Rf)βp
=return − required return
The Jensen Ratio
Compares the return of the portfolio to the required return a Positive ratio = “out performance.” Negative = “under performance”
Sometimes called Jensen’s “alpha”—or just “alpha.”
Be careful not to confuse it with Active Return “alpha”
The Information Ratio
IRp=Active Return / Active Risk = Rp–Rm / σ(Rp–Rm)
The Information Ratio is the risk-adjusted performance evaluation statistic calculated by taking Active Return “alpha” and dividing by Active Risk. Active risk represents the standard deviation (risk undertaken) to generate the active return.
A higher ratio means better risk-adjusted returns.
Total Portfolio Return
Alpha + Beta×(market return)
