CFA III - Performance Measurement - Math

Geometric return attribution

(1+ portfolio return)/(1+benchmark return)]-1

allocation effect (BHB method) =

(portfolio weight - benchmark weight)*sector return for the benchmark

Selection effect =

benchmark weight * (portfolio return - benchmark sector return)

Interaction effect =

(portfolio weight - benchmark weight)*(portfolio return - benchmark return)

allocation effect (BF method, use unless otherwise stated)=

portfolio weight - benchmark weight)*(benchmark sector return - overall benchmark return)

Simplified equation for carhart model (no need to specify each factor)

portfolio return - risk free = alpha + factor tilts + error term

Carhart Model factor tilt interpretation method

more positive - tilt towards top factor or top factor outperformed, more negative - tilt toward bottom factor, or bottom factor outperformed, 0 = neutral

absolute return of carhart model =

sensitivity difference * factor return

factor tilt return of carhart model =

Sum of the absolute return of each facto

active return (alpha) of arhart model =

factor tilt return + security selection return

Benchmark quality evaluation breakdown

Portfolio return = market + style + active management

Benchmark quality evaluation breakdown - style components?

benchmark - market

If the wrong benchmark is used in the Benchmark quality evaluation breakdown, what two seperate equation can you use to identify the impact?

apparant active return (p-wrong benchmark) and misfit return (actual benchmark - wrong benchmark)

Sharpe ratio =.

(portfolio return - risk free rate)/portfolio standard deviation

Treynor ratio =

(portfolio return - risk free rate)/portfolio beta

Information ratio =

(expected portfolio return - benchmark return)/standard deviation of the difference in two returns

appraisal ratio =

active return/volatility of the residual term derived from a factor-based regression

Sortino ratio =

(portfolio return - MAR)/standard deviation of returns using returns below MAR

Capture Ratio =

upside capture/downside capture

upside capture =

portfolio return when markets are up/benchmark return when markets are up

For non-private client, GIPS require return to be calculated as

Ending fair value - beginning fair value/(beginning fair value)

Modified Dietz return =

(ending fair - beginning fair value - ECF)/(beginning fair value + (interim cashflow * days in the fund/total return period)

How to find residual risk from regression? (the denominator of appraisal ratio)

(1-R² of the regression) x annualized standard deviation of the portfolio, then square root

Calculating performance fees net of base

manager profit share * (outperformance - base fee)

downside or upside capture when given multiple months of portfolio and benchmark data

portfolio change/benchmark change, but both measured as the geometric mean of (1+down/up ratio) of all gven periods