Investment Analysis Assignment Sample: Diversification, Risk and the Sharpe Ratio

This is a sample investment analysis, written for an undergraduate finance module. It builds one portfolio, then measures it: five asset classes with stated weights, the risk and return of each, the correlation between them, the portfolio's expected return and standard deviation, and its Sharpe ratio set against two simpler alternatives. Every figure comes from one public dataset of annual US returns, so you can reproduce the arithmetic yourself.

The two sections before the sample explain the ideas it assumes you already know. More finance and economics samples are in our business assignment samples, and our MBA and management assignment help page covers finance modules.

What Is Diversification in Investment Analysis?

Diversification means holding assets whose returns do not move together, so a fall in one is partly offset by the others. It reduces the risk specific to a single company or sector without necessarily reducing expected return. It cannot remove market risk, which moves every asset at once, and that limit is the point most assignments lose marks on.

The idea is formalised in modern portfolio theory, set out by Harry Markowitz in his 1952 paper Portfolio Selection. Markowitz's argument is that a portfolio should be judged as a whole rather than as a list of separate holdings, because assets that are imperfectly correlated combine into a portfolio whose risk is lower than the weighted average of its parts. The efficient frontier is the set of portfolios that give the highest expected return for each level of risk. Markowitz shared the 1990 Nobel Memorial Prize in Economic Sciences for this work.

In practice the correlation matrix does most of the work in an assignment like this one. Two assets with a correlation close to plus one give almost no diversification benefit, however different they look. Assets with low or negative correlation are what actually shift the portfolio's standard deviation. Say which pairs are doing the work and why, rather than listing the asset classes and moving on. A clear treatment of risk, return and the risk-return trade-off for a single asset is in OpenStax's open-access Principles of Finance.

How Do You Calculate the Sharpe Ratio?

Subtract the risk-free rate from the portfolio's return, then divide by the portfolio's standard deviation. The result is the excess return earned per unit of total risk. A higher number means better risk-adjusted performance. The ratio is only comparable between portfolios measured over the same period and against the same risk-free rate.

The measure comes from Sharpe's 1966 study of mutual fund performance, which ranked funds by reward per unit of variability rather than by return alone. It uses total risk, that is standard deviation, so it penalises upside volatility as well as downside; measures such as the Sortino ratio exist because of that. It also assumes returns are roughly normally distributed, which is a poor assumption for assets with fat tails, cryptocurrency among them. If your portfolio includes one of those, say so when you report the figure. To explain what that assumption means, our probability and statistics assignment sample sets up a normal distribution and reads it with z-scores.

Investment Analysis: A Worked Five-Asset Portfolio

The Brief, the Data and the Method

The brief was to construct a diversified portfolio for a long-term investor, justify the allocation, and assess it on risk, return, correlation and risk-adjusted performance.

All figures below are computed from one source: Aswath Damodaran's public dataset of annual returns on US stocks, bonds, bills, corporate bonds, real estate and gold, updated on 5 January 2026 and running to the end of 2025. The measurement window is the 30 calendar years from 1996 to 2025, which includes the dot-com fall, the 2008 financial crisis, the 2020 pandemic and the 2022 bond sell-off. Returns are annual and nominal, before tax and dealing costs, and each portfolio is rebalanced to its weights at the start of every year. Risk is measured as the sample standard deviation of annual returns, and the risk-free rate is the average 3-month Treasury bill return over the same 30 years, 2.35 per cent, so that every input covers the same period.

The data has limits, and they belong in the body of the assignment, not in a footnote. A 30-year average is not a forecast; it is the base rate you argue from. The real estate series also has a gap: it is the S&P/Case-Shiller US National Home Price Index, which measures price change only, so it understates property returns by the rental income an owner would also receive, and it ignores transaction costs and maintenance.

The Portfolio: Assets and Weights

Five asset classes, weights summing to 100 per cent, each represented by a series in the dataset above.

Table 1: portfolio weights

The equity weight carries the growth, the two bond sleeves carry the income and most of the defence, real estate adds an asset whose price is set in a different market from either, and the small gold holding is there for the years when financial assets fall together.

Why These Five Asset Classes

Each class is in the portfolio for a stated job, and each has a cost.

• US equities, 45 per cent. The highest long-run return in the dataset and the highest volatility. A long-term investor is paid for holding that volatility, which is why equities take the largest single weight rather than the majority of the portfolio.
• Ten-year Treasury bonds, 20 per cent. Held for the years when equities fall. In 2008 the S&P 500 returned minus 36.55 per cent while 10-year Treasuries returned plus 20.10 per cent, and that single pairing is most of the case for holding them.
• Baa corporate bonds, 15 per cent. A higher yield than Treasuries in exchange for credit risk. Their weakness is that the credit risk shows up in exactly the years equities fall, so they are a partial hedge at best.
• Real estate, 15 per cent. Prices are set in a market with different participants and slower information, so the series moves on its own schedule. It is illiquid and, in this dataset, measured without rental income.
• Gold, 5 per cent. No income and no earnings to value it from, which is why the weight is small. It earns its place through behaviour rather than return: in 2022, when equities and both bond sleeves fell together, gold returned plus 0.55 per cent.

Cryptocurrency was considered and left out. The dataset has no comparable 30-year series, and the Sharpe ratio assumes returns that are roughly normally distributed, which crypto returns are not. If your own brief requires a crypto sleeve, state the window you measured, keep the weight small enough that one year cannot dominate the result, and report the Sharpe ratio with the fat-tail caveat attached.

Risk Assessment: How Much Each Asset Moves

Risk here is the sample standard deviation of annual returns over the 30 years to 2025. Equities and gold are the volatile holdings, at 17.59 and 18.17 per cent, and the two bond sleeves and real estate sit between 6.30 and 8.79 per cent. Worth noting for the analysis: gold is slightly more volatile than the S&P 500 over this window, which is why a 5 per cent weight is the responsible size for it.

Volatility is not the only risk in the portfolio. Real estate is illiquid, corporate bonds carry default risk that volatility understates, and every figure here is nominal, so inflation risk sits underneath all five.

Return Assessment: What Each Asset Earned

Both averages belong in the table. The arithmetic mean is the input to an expected-return calculation; the geometric mean is what an investor actually compounded, and it is always the lower of the two for a volatile asset.

Table 2: annual returns and volatility, 1996 to 2025, computed from Damodaran's dataset

The gap between the two averages is the cost of volatility. For equities it is 1.54 percentage points a year; for real estate, which barely moves by comparison, it is 0.19. That gap is a better argument for managing volatility than any adjective.

Correlation Analysis: Which Pairs Do the Work

Correlations are computed on the same 30 annual observations. Values run from minus one to plus one, and the useful pairs are the ones near zero or below it.

Table 3: correlation of annual returns, 1996 to 2025

Three pairs carry the diversification in this portfolio. Equities against Treasuries at minus 0.28 is the main one, and it is the pair that produced the 2008 result above. Real estate against Treasuries at minus 0.29 and real estate against gold at minus 0.29 do the rest. Equities against gold is effectively zero at 0.00, which is still useful: an uncorrelated asset reduces portfolio variance even when it does not move opposite.

Every pair appears twice in a correlation matrix, once on each side of the diagonal, and the two cells must match: Baa corporate bonds against gold reads plus 0.31 in the Baa row and in the gold row. Check this in any matrix you build by hand; a value pasted into the wrong cell carries straight into the portfolio standard deviation.

The pair that does least is equities against Baa corporate bonds, at plus 0.39, and that is the weak point of the allocation. Corporate credit behaves partly like equity because the same recession that cuts profits also raises default risk. In 2022 the limit showed up plainly: equities returned minus 18.04 per cent, Treasuries minus 17.83 per cent and Baa bonds minus 15.23 per cent, all in the same year, and only real estate at plus 5.65 per cent and gold at plus 0.55 per cent held any ground. A correlation measured over 30 years is an average, not a promise about the next one.

Expected Return and Portfolio Standard Deviation

Expected return is the weighted average of the parts. Standard deviation is not, and the difference between them is the whole point of the exercise.

Expected return: (0.45 x 11.80) + (0.20 x 4.23) + (0.15 x 6.53) + (0.15 x 4.94) + (0.05 x 9.81) = 8.37 per cent a year. Compounded, the same portfolio returned 8.02 per cent a year over the 30 years.

Standard deviation of the portfolio's annual returns: 8.49 per cent. The weighted average of the five standard deviations is 12.56 per cent, so combining the assets removed 4.07 percentage points of volatility, about a third, without giving up any of the expected return. That reduction is the diversification benefit, stated as a number rather than as a claim.

To show the mechanism, here is the two-asset version worked in full for a 60/40 holding of equities and Treasuries, using the standard variance formula. The correlation is carried to three decimals, because rounding it to -0.28 moves the answer:

σ² = (0.6² x 17.59²) + (0.4² x 8.79²) + (2 x 0.6 x 0.4 x -0.283 x 17.59 x 8.79) = 111.39 + 12.36 - 21.00 = 102.75, so σ = 10.14 per cent. Computed directly from the 30 annual returns of the 60/40 mix, with nothing rounded, it is 10.13 per cent, the figure used in Table 4.

The third term is negative only because the correlation is negative, and that single term is what pulls the result below the weighted average of 14.07 per cent. The five-asset figure of 8.49 per cent is the same calculation extended across all ten pairs in Table 3.

The Sharpe Ratio of the Portfolio

Sharpe ratio = (portfolio return - risk-free rate) / portfolio standard deviation = (8.37 - 2.35) / 8.49 = 0.71.

The figure is only meaningful next to an alternative measured the same way, so here are two.

Table 4: risk-adjusted performance against two alternatives, 1996 to 2025

The five-asset portfolio gives up 3.43 percentage points of annual return against holding equities alone, and in exchange its volatility is less than half and its worst year is a loss of 14.53 per cent instead of 36.55 per cent. Per unit of risk it is the better portfolio, at 0.71 against 0.54. Which one is right depends on the investor's horizon and tolerance for a bad year, and that judgement, not the ratio, is what the question is really asking for.

The worst-year column says something the ratios do not. The five-asset portfolio and the equity-only portfolio both had their worst year in 2008. The 60/40 portfolio did not: its worst year was 2022, at minus 17.95 per cent, when equities and Treasuries fell together and the negative correlation that justifies the pairing did not hold. A portfolio built on one correlation has one bad year waiting for it.

The ratio also depends on the risk-free rate. The rate used here is the 30-year average of 2.35 per cent. If you instead use a rate near 4 per cent, the Sharpe ratio of the same portfolio falls to 0.51, and the equity-only portfolio falls to 0.44. The ranking holds, but the level moves, which is why the ratio has to be quoted with the risk-free rate and the period attached.

What the Figures Show About This Portfolio

Over 30 years the portfolio kept the expected return of its parts with about a third less volatility, and in 2008 it lost less than half what equities lost; 2022 showed the limit, when bonds fell with equities.

Value of $100 invested at the end of 1995, five-asset portfolio against US equities, 1995 to 2025

Chart data

Point (USD)	Five-asset portfolio	US equities (S&P 500)
1995	100 USD	100 USD
1996	111 USD	123 USD
1997	132 USD	163 USD
1998	155 USD	210 USD
1999	169 USD	253 USD
2000	172 USD	230 USD
2001	169 USD	203 USD
2002	165 USD	159 USD
2003	193 USD	203 USD
2004	212 USD	225 USD
2005	225 USD	236 USD
2006	247 USD	273 USD
2007	262 USD	288 USD
2008	224 USD	183 USD
2009	253 USD	230 USD
2010	280 USD	264 USD
2011	297 USD	270 USD
2012	328 USD	313 USD
2013	370 USD	413 USD
2014	409 USD	469 USD
2015	412 USD	476 USD
2016	447 USD	532 USD
2017	506 USD	646 USD
2018	497 USD	619 USD
2019	595 USD	812 USD
2020	683 USD	959 USD
2021	783 USD	1,232 USD
2022	681 USD	1,010 USD
2023	785 USD	1,273 USD
2024	887 USD	1,589 USD
2025	1,012 USD	1,871 USD

• Diversification worked, and by a measurable amount. Volatility of 8.49 per cent against a weighted-part average of 12.56 per cent, for the same expected return.
• The defence held in the crisis year. In 2008 the portfolio lost 14.53 per cent while equities alone lost 36.55 per cent. Over the 30 years the portfolio had five negative years against six for equities, and the negative years were shallower.
• It did not hold in 2022. Equities, Treasuries and corporate bonds all fell together, and the portfolio lost 13.09 per cent. Diversification across financial assets is not protection against a shock to interest rates.
• One small holding can dominate a single year. Gold returned 66.22 per cent in 2025, which added 3.3 points to the portfolio's 14.13 per cent that year from a 5 per cent weight. That is an argument for reporting long windows, not for raising the weight.

Conclusion and What a Marker Will Look For

The allocation is defensible on this evidence: a Sharpe ratio of 0.71 against 0.54 for equities alone, with a worst year less than half as deep, is a reasonable trade for a long-term investor who has to live through the bad years. The case for it rests on three negative or near-zero correlations, and its weakness is that those correlations are averages, which did not hold in 2022.

Two companion samples show the parts this one leaves out. The financial analysis sample works through ratio analysis on a single company's published accounts, which is the other half of most investment modules, and the essay on purchasing power parity covers the exchange-rate side if your portfolio holds assets priced in another currency.

If you are writing this assignment, the marks are in four places. State your data source and window, and use one source throughout so your figures reconcile. Show the correlation matrix and say which pairs are doing the work. Show the portfolio standard deviation calculation rather than asserting the benefit. And close with a recommendation that names the investor you are advising, because a risk-adjusted number on its own does not answer the question.

Need help with a similar investment analysis or portfolio management assignment? Message us on WhatsApp with the brief, the word count and the deadline.

Sources

• Damodaran, A. (2026) Historical returns on stocks, bonds and bills: United States, annual series 1928 to 2025, updated 5 January 2026. New York University Stern School of Business. Available at: pages.stern.nyu.edu. Every return, standard deviation and correlation in this sample is computed from this dataset; the spreadsheet version carries the source notes for each series, including that real estate is the S&P/Case-Shiller US National Home Price Index and is price appreciation only.
• Markowitz, H. (1952) 'Portfolio selection', The Journal of Finance, 7(1), pp. 77-91. Available at: JSTOR. The founding paper of modern portfolio theory.
• Sharpe, W.F. (1966) 'Mutual fund performance', The Journal of Business, 39(1), Part 2, pp. 119-138. doi:10.1086/294846. The paper the ratio comes from.
• The Nobel Prize (1990) Harry M. Markowitz, facts. Available at: nobelprize.org
• OpenStax (2022) Principles of Finance, section 15.1, Risk and return to an individual asset. Available at: openstax.org