| Course | MT483 Investments |
|---|---|
| Unit | Unit 3 |
| Paper type | Risk and return calculation |
| Length | About 910 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 MT483 Unit 3
Ten Years of the S&P 500, With and Without Dividends: An MT483 Unit 3 Risk and Return Calculation
[Student Name]
Purdue University Global
MT483: Investments
Unit 3 Risk and Return Calculation
[Instructor Name]
[Date]
The index levels and total returns are S&P Dow Jones Indices' published figures; the fund expense and the reading for an investor are illustrative.
The Data
The series is the S&P 500's closing level on the last trading day of each year from 2014 through 2024, as published by the index's owner (S&P Dow Jones Indices, 2025), together with the index's published calendar-year total returns, which assume dividends are reinvested. The closes are 2,058.90 (2014), 2,043.94 (2015), 2,238.83 (2016), 2,673.61 (2017), 2,506.85 (2018), 3,230.78 (2019), 3,756.07 (2020), 4,766.18 (2021), 3,839.50 (2022), 4,769.83 (2023) and 5,881.63 (2024). Eleven closes give ten annual returns. Both series come from the same publisher, so the gap between them can be read as the dividend component without mixing index families.
Price Returns, One Year Worked
A holding-period return is the ending level divided by the starting level, minus one. For 2016, the close of 2,238.83 divided by 2015's close of 2,043.94 is 1.0954, a price return of 9.54 percent. The same computation for the other nine years gives minus 0.73 percent in 2015, 19.42 in 2017, minus 6.24 in 2018, 28.88 in 2019, 16.26 in 2020, 26.89 in 2021, minus 19.44 in 2022, 24.23 in 2023 and 23.31 in 2024. The range runs from a loss of almost a fifth in 2022 to a gain of almost three-tenths in 2019, which is already a hint about volatility before any formula is applied.
The Dividend Column
The published total returns for the same years are 1.38, 11.96, 21.83, minus 4.38, 31.49, 18.40, 28.71, minus 18.11, 26.29 and 25.02 percent. Subtracting each price return from its total return gives the dividend contribution: 2.11 points in 2015, 2.42 in 2016, 2.41 in 2017, 1.86 in 2018, 2.61 in 2019, 2.14 in 2020, 1.82 in 2021, 1.33 in 2022, 2.06 in 2023 and 1.71 in 2024, an average of 2.05 points a year.
Dividends turned 2015 from a small loss into a small gain, and over ten years they were worth more than $5,600 on a $10,000 start.
The column also shows the dividend share falling late in the decade. As prices rose faster than payouts, the yield shrank, so the 2024 contribution of 1.71 points is smaller than the 2.42 points of 2016 even though the index was far higher.
Averages in Pairs
The arithmetic mean of the ten price returns is 12.21 percent. The geometric mean, the constant rate that would turn the 2014 level into the 2024 level, is 11.07 percent, found by taking the tenth root of 5,881.63 over 2,058.90 and subtracting one. On total returns the arithmetic mean is 14.26 percent and the geometric mean 13.10. The gap between the two averages, 1.16 points on total returns, comes from volatility: a 19 percent loss followed by a 24 percent gain does not return the investor to the starting balance, and the compound rate records that while the simple average does not. Jacquier et al. (2003) show that the arithmetic mean suits a one-year forecast and the geometric mean suits a description of what was actually earned over the full period, so both belong in the report with their uses stated.
Standard Deviation
The sample standard deviation of the price returns is 16.15 percent, using ten observations and dividing by nine. The population formula, dividing by ten, gives 15.32 percent; the sample version is reported because these ten years are a sample of the index's possible outcomes, not the whole of them. Total returns have a sample standard deviation of 16.35 percent, slightly higher because dividends were not a constant addition from year to year.
Growth of $10,000
Compounding the price returns turns $10,000 at the end of 2014 into $28,567 at the end of 2024. Compounding the total returns turns it into $34,257. An index fund charging 0.03 percent a year would have delivered about $34,166, so the fund's fee over the decade cost roughly $91 while the dividends it collected were worth $5,690. Bodie et al. (2024) treat total return as the measure an investor actually experiences, and the two endings make the reason concrete: a report built from price levels alone would have understated the fund holder's result by about a fifth.
What 16 Percent Volatility Means
Under a bell-curve assumption, roughly two of every three yearly results should land no further than 16.35 points from the 14.26 percent average. For total returns that band runs from about minus 2 percent to plus 31 percent. Seven of the ten years fell inside it, which fits the rule well enough, while 2018 and 2022 fell below it and 2019 above it.
The figures describe one decade, not the index's nature. The period began after the 2008 crisis had passed and included a long expansion and a fast recovery from 2020's sell-off, so its 13.10 percent compound total return is well above the long-run record. Ten annual observations are also too few to estimate a mean precisely: with a standard deviation of 16 percent, the standard error of a ten-year average is about 5 points. The calculation measures what happened from 2015 through 2024; it is not a forecast for any later decade, and any reader planning on these returns should first look at a much longer history.
References
Bodie, Z., Kane, A., & Marcus, A. J. (2024). Investments (13th ed.). McGraw Hill.
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
S&P Dow Jones Indices. (2025). S&P 500 [Index data and performance]. https://www.spglobal.com/spdji/en/indices/equity/sp-500/
What the MT483 Unit 3 assignment asks for
For Unit 3 of MT483, students usually take a real price history, an index or a stock, and measure its return and risk. Convert the levels into annual holding-period returns and show one year worked in full. If total return figures are available from the same publisher, add them so dividends appear as a computed column rather than an assertion. Report the arithmetic and geometric means together and explain the gap between them. State whether the standard deviation uses the sample or population formula. Then interpret: what does the volatility figure mean for someone holding the asset, and how far can ten observations be trusted? Cite the data source with its publisher and dates, since the series is real and anyone grading it may look the numbers up.
Inside the MT483 Unit 3 example
All eleven closes are printed with their source before any arithmetic, and 2016's 9.54 percent return is worked from 2,238.83 over 2,043.94. The other nine years follow in sentences. Total returns sit beside them, and subtracting the two series produces a dividend column averaging 2.05 points, with a highlighted line noting that dividends turned 2015 from a loss into a gain. The means come in pairs, the 1.16 point gap on total returns tied to year to year swings, and Jacquier and colleagues explain which mean suits which purpose. Growth of $10,000 is shown on price alone, with dividends, and after a 0.03 percent fund fee. The volatility section counts seven of ten years inside one deviation and puts the standard error of the average near five points.
MT483 Unit 3 rubric: what earns full points
Return calculations that stop at price levels understate what a fund holder received, and instructors in this unit generally expect dividends to be addressed. Credit depends on correct holding-period returns, divided by the starting level and not the ending one, since that slip shifts every figure after it. A mean reported alone draws comment; pairing the arithmetic and compound averages and explaining the difference shows understanding of compounding. The deviation should carry its formula. Sourcing is graded more closely here than in many units because the data are real, so the publisher, index and dates belong in the text and the references. Interpretation earns the remaining points: reading the band for an investor, noting the decade's strength and avoiding any forecast built from ten numbers.
MT483 Unit 3 help from the desk
A common problem is mixing sources, with price levels from one website and total returns from another, so the dividend column fails to reconcile. Students also compute returns with calendar dates that do not match year ends, or skip the first year because eleven levels produce only ten returns. Spreadsheet functions sometimes return the population deviation by default; check which one was used and say so. Writing the arithmetic mean as the rate a buyer actually earned overstates the result whenever returns vary. Interpretation is where many papers end abruptly with a number and no meaning attached. Before submitting, recompute one return by hand, add the dividend column, and write two sentences on what the period was like and why it may not repeat.
Get an MT483 Unit 3 example written to your instructions
Some sections name the security and the window for Unit 3, while others let the writer pick both. Either way, the rubric plus those choices is enough: a first MT483 calculation is built free from the real price history, sources and dates cited, dividends included and every return traceable, delivered within 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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MT483 Unit 3 questions, answered
Can I use a different index or a single stock?
Yes, if the prompt allows. Any series with published prices works, and a single stock shows higher volatility than a broad index. Make sure the total return figures come from the same provider as the prices, so the dividend column reconciles. Cite the source and the exact dates of each closing value you use.
Why do price returns and total returns differ?
Price returns track only the change in the index level. Total returns assume dividends are reinvested, which is closer to what a fund holder receives before fees. For a broad US stock index the gap has run around two points a year recently. A calculation that ignores it describes the index, not the investor holding it.
Is ten years of annual data enough?
It is common for coursework and easy to check, but ten observations support only a loose estimate. Many prompts ask for monthly data instead, which produces more observations and requires annualizing. Whatever the frequency, a sentence noting that the period may not represent future conditions shows mature judgment about the numbers.
Where can I find a free MT483 Unit 3 sample paper?
This page shows the full MT483 Unit 3 calculation built from ten years of S&P 500 closes and total returns, with means, deviations, a dividend column and growth of $10,000.
What is the difference between the 14.26 and 13.10 percent averages in the MT483 Unit 3 sample?
The first is the simple average of yearly total returns; the second is the compound rate actually earned over the decade, lower because gains and losses of equal size do not cancel.