| Course | GF570 Portfolio Management |
|---|---|
| Unit | Unit 7 |
| Paper type | Risk-adjusted performance exercise |
| Length | About 850 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | MS in Finance |
| Updated | October 2026 |
Free sample paper for GF570 Unit 7
Five Measures Say B, One Says A: A Unit 7 Risk-Adjusted Performance Exercise for Two Equity Managers
[Student Name]
Purdue University Global
GF570: Portfolio Management
Unit 7 Risk-Adjusted Performance Exercise
[Instructor Name]
[Date]
Both managers, the benchmark and every return are composite and illustrative; the articles cited are real.
The Data
Annual returns, in percent, for six years:
1. Manager A: 22.0, negative 12.5, 28.0, 6.5, 18.0 and 0.6.
2. Manager B: 14.0, negative 1.5, 16.0, 4.5, 12.0 and 5.3.
3. Benchmark, a broad equity index: 18.0, negative 9.0, 24.0, 5.5, 15.5 and 0.5.
4. Treasury bills: 1.5, 2.0, 0.5, 0.2, 2.8 and 4.2.
Summary Statistics
Manager A averaged 10.43 percent with a sample standard deviation of 15.08 percent and a beta against the benchmark of 1.22. Manager B averaged 8.38 percent with a standard deviation of 6.71 percent and a beta of 0.54. The benchmark averaged 9.08 percent with a standard deviation of 12.30 percent. Bills averaged 1.87 percent.
The Six Measures
Sharpe ratio, excess return over bills per unit of total risk. A: 10.43 less 1.87, divided by 15.08, about 0.568. B: about 0.972. The benchmark's is about 0.587. B leads (Sharpe, 1966).
Treynor ratio, excess return measured against market sensitivity rather than total swings. A: 8.56 divided by 1.22, about 6.99. B: 6.51 divided by 0.54, about 12.15. B leads.
Jensen's alpha, return above what beta predicts. A: 10.43 less a predicted 10.70, which is 1.87 plus 1.22 times the benchmark's 7.21 excess return, about negative 0.27. B: about positive 2.64. B leads.
M-squared, Sharpe ratio scaled to the benchmark's volatility and added to the bill rate. A: about 8.85 percent. B: about 13.82 percent. B leads.
Sortino ratio, excess return per unit of downside deviation below the bill rate. A: about 1.40. B: about 4.56. B leads, because its only shortfall year was small.
Information ratio, return above the benchmark per unit of tracking error. A beat the benchmark by about 1.35 points a year with tracking error of about 2.85, a ratio of about 0.47. B trailed the benchmark by about 0.70 points with tracking error of about 5.82, a ratio of about negative 0.12. A leads.
Every measure that treats the manager as the investor's whole portfolio favors B's lower risk, while the one measure that treats the manager as a sleeve judged against an index favors A, because A delivered steady excess return over the benchmark and B simply held less equity risk.
What Each Measure Assumes
The Sharpe ratio and M-squared assume the manager is the investor's entire risky portfolio, so total volatility is the relevant risk. Treynor and Jensen assume the investor is already diversified, so only market risk matters. Sortino assumes investors care only about returns below a target. The information ratio assumes the manager fills a slot in a larger allocation and is judged by how reliably it beats the index for that slot (Goodwin, 1998).
Which Measure Fits the Foundation
The foundation sets its total equity exposure through its policy allocation. A manager hired for a U.S. equity sleeve is expected to deliver that sleeve's market exposure plus something extra. B's attractive Sharpe ratio comes largely from holding less equity risk, a beta of 0.54, which the foundation would then have to make up elsewhere. A delivered the exposure the sleeve was meant to have and added about 1.35 points a year with modest tracking error. For this purpose, the information ratio is the measure that matters, and A is the better hire.
Cautions
Six years is a short record, and an information ratio of 0.47 over six years is not statistically distinguishable from zero. A's beta above one also means some of its excess return may reflect market exposure rather than skill. Research on fund performance finds that apparent skill over short periods often fails to persist (Carhart, 1997).
A Note on Scaling Results
One more check helps. If Manager B's returns were scaled up to the benchmark's volatility, as M-squared does, they would beat both A and the benchmark. But the foundation cannot borrow to scale up a manager, and asking B to take more risk would change its process. M-squared describes what B's skill would earn at a different risk level; it does not describe a portfolio the foundation can actually hold.
Using Both Results
The foundation could still learn from B. Its low beta and strong Sortino ratio suggest a manager that protects capital in falling markets. If the trustees later want a defensive equity sleeve, B would be a natural candidate for that role, judged against a lower-beta benchmark.
Data Quality
The six annual returns were supplied gross of fees for A and net of fees for B. Adjusting A for its 60-basis-point fee lowers its excess return to about 0.75 points and its information ratio to about 0.26, still ahead of B's.
Recommendation
Shortlist Manager A for the U.S. equity sleeve, subject to a review of its process and holdings that explains the excess return, and require a longer record or a lower fee before committing a large allocation.
References
Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57-82. https://doi.org/10.1111/j.1540-6261.1997.tb03808.x
Goodwin, T. H. (1998). The information ratio. Financial Analysts Journal, 54(4), 34-43. https://doi.org/10.2469/faj.v54.n4.2196
Sharpe, W. F. (1966). Mutual fund performance. The Journal of Business, 39(1), 119-138. https://doi.org/10.1086/294846
Reading the GF 570 Unit 7 instructions
The seventh GF570 unit asks you to compute and interpret risk-adjusted performance measures for competing managers. Present the return data and summary statistics, including means, standard deviations and betas. Compute the Sharpe ratio, Treynor ratio, Jensen's alpha, M-squared, Sortino ratio and information ratio, showing each calculation. Explain what each measure assumes about the investor and the manager's role. Decide which measure fits the question your investor is actually asking, and recommend accordingly. Note cautions about short records and data quality. Write so that a committee member could follow the logic without a finance background. Cite the original sources for the measures and research on performance persistence in APA 7.
How the GF 570 Unit 7 example is put together
Six years of returns for both managers, the benchmark and bills open the example, followed by summary statistics. Each of the six measures gets a short paragraph with its calculation and leader, beginning with Sharpe's ratio and ending with the information ratio, where A's 1.35-point excess return over 2.85 points of tracking error wins. The highlighted sentence explains why whole-portfolio measures favor B and the sleeve measure favors A. A section on assumptions cites Goodwin on the information ratio. The fit section argues that a sleeve manager should be judged against its index. Cautions about six years cite Carhart, a note on scaling explains why M-squared does not describe a portfolio the foundation can hold, a fee adjustment trims A's ratio to about 0.26, and a conditional shortlist closes the exercise.
Reading the GF570 Unit 7 grading rubric
GF570 performance exercises award most points for correct calculation of every measure with visible inputs. The next share rewards a clear explanation of what each measure assumes, since that is what lets a student choose among them. The analytical heart of the unit is matching the measure to the investor's question, and graders reward a recommendation that follows from that match rather than from counting which manager wins more measures. Instructors in the MS in Finance program value cautions about short records, beta effects and fee treatment. A recommendation conditioned on further review, clear presentation and APA 7 references to the original measures complete the grade.
Common GF570 Unit 7 mistakes, and how to avoid them
A frequent GF570 Unit 7 error is ranking managers by how many measures they win, which ignores that the measures answer different questions. Others compute the information ratio against the bill rate instead of the benchmark. Sortino is computed without stating the target return. Gross and net returns are mixed. Six years of data are treated as conclusive. Recommendations favor the highest Sharpe ratio for a sleeve that will be combined with other managers, where total volatility matters little. For any managers your case supplies, keep the steps: data and statistics, six measures with calculations, assumptions, fit to the question, cautions and a conditional recommendation.
Get a GF570 Unit 7 example written to your instructions
Supply the return series, risk-free rate and benchmark from your GF570 Unit 7 prompt with the rubric; the calculations are shown in spreadsheet form or by hand as your section prefers. Each measure is computed, its assumption named, and the investor's own question decides which one leads. The first custom sample is free, typically inside 24-48h. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
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GF570 Unit 7 questions, answered
Which measure should I recommend?
The one matching the question your prompt asks. Sharpe fits an investor holding the manager as the whole risky portfolio; Treynor and alpha fit a manager who is one part of a diversified whole; the information ratio fits a mandate judged against an index. The sample reports all six, then chooses based on how the foundation would actually use the manager.
Is six years of data enough?
It is enough to compute every measure and too little to trust any of them fully. Six annual observations give beta and alpha wide margins of error, and one unusual year can reverse a ranking. The sample says so plainly and treats the results as evidence for further review rather than a final verdict, which most graders expect at this level.
What minimum acceptable return does Sortino use?
Whatever your prompt specifies, stated before the calculation. The sample uses the average bill rate so that Sortino and Sharpe share a hurdle and differ only in how they measure risk. Some texts use zero or the investor's required return instead, and changing the hurdle changes the downside deviation, so the choice must be visible.
Where can I find a free GF570 Unit 7 sample paper?
This page carries a full GF570 Unit 7 risk-adjusted performance exercise comparing two equity managers on six measures, with calculations, assumptions, a recommendation and APA 7 references.
Why does the information ratio favor Manager A?
It measures return above the benchmark per unit of tracking error. A beat the index by about 1.35 points a year with modest tracking error, while B trailed the index because it held much less equity risk.