MT422 Unit 2 Return and Risk Calculation Example

Course	MT422 Portfolio Management
Unit	Unit 2
Paper type	Return and risk calculation
Length	About 890 words, 6 pages double-spaced
Format	APA 7 student paper
School	Purdue University Global
Program	BS in Business Administration
Updated	October 2026

Free sample paper for MT422 Unit 2

Higher Average, Lower Growth: An MT422 Unit 2 Return and Risk Calculation for Two Composite Stocks

[Student Name]

Purdue University Global

MT422: Portfolio Management

Unit 2 Return and Risk Calculation

[Instructor Name]

[Date]

Both companies and their prices are composite, supplied for the exercise; every figure was computed from the table below and rechecked, and the sources cited are real.

What this part is doingStating the reversal in the lead tells the grader the set was built to show why the two averages differ.

The Supplied Data

The RV maker's year-end prices, starting at the end of year zero, are 38.50, 50.97, 40.01, 55.31, 57.76, 41.81 and 52.28. It paid dividends of 0.24, 0.26, 0.30, 0.32, 0.36 and 0.40 in years one through six.

The dollar-store chain's year-end prices are 64.20, 72.08, 80.80, 73.03, 89.58, 78.58 and 91.15. Its dividends rose from 1.10 in year one to 1.16, 1.22, 1.28, 1.34 and 1.40 in year six, 7.50 in all.

Holding-Period Returns

Each year's holding-period return is the price change plus the dividend, divided by the price at the start of the year. For the RV maker in year one, that is 50.97 minus 38.50 plus 0.24, or 12.71, divided by 38.50, which gives 33.01 percent. The same calculation for the other five years gives minus 20.99, 38.99, 5.01, minus 26.99 and 26.00 percent.

For the chain in year one, 72.08 minus 64.20 plus 1.10 is 8.98, divided by 64.20, which gives 13.99 percent. The other years give 13.71, minus 8.11, 24.41, minus 10.78 and 17.78 percent.

The denominator is always the opening price. Dividing by the year-end price instead would shrink every gain and enlarge every loss, and the error would carry into every figure that follows.

Dividends matter more for the chain. Its price rose 26.95 over the six years, and its dividends added 7.50, about 22 percent of its total gain. For the RV maker, dividends of 1.88 were about 12 percent of its total gain of 15.66.

Arithmetic Mean

The arithmetic mean is the sum of the yearly returns divided by six. The RV maker's returns sum to 55.03 percent, a mean of 9.17 percent. The chain's sum to 51.00 percent, a mean of 8.50 percent. On this measure the RV maker looks like the better performer.

Sample Standard Deviation

Spread is measured with the sample standard deviation, the usual yardstick for risk since Markowitz (1952) built portfolio theory on it. Each year's gap from the six-year mean is squared; the six squares are added; the total is divided by five, since one degree of freedom is spent on the mean; and the result is square-rooted. The RV maker's deviation is 28.20 percent; the chain's is 14.45 percent. The RV maker's returns swing almost twice as widely.

These figures rest on only six observations, so they are rough. Another six years could produce noticeably different deviations, and the two decimal places reported here are arithmetic precision, not statistical precision.

Geometric Mean

The geometric mean is the constant annual rate that would turn the starting investment into the ending value. Multiply one plus each year's return, take the sixth root of the product and subtract one. For the RV maker, the product of the six growth factors is 1.4110, and its sixth root minus one is 5.91 percent a year. For the chain, the product is 1.5571, giving 7.66 percent a year. Over the six years, an investment in the RV maker with dividends reinvested grew 41.10 percent, and one in the chain grew 55.71 percent.

The RV maker has the higher average year and the lower compound growth, and both figures are correct.

What this part is doingHighlighting the reversal makes the central lesson of the set impossible to miss.

Why the Averages Disagree

The arithmetic mean answers one question: what return should be expected in a typical single year? The geometric mean answers another: what rate did the investment actually compound at over the whole period? The gap between them grows with volatility. A loss of 26.99 percent requires a gain of about 37 percent just to break even, so large swings pull compound growth below the simple average. A useful approximation is that the geometric mean is close to the arithmetic mean minus half the variance. For the RV maker, half of 0.2820 squared is about 4.0 points, which takes 9.17 roughly to 5.2, close to the actual 5.91 given only six years. For the calmer chain the drag is only about 1.0 point.

Jacquier et al. (2003) show that the right average for forecasting depends on the horizon: the arithmetic mean suits one-year forecasts, while longer horizons call for a figure nearer the geometric mean. Bessembinder (2018) found that most individual U.S. stocks have earned less over their lifetimes than one-month Treasury bills, because a few very large winners account for the market's long-run gains while volatile individual stocks compound poorly, which is the same effect at a larger scale.

Annualizing the Six-Year Return

The chain's six-year return of 55.71 percent should not be divided by six. That gives 9.29 percent a year, which overstates compound growth because it ignores compounding. The correct annual rate is the sixth root, 7.66 percent.

What the Set Shows

Judged by arithmetic mean alone, the RV maker looks like the better stock. Judged by compound growth, the chain delivered more wealth with half the volatility. The calculation does not say which to buy; it shows that a high average with large swings can produce less wealth than a lower, steadier one.

What this part is doingClosing on what the numbers show, not on a purchase, keeps the set inside the unit's question.

References

Bessembinder, H. (2018). Do stocks outperform Treasury bills? Journal of Financial Economics, 129(3), 440-457. https://doi.org/10.1016/j.jfineco.2018.06.004

Jacquier, E., Kane, A., & Marcus, A. J. (2003). Geometric or arithmetic mean: A reconsideration. Financial Analysts Journal, 59(6), 46-53. https://doi.org/10.2469/faj.v59.n6.2574

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

MT422 Unit 2 instructions, in plain terms

Unit 2 asks students to compute returns and risk for two stocks from supplied prices and dividends. Instructors expect each year's holding-period return to include the dividend and to divide by the price at the start of the year. Both the arithmetic and geometric means are usually required, with a sentence on what each measures. The standard deviation should be the sample version unless the prompt says otherwise, and the formula should be named. At least one calculation should be worked by hand, so partial credit is possible if a later figure is wrong. A multi-year return should be annualized with a root, not by division. Interpretation should explain why the two means differ and should not treat the higher arithmetic mean as proof of a better investment. Spreadsheet functions are fine when named.

How the MT 422 Unit 2 example is put together

Tables of supplied prices and dividends open the example, exactly as given. Holding-period returns follow, with year one worked by hand for each stock and a warning about using the wrong denominator. A dividend section shows how much of each stock's gain came from payments. Arithmetic means, sample deviations and geometric means come next, each with its method, and the deviations carry a caution about six observations. A highlighted line states that both averages are correct. The explanation section uses the half-variance approximation to show why volatility lowers compound growth, then cites Jacquier and colleagues on forecasting horizons and Bessembinder on how single stocks compound. A short section shows the error of dividing a six-year return by six.

Reading the MT422 Unit 2 grading rubric

Graders of an MT422 return set look for correct holding-period returns, correct means and deviation, a worked example and interpretation. Graders often check the first year for the opening-price denominator, since that error shifts everything after it. Rubrics reward including dividends, which matter most for the steadier stock. Credit goes to reporting both means and explaining the reversal, because that is what the data were chosen to show. Annualizing with a root rather than division earns method points. A caution about how little six years can establish shows statistical judgment. Naming the better investment on the arithmetic mean alone tends to lose interpretation marks. Clear tables, consistent decimals and APA 7 references for any reading complete the grade.

Common MT422 Unit 2 mistakes, and how to avoid them

The most frequent weak calculation divides each year's gain by the ending price, or leaves dividends out, so every return is slightly wrong. Another common error reports only the arithmetic mean and declares the higher-average stock the winner. Students often annualize a six-year return by dividing by six, which overstates growth. Population and sample deviations get mixed without comment. Some papers show only a final table, so a single typing error costs every mark that depends on it. Before submitting, rebuild one stock's ending value by compounding your six returns from the starting price, adding back dividends if you treated them as reinvested. If the result does not match the growth your geometric mean implies, one of the yearly returns is wrong.

Get an MT422 Unit 2 example written to your instructions

Price data from the Unit 2 prompt, or tickers and dates if the section asks for real series, are enough to start. The free first MT422 calculation arrives in 24-48h with every return, mean and deviation shown in the order the rubric expects, worked in Excel or by hand as instructed, with any data source cited. 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.

More MT422 papers and BS in Business Administration samples

MT422 Unit 2 questions, answered

Should the geometric or the arithmetic mean be reported?

Both, with a sentence on what each answers. The arithmetic mean estimates a typical single year and feeds later expected-return work; the geometric mean describes what the money actually compounded to. When they differ sharply, as they do for a volatile stock, that difference is worth a sentence, because it shows volatility costing growth.

Do I use sample or population standard deviation?

Historical returns are almost always treated as a sample, so dividing by one fewer than the number of observations is the usual choice. Some instructors accept either if it is named. What costs marks is switching between them or leaving the reader to guess, so state the formula once and keep it throughout.

Can Excel functions replace the worked formulas?

Usually, provided the function is named and at least one result is shown by hand, so a grader can see the method as well as the output. STDEV.S and STDEV.P give different answers on the same data, which is exactly the kind of difference a short note beside the table should explain.

Where can I find a free MT422 Unit 2 sample paper?

This page holds the complete MT422 Unit 2 calculation, turning six years of prices and dividends for two composite stocks into returns, means and deviations.

Why does the stock with the higher average grow more slowly in the MT422 Unit 2 sample?

Its swings are twice as large, and large losses need even larger gains to recover, so volatility drags its compound growth below the steadier stock's.