MT422 Unit 8 Performance Measurement Exercise Example

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Each of four measures names a different winner in this MT422 Unit 8 performance measurement exercise, built on ten years of composite returns. The index averaged 8.80 percent with 14.61 deviation, and bills averaged 2.44. Sharpe ratios favor a low-volatility fund at 0.573 over a concentrated fund at 0.505; Treynor reverses them, 8.84 to 8.72. The concentrated fund's alpha is 2.49 percent, but its t-statistic of 0.63 cannot separate skill from luck. A diversified fund with a 0.94 beta and only 1.09 tracking error trails on every measure, an index portfolio sold at an active fee of 0.78 percent. The exercise explains which measure suits which holder, drawing on Sharpe, Treynor, Jensen and Cremers and Petajisto. Purdue Global MT 422 sets this exercise in the BS in Business Administration.

CourseMT422 Portfolio Management
UnitUnit 8
Paper typePerformance measurement exercise
LengthAbout 940 words, 6 pages double-spaced
FormatAPA 7 student paper
SchoolPurdue University Global
ProgramBS in Business Administration
UpdatedOctober 2026

Free sample paper for MT422 Unit 8

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Four Measures, Three Winners: An MT422 Unit 8 Performance Measurement Exercise With a Test for Luck

[Student Name]

Purdue University Global

MT422: Portfolio Management

Unit 8 Performance Measurement Exercise

[Instructor Name]

[Date]

The three funds, the index and all ten years of returns are composite, built for the exercise; every measure was computed from the returns table, and the sources cited are real.

What this part is doingSaying in the lead that the measures disagree tells the grader the exercise will explain why rather than average the ranks.
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The Data

Returns are annual, in percent, for years one through ten. Treasury bills returned 0.90, 1.40, 1.90, 2.10, 0.40, 0.10, 2.00, 5.10, 5.00 and 5.50, an average of 2.44. The index returned 10.87, 18.13, minus 3.82, 24.88, 14.07, 22.02, minus 13.76, 20.73, 9.66 and minus 14.80, an average of 8.80 with a standard deviation of 14.61.

The diversified large-cap fund returned 10.14, 17.33, minus 3.76, 23.14, 12.79, 19.94, minus 12.97, 21.24, 9.57 and minus 13.62, averaging 8.38 with a deviation of 13.78. Its expense ratio is 0.78 percent.

The concentrated fund, which holds about twenty-five stocks, returned 24.74, 27.59, 11.30, 12.93, 18.27, 33.59, minus 16.35, 20.85, minus 7.60 and minus 12.36, averaging 11.30 with a deviation of 17.53.

The low-volatility fund returned 4.12, 12.88, minus 0.86, 17.96, 11.85, 14.51, minus 9.59, 14.31, 10.48 and minus 0.68, averaging 7.50 with a deviation of 8.83.

Excess Returns and Beta

Every measure below uses excess returns: each year's fund return minus that year's bill return. Using raw returns would overstate every ratio, since bills alone earned 2.44 percent a year. Beta comes from regressing each fund's excess returns on the index's excess returns over the ten years. The diversified fund's beta is 0.94, the concentrated fund's 1.00 and the low-volatility fund's 0.58. Ten annual points give each beta a wide error band, so the figures are rough.

Sharpe Ratio

The ratio Sharpe (1966) proposed divides average excess return by the standard deviation of total return. It measures reward per unit of total risk. The low-volatility fund scores 0.573, the concentrated fund 0.505, the index 0.435 and the diversified fund 0.431. The low-volatility fund wins because its deviation is so small.

Treynor Ratio

The ratio Treynor (1965) proposed divides average excess return by beta instead of total deviation. It measures reward per unit of market risk. The concentrated fund scores 8.84, the low-volatility fund 8.72, the index 6.36 and the diversified fund 6.32. The ranking of the top two reverses, because Treynor ignores the concentrated fund's large company-specific risk.

Jensen's Alpha

Alpha, as Jensen (1968) defined it, is the intercept of the regression: the average excess return a fund earned beyond what its beta predicts. The concentrated fund's alpha is 2.49 percent a year, the low-volatility fund's 1.37 and the diversified fund's minus 0.04.

Information Ratio

The information ratio divides a fund's average return above the index by its tracking error, the standard deviation of the yearly differences between fund and index. It measures how consistently a manager beats the benchmark. The concentrated fund has a tracking error of 10.82 and an information ratio of 0.23. The low-volatility fund has a tracking error of 6.94 and a ratio of minus 0.19, because it averaged 1.30 points below the index even though it did well on a risk-adjusted basis. The diversified fund has a tracking error of only 1.09 and a ratio of minus 0.38.

Each measure answers a different question, so a fund can win one and lose the next without any contradiction.

What this part is doingStating the principle before interpreting the rankings explains why the exercise refuses a single league table.
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Which Measure for Which Question

Sharpe's ratio fits an investor who holds the fund as her whole risky portfolio, since total volatility is what she bears. On that basis the low-volatility fund is the best of the three, and M-squared, which rescales its risk to the index's, would have earned 10.81 percent against the index's 8.80.

Treynor's ratio and alpha fit an investor who holds the fund as one piece of a diversified portfolio, since its company-specific risk will be diversified away. On that basis the concentrated fund looks best.

The information ratio fits an investor or committee that hired a manager to beat a specific index. On that basis only the concentrated fund beat the index at all, and not consistently.

The Near-Index Fund

The diversified fund's figures tell their own story. Its beta of 0.94 and tracking error of only 1.09 mean it behaves almost exactly like the index. Its alpha of minus 0.04 is essentially zero before fees, which means its 0.78 percent expense ratio buys nothing a low-cost index fund would not deliver. Cremers and Petajisto (2009) describe funds like this as closet indexers, funds that charge active fees while holding portfolios close to their benchmark, and found that they tend to trail their index by roughly their fees.

Luck or Skill

The concentrated fund's alpha of 2.49 percent looks impressive, but its standard error is large. Its t-statistic, alpha divided by its standard error, is 0.63, far below the roughly 2.0 usually needed to rule out chance at conventional levels. A fund with no skill at all could easily produce this record. With an information ratio of 0.23, a manager would need roughly 75 years of returns for the t-statistic to reach 2.0, because the statistic rises only as fast as the root of the sample length. The low-volatility fund's alpha has a t-statistic of 1.47, stronger but still short of the threshold.

What the Exercise Shows

No single measure ranks the funds correctly, because the right measure depends on how the fund will be held. The concentrated fund's apparent skill cannot be separated from luck in ten years, and the near-index fund is the clearest finding of all: it delivered index returns at an active price.

What this part is doingClosing on the near-index fund turns the weakest performer into the most useful conclusion.
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References

Cremers, K. J. M., & Petajisto, A. (2009). How active is your fund manager? A new measure that predicts performance. Review of Financial Studies, 22(9), 3329-3365. https://doi.org/10.1093/rfs/hhp057

Jensen, M. C. (1968). The performance of mutual funds in the period 1945-1964. Journal of Finance, 23(2), 389-416. https://doi.org/10.1111/j.1540-6261.1968.tb00815.x

Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119-138. https://doi.org/10.1086/294846

Treynor, J. L. (1965). How to rate management of investment funds. Harvard Business Review, 43(1), 63-75.

What the MT422 Unit 8 assignment asks for

Unit 8 asks students to evaluate fund performance with risk-adjusted measures and to interpret what they show. Instructors expect excess returns computed year by year against the bill rate before any ratio. Most sections want four measures, reward per unit of total risk, reward per unit of beta, regression alpha and the information ratio, and some add M-squared. Beta should come from a regression on the benchmark's excess returns, and its limited precision with few observations should be acknowledged. Alpha should be reported with a standard error or t-statistic, so the reader can judge whether it could be luck. The information ratio needs tracking error against the correct benchmark. Interpretation should explain that each measure answers a different question, not average the ranks into a single league table.

Inside the MT422 Unit 8 example

The example first prints the ten years of returns for bills, the index and each fund, with the diversified fund's fee. A short section explains excess returns and the regression betas. The four measures follow one by one, each with its definition, its figures and what changes in the ranking, under a highlighted line that each measure answers its own question. A section matches each measure to a kind of holder, adding M-squared for the low-volatility fund. The near-index fund gets its own discussion, citing Cremers and Petajisto on closet indexing. The luck section tests the concentrated fund's alpha and estimates how many years a t-statistic of 2.0 would take. The conclusion turns on the near-index result.

MT422 Unit 8 rubric: what earns full points

Performance exercises are usually graded on correct excess returns, correctly computed measures, attention to statistical precision and interpretation matched to how a fund is held. Ranking on one ratio, or averaging ranks, misses the point the unit is built around. Graders check excess returns next, since raw returns overstate every ratio. Rubrics reward betas and alphas reported with their uncertainty. Credit goes to computing the information ratio with tracking error against the benchmark, not with the fund's own deviation. Interpreting the near-index fund's low tracking error and fee earns insight marks. Calling a manager skilled on a t-statistic well below two draws comment. Returns and measures tables with percent units marked let a grader trace every ratio.

Common MT422 Unit 8 mistakes, and how to avoid them

The most common weak exercise computes ratios on raw returns, skipping the bill rate. Another frequent error ranks funds on the Sharpe ratio and declares a winner without asking how the fund is held. Students often divide active return by the fund's total deviation instead of tracking error. Alpha is usually reported without a standard error, inviting a conclusion the data cannot support. Ten-year betas are treated as exact. The near-index fund is often dismissed as average rather than recognized as the clearest finding. Before submitting, rank the funds separately on each measure and write one sentence on why the ranking changes. If you cannot explain a change, recheck which risk each measure divides by.

Get an MT422 Unit 8 example written to your instructions

Some sections name real funds and a data source for Unit 8; others supply return series. Either suits a free first MT422 performance exercise, all four measures with their assumptions explained and alpha tested for significance, following the rubric and returned in 24-48h. Spreadsheet formulas can be shown alongside the results. 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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MT422 Unit 8 questions, answered

Which performance measure is the right one?

It depends on how the fund will be held. For a fund that is the investor's entire portfolio, total risk matters and the Sharpe ratio fits. For one holding among many, only market risk adds to the whole, so Treynor or alpha fit better. The information ratio suits judging a manager against a stated benchmark.

Can real fund returns be used?

Many sections ask for exactly that, with returns drawn from a named data provider over a stated period. Composite funds avoid claims about how any real fund performed. With real data the same cautions apply: cite the provider and dates, compute excess returns year by year and report the uncertainty around each alpha.

What is a t-statistic doing in a performance exercise?

It asks whether an alpha is large relative to the noise around it. A t near 2 or above is the usual threshold for calling a result unlikely to be luck. Ten annual observations rarely get there, and saying so is what separates a careful interpretation from a simple ranking.

Where can I find a free MT422 Unit 8 sample paper?

The complete MT422 Unit 8 exercise is here, ranking three composite funds by Sharpe, Treynor, alpha and information ratio over ten years.

How many years would the MT422 Unit 8 sample's concentrated fund need to prove skill?

With an information ratio of 0.23, about 75 years of returns before its t-statistic would reach the usual 2.0 threshold.