Bad5shah

The two period active return for a portfolio can be determined by:

A) compounding the individual one period active returns.

B) taking the active return on the portfolio in the first period multiplied by the return on the benchmark in the second period plus the active return in the second period multiplied by the total return on the portfolio in the first period.

C) maintaining the same security or market allocation proportions for each period, compounding the individual one period active returns for each attribute, and then summing the compounded returns to get an overall total active return.

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To measure the overall return to active management we use the following formula:

RA,2 = Ra,1(1 + Rb,2) + Ra,2(1 + Rp,1)
Where:
RA,2 = the two-period active return
Ra,1 = active return for period 1
Rb,2 = return of the benchmark in period 2
Ra,2 = active return for period 2
Rp,1 = return on the portfolio for period 1

The first term in the equation, Ra,1(1 + Rb,2), is the active return on the portfolio in the first period multiplied by the return on the benchmark in the second period. It shows the value added by the manager’s actions in the first period. The active return in the first period will compound at least at the benchmark rate of return over the second period, even if the manager pursues a pure indexing strategy in that period.
The second term, Ra,2(1 + Rp,1), takes into account the manager’s active decisions in the second period. It is measured as the active return in the second period multiplied by the total return on the portfolio in the first period.

• The multiple-period return to active management for an individual attribute cannot be determined by adding or compounding the attribute’s contributions in each period.
• The multiple-period return to active management for an individual attribute cannot be determined by assuming it stays at the same proportion of the active return in each period.

Bad5shah

If the return on a portfolio over two periods is 8.6% and 14.32% respectively and the benchmark’s returns are 6.9% and 11.7% respectively what is the two period active return?

A) 4.74%.

B) 4.36%.

C) 4.32%.

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The active return is most easily determined by compounding the portfolio’s return over the two periods and subtracting the compounded benchmark’s return over the same period as follows:
Portfolio’s compounded return: (1.086)(1.1432) − 1 = 24.15%
Benchmark’s compounded return: (1.069)(1.117) − 1 = 19.41%
Active return = 24.15 − 19.41 = 4.74%
Alternatively, the two period active return can be determined using the following equation:

RA,2 = Ra,1(1 + Rb,2) + Ra,2(1 + Rp,1)

Where:
Ra,1 = active return for period 1 = 8.6 − 6.9 = 1.70%
Rb,2 = return of the benchmark in period 2 = 11.7%
Ra,2 = active return for period 2 = 14.32 − 11.7 = 2.62%
Rp,1 = return on the portfolio for period 1 = 8.6%
RA,2 = 1.7(1 + 0.117) + 2.62(1 + 0.086)
= 1.899 + 2.845 = 4.74%

Bad5shah

In determining the two period active return for a multi-attribution analysis which of the following statements is least accurate?

A) Each attribute’s contribution in the first period is compounded at the benchmark rate of return over the second period.

B) Each attribute’s contribution in the second period is compounded with the portfolio return from the first period.

C) The total active return for the portfolio is found by summing the compounded active return for each attribute.

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The equation for a 2 period multi-attribution analysis is:

RA,2 = Ra,1(1 + Rb,2) + Ra,2(1 + Rp,1)
Where:
RA,2 = the two-period active return
Ra,1 = active return for period 1
Rb,2 = return of the benchmark in period 2
Ra,2 = active return for period 2
Rp,1 = return on the portfolio for period 1

The equation shows that the two period active return for each attribute is found by taking its active return in the first period and compounding it at the benchmark rate of return over the second period and then adding this to the attribute’s contribution in the second period and compounding this with the portfolio return from the first period. This method would be repeated for each separate attribute in the portfolio such as security selection and market allocation. Then each separate attribution’s active return is added together to get the total active return for the portfolio.

Bad5shah

The total active return over multiple periods is most accurately determined by:

A) compounding the active return for each period.

B) taking the difference between the compounded portfolio and benchmark returns.

C) summing the active return for each period.

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Taking the difference between the compounded portfolio and benchmark returns will result in the true total active attribution analysis this can also be accomplished by taking each attribute’s contribution in the first period and compounding it at the benchmark rate of return over the second period and adding that to the attribute’s contribution in the second period which is compounded with the portfolio return from the first period. This process can be seen in the following formula:

RA,2 = Ra,1(1 + Rb,2) + Ra,2(1 + Rp,1)
Where:
RA,2 = the two-period active return
Ra,1 = active return for period 1
Rb,2 = return of the benchmark in period 2
Ra,2 = active return for period 2
Rp,1 = return on the portfolio for period 1

Bad5shah

ABC fund earned a total return of 19.5% for calendar year 2003. Its benchmark return during the same period of time is 17.50%. The risk-free rate of return for the period was 2.0%. ABC’s standard deviation is 16% and the standard deviation of the benchmark is 12%. Did the fund outperform its benchmark based on the Sharpe ratio?

A) No, the Sharpe ratio of the fund is 1.09 versus 1.29 for the benchmark.

B) No, the Sharpe ratio of the fund is 1.29 versus 1.09 for the benchmark.

C) Yes, the Sharpe ratio of the fund is 1.09 versus 1.29 for the benchmark.

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Sharpe Ratio for the fund = (19.5−2)/16 = 1.09 Sharpe Ratio for the benchmark = (17.5−2)/12 = 1.29

Bad5shah

Advanced quantitative models (AQM) global equity fund has averaged a return of 12.5% per year over the last 10 years. The benchmark average return over the same period was 11% per year. The risk-free rate of return during the same period averaged 3.50%. The standard deviation of the fund’s return is 16.15%, and the standard deviation of the surplus return is 10.50%.What is the Information Ratio for the fund?

A) 0.14.

B) 1.05.

C) 0.86.

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Information Ratio = (12.50−11)/10.5 = 0.14

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What is the Sharpe Ratio for the fund?

A) 1.19.

B) 0.14.

C) 0.56.

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Sharpe Ratio = (12.50−3.50)/16.15 = 0.56

Bad5shah

Sector risk is defined as the risk of:

A) individual countries in a passive benchmark portfolio.

B) all the sectors in the portfolio.

C) assigning the wrong weight to a sector in the portfolio.

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Sector risk is the risk of individual countries or sectors in a passive benchmark portfolio

Bad5shah

What is risk budgeting?

A) Identification of sources of portfolio risk.

B) Determination of a risk measure that the portfolio can take.

C) Determination of the amount of risk the portfolio can take.

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Risk budgeting is the risk counterpart of performance attribution. It identifies the sources of the portfolio risk.

Bad5shah

Selection risk is defined as the:

A) additional risk taken by deviating from the benchmark portfolio.

B) risk of individual companies in a sector in the benchmark portfolio.

C) risk of all the companies in a sector of the portfolio.

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Selection risk is the additional risk taken by deviating from the benchmark portfolio.

Bad5shah

For a global portfolio, the benchmark has to:

A) have the same amount of risk as the portfolio under consideration.

B) be consistent with the investment objective of the portfolio.

C) be custom defined by the manager of the portfolio.

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The benchmark should be consistent with the investment objective of the portfolio.