GF540 Unit 2 Risk and Return Computation Set Example

Course	GF540 Investment and Securities Analysis
Unit	Unit 2
Paper type	Risk and return computation
Length	About 890 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 GF540 Unit 2

Expected Versus Realized, Then a 60/40 Blend: A Unit 2 Risk and Return Computation

[Student Name]

Purdue University Global

GF540: Investment and Securities Analysis

Unit 2 Risk and Return Computation

[Instructor Name]

[Date]

The funds, the stock, the index and every return are composite and illustrative; the article and textbooks cited are real.

What this part is doingNaming the three parts and the distinction they test in the lead tells the grader how the set is organized.

Part 1: Expected Return and Risk From a Probability Table

Given. Four economic states with probabilities of 0.20, 0.30, 0.30 and 0.20, from recession to boom. An equity fund returns negative 14, 4, 12 and 26 percent in those states; a bond fund returns 5, 6, 2 and 3 percent.

Expected returns. Each return is weighted by its probability and summed. For the equity fund: 0.20 times negative 14, plus 0.30 times 4, plus 0.30 times 12, plus 0.20 times 26, which is negative 2.8 plus 1.2 plus 3.6 plus 5.2, or 7.20 percent. For the bond fund: 1.0 plus 1.8 plus 0.6 plus 0.6, or 4.00 percent.

Standard deviations. For each state, the squared gap between that state's return and the expected return is weighted by probability. For the equity fund the four weighted terms are 89.89, 3.07, 6.91 and 70.69, summing to a variance of 170.56 and a standard deviation of 13.06 percent. For the bond fund they are 0.20, 1.20, 1.20 and 0.20, a variance of 2.80 and a standard deviation of 1.67 percent.

Covariance and correlation. Multiplying each state's two deviations and weighting by probability gives negative 4.24, negative 1.92, negative 2.88 and negative 3.76, a covariance of negative 12.80 in percent-squared terms, or negative 0.00128 in decimals. Dividing by the product of the standard deviations gives a correlation of about negative 0.59.

Meaning. These are expected figures: they describe what the analyst believes about the next year, not what has happened. The bond fund tends to do best exactly when the equity fund does worst.

Part 2: Realized Return and Risk From History

Given. A composite stock returned 18, negative 9, 12, negative 6 and 14 percent over five years. A broad index returned 6, negative 6, 13, 2 and 15 percent.

Arithmetic mean. The stock's five returns sum to 29, an average of 5.80 percent.

Geometric mean. Compounding 1.18, 0.91, 1.12, 0.94 and 1.14 gives 1.2886; its fifth root, less one, is about 5.20 percent. The geometric figure is lower because volatility drags on compounded growth: a 10 percent loss needs more than a 10 percent gain to recover (Bodie et al., 2024).

Sample standard deviation. Squared deviations from 5.80 sum to 612.80; dividing by four, the count of years less one, gives a variance of 153.20 and a standard deviation of about 12.38 percent, the sample convention used for historical data (Reilly et al., 2019).

Correlation and beta. The index's average is 6.00 percent and its standard deviation about 8.51 percent. The sample covariance of the two series is about 85.45. The correlation is about 0.81, and beta, covariance divided by the index's variance, is about 1.18.

Meaning. These are realized figures. Five years is a short history, and a single bad year moves every estimate, so beta of 1.18 should be read as a rough indication that the stock amplifies market moves.

Part 3: The 60/40 Blend and Its Diversification Gain

Given. A portfolio holds 60 percent in the equity fund and 40 percent in the bond fund from Part 1.

Expected return. 0.60 times 7.20 plus 0.40 times 4.00, or 5.92 percent.

Variance. The weights squared times each variance, plus twice the product of the weights times the covariance: 0.36 times 170.56, plus 0.16 times 2.80, plus 2 times 0.60 times 0.40 times negative 12.80. That is 61.40 plus 0.45 less 6.14, or 55.71. The standard deviation is about 7.46 percent.

Diversification gain. If risk simply averaged by weight, it would be 0.60 times 13.06 plus 0.40 times 1.67, or about 8.51 percent. The portfolio's actual risk is about 7.46 percent, so diversification removes about 1.05 points of risk.

The blend keeps about 82 percent of the equity fund's expected return while carrying only 57 percent of its risk, and the gain comes from the negative correlation: if the two funds moved together perfectly, the portfolio's risk would be the simple weighted average of 8.51 percent.

What this part is doingThe highlighted sentence explains where the diversification gain comes from, the insight graders look for at the end of the set.

Why the Distinction Matters

Expected figures from Part 1 belong in decisions about future allocations. Realized figures from Part 2 are evidence that informs those expectations but should not replace them, especially over five years. Markowitz's framework, which underlies Part 3, works with expected returns and covariances; using a short realized history in their place is a common source of error (Markowitz, 1952).

Using the Results

An investor choosing between the two funds alone would face a stark choice: 7.20 percent expected return with 13.06 percent risk, or 4.00 percent with 1.67 percent. The blend offers a middle path that is better than a straight line between them, because the funds offset each other in bad states. Shifting further toward bonds would lower risk faster than return, until the negative covariance is fully used. Finding the mix with the least risk is a natural next exercise.

Conventions

Returns are in percent unless stated as decimals. Probability-weighted variances use the full probability; historical variances divide by the number of observations less one. Intermediate figures carry two decimals.

What this part is doingStating the two variance conventions shows the writer knows why the parts are computed differently.

References

Bodie, Z., Kane, A., & Marcus, A. J. (2024). Investments (13th ed.). McGraw Hill.

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Reilly, F. K., Brown, K. C., & Leeds, S. J. (2019). Investment analysis and portfolio management (11th ed.). Cengage.

What the GF540 Unit 2 assignment asks for

The second GF540 unit asks you to compute risk and return measures from supplied data and to keep their meanings straight. When the data is a probability table, compute expected return, variance, standard deviation, covariance and correlation by weighting each state by its probability. When the data is a history of returns, compute the arithmetic and geometric means, the sample standard deviation dividing by one less than the number of observations, and the correlation and beta against an index. Combine assets into a portfolio and show how covariance changes its risk compared with a weighted average. After each part, say in a sentence what the figures mean and whether they describe the future or the past. State your conventions. Cite the course text and Markowitz's portfolio theory in APA 7.

How this GF540 Unit 2 example is built

Part 1 of the example lists the probability-weighted terms for each state so every sum can be checked, ending with a correlation of about negative 0.59 and a note that these are beliefs about next year. Part 2 computes both means from five realized returns and explains the volatility drag with Bodie, Kane and Marcus. It then gives the sample deviation, citing Reilly, Brown and Leeds on the sample convention, along with the covariance, correlation and beta, and cautions that five years is short. Part 3 builds the 60/40 portfolio's variance term by term and measures the diversification gain. The highlighted sentence explains that the gain comes from negative correlation. A short section on using the results describes the trade-off an investor faces, another on the distinction cites Markowitz, and a conventions note closes the set.

Reading the GF540 Unit 2 grading rubric

Marks in this GF540 set go mostly to correct computation with visible steps, since graders check each weighted term and sum. Using the right divisor for each type of data, full probability weights for scenarios and one less than the count for history, is a common point of separation. Interpretation lines after each part earn the next share, particularly when they say whether a figure is expected or realized. The portfolio section is graded on applying the covariance term correctly and quantifying the diversification gain. Instructors in the MS in Finance program value a brief explanation of where the gain comes from. Neat layout, consistent decimals and APA 7 entries for the text and Markowitz complete the scoring.

GF540 Unit 2 help from the desk

The most common GF540 Unit 2 error is dividing probability-weighted squared deviations by the number of states, which double counts the weighting. Students also compute portfolio risk as a weighted average of standard deviations and miss the diversification gain entirely. Arithmetic and geometric means are confused, or the geometric mean is computed from percentages rather than growth factors. Covariance signs get lost in the arithmetic. Interpretation is skipped, so expected and realized figures are treated as interchangeable. Whatever data your own set supplies, keep the parts distinct: probability-weighted measures for scenarios, sample measures for history, portfolio measures with the covariance term, and a sentence of meaning after each.

Get a GF540 Unit 2 example written to your instructions

Send the data tables from your GF540 Unit 2 assignment along with the prompt and rubric, and mention whether your instructor wants spreadsheet output or hand-worked formulas. Every figure is derived from those numbers in dependency order, with interpretation after each part. The first custom sample is free, and it typically comes back 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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GF540 Unit 2 questions, answered

Should I divide by n or n minus one?

For historical returns treated as a sample of what the asset could produce, n minus one is the usual choice, and most finance texts use it. For probability-weighted scenarios there is no division at all, since the weights already sum to one. The sample states its choice in each part and reports the alternative beside it, so a grader who prefers the other convention can see both.

Why is the geometric mean lower than the arithmetic mean?

Because volatility drags compound growth below the simple average. A loss followed by an equal percentage gain leaves an investor behind, and the geometric mean captures that while the arithmetic mean does not. The gap widens as returns become more dispersed. Both appear in the sample, with a note that the arithmetic figure suits expected single-period return while the geometric suits growth over several years.

Where can I find a free GF540 Unit 2 sample paper?

This page holds a full GF540 Unit 2 risk and return computation, with probability-weighted measures, historical measures, beta, a 60/40 portfolio and APA 7 references.

Why is the portfolio's risk below the weighted average?

Because the two funds tend to move in opposite directions, with a correlation near negative 0.59. When one fund has a bad state the other usually has a decent one, so the blend's swings are smaller than the average of the two.

What does a beta of 1.18 mean?

The stock has tended to move about 1.18 percent for each 1 percent move in the index. With only five years of data, the figure is a rough guide rather than a precise measure.