Performance Evaluation

 

Performance measurement – returns over a specific period of time

 

Performance attribution – look into the source of account performance

 

Performance appraisal – whether performance is due to investment decisions or lucks

 

External cash flow – contribution or withdrawal

 

Internal cash flow – dividends or interests

 

MWR – also called LIRR linked internal rate of return

-       Only need to evaluate the portfolio value at the beginning and ending of the period (cheaper and less prone to error)

-       Appropriate if manager has control of cash flow

-       Assume all sub-period as the same rate of return (GM rate of return per dollar)

-      

Can be distorted by large cash flow

 

TWR – really calculate return of $1 investment

 

Trade Date Accounting – record transaction on the trade date instead of the settlement date

 

Matrix Pricing – estimation of illiquid securities based on dealers’ quotes on securities with similar attributions

 

P=M+S+A

 

Portfolio return = Market return + excess of return due to manager’s style (B-M) (This is passive return)+ (P-B) active return (manager’s overall return – style benchmark return)

 

Benchmark properties: (SAMURAI)

Specified in Advanced

Appropriate – consistent with manager’s approach and style

Measurable

Unambiguous

Reflective of the manager’s current investment opinions

Accountable

Investable

 

Type of benchmark:

Absolute – with a return objective but no investable

Manager Universes – the median manager return – no “S” => no “U”,”I”, survivorship bias, has to rely on complier’s accuracy

Broad Market Indices – “A” may not exist.

Style indices – e.g. large/small cap growth/value

Factor model based – no “I”, no “S”.

R = ap + sum(bi*Fi)+error

Returns-based – constructed using managed account returns over specified periods and corresponding returns of several style indices for the same periods

 

Custom security-based: identify the manager’s investment process and selection and construct with the same asset and weighting

 

 

Test of Benchmark Qualities

 

1. Systematic bias – portfolio should have beta~1 to the benchmark
2. A should be uncorrelated to S
3. Tracking error (sigma(P-B)) should be smaller than sigma(B-M)
4. Risk should be similar
5. Coverage should be high – % of securities in the portfolio also in the benchmark
6. Turnover of benchmark should be low
7. Positive active position in long account or negative active position in short account– difference between security portions in portfolio and benchmark – reflecting manager’s active management

 

Misfit return/ style bias = difference between the manager benchmarks and the asset benchmark in the same category

 

 

Macro-performance Attribution:

 

1. Net Contribution
2. Risk-free asset
3. Asset Categories
4. Benchmarks
5. Investment managers (their actual portfolios)
6. Allocation Effects
7.  

Allocation effect: deviated from policy allocation

 

Micro-attribution

 

1. Sector allocation
2. Allocation/selection interaction
3. Within-sector selection

 

Fundamental Factor Model Micro Attribution

 

Fixed income performance evaluation:

 

External Interest Rate Effect – the return on Treasuries over the holding period (which can be different from the expected one due the change of the yield curve)

 

Interest Rate Management Effect – Price each bond using Treasury forward rates, get the total return then minus the external interest rate effect

 

Sector/Quality Management Effect – Price using Treasury forward rate + average risk premium for a bond to get the return, then minus interest rate management effect and external interest rate effect

 

Security selection effect – Price using Treasury forward rate + average risk premium for the sector to get the return

 

Trading Effect – overall return minus all above

 

Performance Appraisal

 

1. Ex-post Alpha (Jensen’s Aplha)
2. Information Ratio = Active Return / Active Risk = (RA-RB)/sigma(RA-RB)
3. Treynor return = (RA-Rrf)/beta
4. Sharpe Ratio = (RA-Rrf)/sigma_p
5. M² measure (Modigliani and Modigliani) = Rfr + sigmaM *(Rp-Rrf)/sigma_p (Just rearrange the CML, so give RM if the return is appropriate, and above RM if return is higher than CML)

 

 

Alpha and Treynor give the same result (Systematic risk only). Sharpe Ratio and M2 measure give the same result (total risk). If non-systematic risk is higher, Sharpe and M2 gives lower values.

 

Quality Control Chart