Benchmarks

return, market, control, account, position

Money weight return>Time weighted prior to strong performance
Money weight return< time weighted prior to weak performance.

Time weighted return does not take into account cashflow, which is
generally out of mgmt control. GIPS prefers Time weighted.

Portfolio return=market return+style return+active return
P=market return+(benchmark return-market return)+(portfolio return-benchmark return)

Active return is composed of a set of under weight and over weight position in benchmark

Properties of a Valid Benchmark

S-specified in advance (everyone knows in advance what the benchmark is. Benchmark based on
Relative manager performance is not considered to be Specified in advance)

A-Appropriate-should be consistent with managers investment style and area of expertise. Using a broad market index for a value investor is not appropriate.

M-measurable-return calcs are easy to calculate.

U-Unambigious-weight and identity of securities are known.

O-Owned meaning that there is accountability

R-Reflective on current investment opinion, that is the manager has knowledge of the securities and factor exposures of the benchmark

I-Investable-you can passively invest in securites. Not possible with an absolute or relative benchmark. Should have low turnover.

Test of a Benchmark Quality

Systematic Biases-Beta of manager and benchmark close to 1 plus low correlation between (B-M) and (P-B) and strong correlation between style and (B-M)

Tracking error-volatility of (P-B) should be less than (P-M)

Risk characteristics-manager should have exposure at times great and less than benchmark but not consistently in one direction.

Turnover-benchmark should have low turnover so that it is INVESTABLE(see above)

Positive active positive-manager should hold a net positive active position (weight in portfolio-weight in benchmark)

Performance Attribution

EQUITY

Macro Attribution

Beginning Value
Plus
A a cash contributions-Cash inflows
R Risk free-BV+ Net cashflows invested at RF rate
A Asset Class return-incremental return based on passive investment in asset class using asset class weights
B Benchmark-increm, return based on passive investment in benchmark using benchmark weights
I Investment manager-increm. return based on active investment managers return using benchmark weights
A Active Allocation-reconciling factor

Micro Attribution

Attributable to Portfolio manager skill
(security weight in portfolio- security weight in benchmark)*(return in benchmark-TOTAL Benchmark)

Attributable to Security analyst skill
security weight in benchmark*(portfolio return – benchmark return)

Asset/selection interaction
(security weight in portfolio- security weight in benchmark)*(return in portfolio-return in benchmark)

FIXED INCOME

Total return = External interest rate effects + mgmt effects

External Effects=expected and unexpected interest rate effects
Expected is the implied forward rate
Unexpected is difference between actual and implied forward rate from above

Mgmt effects

Interest rate effect
Indicates how well mgmt predicted interest rate changes due to
Duration-parallel shifts
Convexity-parallel shifts
Yield Curve changes-twist

Sector Quality
Measures ability to select right issuing sectors and quality group

Security Selection
Measures how the return of a specific security within a specific sector relates to avg performance of sector

Trading activity
Captures the effects of sale and purchase

When examining return look at mgmt effect separately and determine where the majority of the return was coming from. Compare that with manager style to see if both are consistent.

Risk Based Performance Measures-NON NORMAL RETURNS INVALIDATE ALL THESE MEASURES

Beta Based Measures

ExPost Alpha=Return on account – RF- estimated Beta during EVALUATION PERIOD
*(Return on market- RF)

Treynor Method= (Average Return over evaluation period – Average RF return)/estimated Beta during
EVALUATION PERIOD

Volatility Based Measure

Ex Post Sharpe= (Average Return over evaluation period – Average RF return)/ estimated Standard Deviation over evaluation period

M2-measures what the account would have returned if it had taken the same total risk as the market

Information ratio=(Average portfolio Return over evaluation period – Average Benchmark return over same period)/ estimated tracking risk over evaluation period

It is possible for Volatility based measure to indicate poor performance relative to Beta based measure. This may be the result of the manager taking large nonsystematic/Unique/idiosyncratic risk relative to systematic.

Critics have attacked these risk based methods based on their reliance on single variable CAPM, Market proxy used, benchmarks used (for example it is difficult to passively invest a broad market index or custom based index and the costs associated with creating and managing them are ignore) and stability of the parameters.