Performance Measurement and Attribution

Question 1

EAR vs APR

Answer 1

EAR is the effective percentage change of an amount invested (i.e., rate of return), after factoring in compounding and assuming the investment was made over a one year period.
Annual Percentage Rate APR is often used for periods of time less than one year and which reflects a simple interest rate applied over the whole year.
APR = rate for the period * the number of periods in a year = R nom.* freq

Question 2

Time-weighted and Dollar Dollar-weighted Returns

Answer 2

• Time-weighted returns
– Manager’s return
– Does not consider cash flows
• Dollar-weighted returns
– Investor’s return
– Considers cash flows
– IRR

Question 3

Alpha

Answer 3

• risk adjusted
• also considered the value added by the investment manager through security selection or market timing
• also known as the return in excess of the required rate of return
• mathematically: Jensen’s alpha

Question 4

R^2 Formula

Answer 4

R^2 = Beta^2 x Standard Deviation of Market^2 / Standard Deviation of Portfolio^2

Note, if you square the correlation coefficient formula on the formula sheet and solve for coefficient you get this

Question 5

The Reward-to-Volatility (Sharpe) Ratio

Alternative formula

Answer 5

Another way Sharpe Ratio is expressed (not as common but occasionally shows up on the exam)

Sharpe Ratio (alt) =(Risk Premium) / (SD of Excess Returns)

Question 6

Modigliani^ 2 Ratio

Answer 6

• Modigliani squared (M^2) is a risk adjusted performance metric that adjusts for total risk using standard deviation.
M^2 measures returns of a portfolio adjusted for that portfolio’s risk relative to the market or benchmark (e.g., S&P 500 Index).
• M^2 is considered more user friendly compared to the Sharpe Ratio as it is expressed in units of return percentage as opposed to the Sharpe Ratio which is abstract.
• M^2 is directly related to the Sharpe Ratio (i.e., a higher M^2 means a higher Sharpe Ratio and a lower M^2 means a lower Sharpe Ratio)

Question 7

Omega

Answer 7

A measure of the change in an option’s value based on the change in the underlying price of the asset.

Question 8

Treynor Ratio

Answer 8

• Also known as the “reward to volatility ratio” or “Treynor measure”.
• Best for comparing two funds or investments within the same category.
• Treynor Ratio is useful if the portfolios being measured are part of a broader, more fully diversified portfolio.

Question 9

Tracking Error

Other names for tracking error

Answer 9

• Tracking Error (TE) is an important statistic.
• Multiple versions (formulas) of TE are encountered in practice.
• All are designed to measure how much a portfolio deviates from its benchmark.
• As a result, TE is sometimes referred to as:
-Active Risk, Active Return, Extra Return
-the “annualized standard deviation of returns”; or
-the “residual standard deviation”
• TE is used in the Information Ratio (IR).

Question 10

Simple tracking error calculation

Answer 10

Portfolio return - benchmark return

As opposed to formula from CIMA formula sheet

Question 11

Tracking error approximation using Standard Deviation

Answer 11

TE Ratio = standard deviation of the portfolio / standard deviation of the benchmark
Between two portfolios, the one with the lower ratio has the lower TE.

Question 12

Calculate Tracking error with frequency other than one year

Answer 12

If given a tracking error with greater frequency than 1 year, you can calculate the annual TE by multiplying that periodic TE by the square root of the number of periods in one year. Like the SD annualized formula.
Annual TE = Quarterly TE * √4
Annual TE = Daily TE * √252 (there are 252 trading days in a year)

Question 13

Information Ratio

Answer 13

• IR equals the average excess portfolio return above a BENCHMARK (not risk-free-rate), divided by risk (measured by standard deviation).
• Measures a manager’s ability to select securities relative to a benchmark.
• Captures the size (amount) of excess return and the ability to do so consistently.
• IR = excess return/standard deviation
• IR = portfolio return - benchmark return/tracking error
• The contribution of the active portfolio depends on the ratio of its alpha to its residual standard deviation (aka tracking error).
• The information ratio measures the extra return we can obtain from security analysis.

Question 14

Attributes of effective benchmarks (5)

Answer 14

• Transparency
• Replicability
• Specific
• Measurable
• Representative

Question 15

Holdings vs. Returns Based Analysis

Answer 15

Holdings based analysis breaks down the composition of a fund for analysis and comparison while a Returns based analysis compares style performance (e.g., size and value) to benchmark styles.
• Holdings-based Analysis
– Analyzes a fund by reviewing the underlying securities that it holds
– Focuses exclusively on fund composition
– Based on current data current data
• Returns-based Analysis
– Commonly used to reveal a stock fund’s style (e.g., size and value orientation)
– Analyzes the behavior of a fund vs. benchmark
– Based on historical data historical data

Question 16

Returns-based analysis

Answer 16

“If it acts like a duck, assume it’s a duck.” As managers rarely have a pure style, Sharpe proposes a method whereby one can find the combination of style indices which gives the highest R-squared with the returns on the portfolio being studied.

The success of this technique relies heavily on the correct specification of the style benchmark indices used as regressors.

It is therefore the only method that can be used when there is no data available on the composition of the portfolio

Question 17

Holdings-based analysis

Answer 17

consists in analyzing each of the securities that make up the portfolio. The securities are studied and ranked according to the different characteristics that allow their style to be described. The results are then aggregated at the portfolio level to obtain the style of the portfolio as a whole. This method therefore requires the present and historical composition of the portfolio, together with the weightings of the different securities that it contains, to be known with precision. The analysis has to be carried out regularly,

Question 18

Survivorship Bias Impact

Answer 18

Impact on performance of a “group”
–Does it make the group, as a whole, look better or worse?
•Answer = better
•Rationale = the worse performing funds are removed from the database and the entire group’s aggregate return is higher as a result Impact on performance of an “individual”
– Does it make the individual look better or worse?
• Answer = worse

Question 19

Reporting Bias

Answer 19

Financial reporting is sometimes voluntary Financial reporting is sometimes voluntary depending on investment structure (e.g., hedge funds). hedge funds).