CFP - Formulas

Question 1

Rp

Answer 1

Portfolio Return

Question 2

Rm

Answer 2

Market or Benchmark Return

Question 3

σp

Answer 3

standard deviation of portfolio returns (Variability)

Question 4

σm

Answer 4

standard deviation of market returns

Question 5

ρpm

Answer 5

Correlation of p to m
(ranges from -1 to +1)

Question 6

R-Squared

Answer 6

Correlation Squared. AKA “Coefficient of Determination”

This number must be 80%. Otherwise risk-adjusted performance numbers are not valid.

Question 7

Rf

Answer 7

Risk Free rate of return (90 day T-Bill)

Question 8

βp

Answer 8

Portfolio Beta (systematic risk) (Volatility) = relative variability

Question 9

Risk Premium of the Market

Answer 9

Rm – Rf

Market or Benchmark Return - Risk Free rate of return (90 day T-Bill)

Question 10

Risk Premium of a portfolio

Answer 10

β(Rm – Rf)

Question 11

Active Return

Answer 11

Rp – Rm

Portfolio Return - Market or Benchmark Return

“alpha” (be careful not to confuse this with Jensen’s alpha)

Question 12

Active Risk

Answer 12

σ(Rp – Rm)

(Tracking Error (TE)) = standard deviation of active returns

Question 13

Portfolio Beta

Answer 13

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

Question 14

Portfolio required rate of return

Answer 14

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.

Question 15

The Sharpe Ratio

Answer 15

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

Question 16

The Treynor Ratio

Answer 16

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.

Question 17

The Jensen Ratio/The Jensen’s alpha

Answer 17

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”

Question 18

The Information Ratio

Answer 18

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.

Question 19

Total Portfolio Return

Answer 19

Alpha + Beta×(market return)