MT422 Unit 3 Two-Asset Portfolio Problem Example

Course	MT422 Portfolio Management
Unit	Unit 3
Paper type	Two-asset portfolio problem
Length	About 1,020 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 3

Why a 28 Percent Stock Calms a 14 Percent One: An MT422 Unit 3 Two-Asset Portfolio Problem

[Student Name]

Purdue University Global

MT422: Portfolio Management

Unit 3 Two-Asset Portfolio Problem

[Instructor Name]

[Date]

Both stocks are the composite companies from Unit 2; historical means stand in for expected returns as the problem directs, every figure was computed from the Unit 2 returns, and the sources cited are real.

What this part is doingStating the counterintuitive result first gives the reader a reason to follow the arithmetic.

Inputs

The two stocks are the composite RV maker and dollar-store chain from Unit 2. The RV maker's six yearly returns have a mean of 9.17 percent and a sample standard deviation of 28.20 percent. The chain's have a mean of 8.50 percent and a deviation of 14.45 percent. The problem treats these historical means as expected returns. Six years say very little about the future, so the means are labeled as historical inputs, not forecasts.

Covariance and Correlation

Covariance measures whether the two stocks tend to be above or below their own means in the same years. For each year, the RV maker's deviation from its mean is multiplied by the chain's deviation from its mean. The six products are summed and divided by five. The result is 0.00532, in decimal terms.

Correlation rescales covariance to a range from minus one to plus one by dividing it by the product of the two deviations: 0.00532 divided by 0.2820 times 0.1445 gives 0.13. The two stocks barely move together. In year three, for example, the RV maker gained 38.99 percent while the chain lost 8.11 percent, and in year five the RV maker lost 26.99 percent while the chain lost 10.78.

The Portfolio Formulas

For return, the mix simply blends the two means by weight. Its variance is not a weighted average. It equals the RV weight squared times the RV variance, plus the chain weight squared times the chain variance, plus two times both weights times the covariance. The deviation is the square root of the variance.

The last term carries the whole lesson. When covariance is small, the cross term adds little, and the portfolio's variance falls below what either weighted variance alone would suggest.

A Worked Example at 20 Percent RV

With 20 percent in the RV maker and 80 percent in the chain, the expected return is 0.2 times 9.17 plus 0.8 times 8.50, or 8.63 percent. The variance is 0.04 times 0.07952, plus 0.64 times 0.02088, plus 2 times 0.2 times 0.8 times 0.00532. Those three terms are 0.00318, 0.01336 and 0.00170, which sum to 0.01825. The square root is 13.51 percent.

A weighted average of the two deviations would give 0.2 times 28.20 plus 0.8 times 14.45, or 17.20 percent. The actual figure is 3.69 points lower, and lower than the chain's own 14.45 percent.

Adding 20 percent of a stock twice as volatile makes the pair calmer than the steadier stock alone.

What this part is doingContrasting the true deviation with the weighted average shows exactly what diversification removes.

Eleven Weightings

The table runs from all chain to all RV maker in steps of 10 percent. Read in order of RV weight, the expected returns rise steadily from 8.50 to 9.17 percent, while the deviations follow a curve.

1. 0 percent RV: return 8.50, deviation 14.45

2. 10 percent RV: return 8.57, deviation 13.66

3. 20 percent RV: return 8.63, deviation 13.51

4. 30 percent RV: return 8.70, deviation 14.01

5. 40 percent RV: return 8.77, deviation 15.10

6. 50 percent RV: return 8.84, deviation 16.66

7. 70 percent RV: return 8.97, deviation 20.75

8. 100 percent RV: return 9.17, deviation 28.20

The deviation first falls, reaches its lowest point between 10 and 20 percent RV, then rises and keeps rising. Plotted with deviation on the horizontal axis and return on the vertical, the points form a curve that bends to the left of the straight line joining the two stocks, and the distance between the curve and that line is the diversification benefit at each mix.

The Minimum-Variance Mix

The weight that minimizes variance can be found by setting the derivative of the variance formula to zero. For the RV maker it equals the chain's variance minus the covariance, divided by the sum of both variances minus twice the covariance: 0.02088 minus 0.00532, divided by 0.07952 plus 0.02088 minus 0.01064. That gives 17.3 percent in the RV maker and 82.7 percent in the chain. This mix has a deviation of 13.48 percent and an expected return of 8.62 percent, both better than holding the chain alone.

Scanning the table would place the answer somewhere between 10 and 20 percent. The formula gives the precise weight, and the table only confirms it.

The portfolio stays less risky than the chain alone until the RV weight passes about 35 percent. Beyond that, the RV maker's own volatility outweighs the benefit of its low correlation.

Testing the Correlation

To show that the benefit depends on correlation, the 30/70 mix is rerun at three other values. At the actual correlation of 0.13 its deviation is 14.01 percent. If the correlation were plus one, the deviation would be 18.58 percent, exactly the weighted average, with no benefit at all. At zero it would be 13.19 percent. At minus one it would fall to 1.66 percent, nearly riskless. The same two stocks, with the same means and deviations, produce very different portfolios depending only on how they move together.

What the Problem Shows

Markowitz (1952) put this at the center of portfolio choice: what matters for the pair is the joint movement of the two stocks, and their separate swings are only half of it. Two stocks with a low correlation can produce a portfolio less volatile than either. The benefit is not automatic: it is large here only because the correlation is 0.13. Elton and Gruber (1977) and Statman (1987) extended the same arithmetic to many stocks and showed how quickly the benefit accumulates as holdings are added, and how much of a single stock's risk remains in a two-stock portfolio.

The 35 percent threshold describes these six years of returns, not a rule for any investor, and a different period could give a different correlation and a different answer.

What this part is doingEnding on the limits of six years keeps the result from being read as advice.

References

Elton, E. J., & Gruber, M. J. (1977). Risk reduction and portfolio size: An analytical solution. Journal of Business, 50(4), 415-437. https://doi.org/10.1086/295964

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

Statman, M. (1987). How many stocks make a diversified portfolio? Journal of Financial and Quantitative Analysis, 22(3), 353-363. https://doi.org/10.2307/2330969

What the MT422 Unit 3 assignment asks for

In the third unit students combine two assets and show how portfolio risk depends on their correlation. Instructors expect the covariance computed from paired returns, the correlation derived from it, and the portfolio variance formula applied with its cross term. A table of weightings and a curve of return against deviation are common requirements. The minimum-variance weight should come from its formula, with the table used only as confirmation. Historical means used as expected returns should be labeled as inputs, not forecasts, since a handful of years says little about the future. Many prompts ask what would change if the correlation were different, and the strongest answers show it with numbers. Interpretation should make clear that the benefit depends on correlation and is not automatic.

How this MT422 Unit 3 example is built

In this example the inputs come first, with the historical means labeled. The covariance and correlation section explains each step and points to two years when the stocks moved apart. The portfolio formulas are stated, followed by a fully worked case at 20 percent RV maker set against the naive weighted average, under a highlighted line on the pair becoming calmer. A list of eight weightings shows deviation falling and then rising. The minimum-variance mix is solved by formula and checked against the table, and the 35 percent threshold is found. The correlation panel reruns the 30/70 mix at three values. Markowitz frames the result, and Elton and Gruber and Statman extend it to more stocks.

Reading the MT422 Unit 3 grading rubric

Two-asset problems are typically graded on a correct covariance and correlation, a correct portfolio variance with its cross term, the minimum-variance weight by formula and interpretation of the correlation's role. Computing portfolio deviation as a weighted average of deviations is the error graders look for first. Rubrics also check the cross term for its factor of two and for covariance rather than correlation. Credit goes to labeling historical means as inputs. Finding the minimum-variance weight by formula earns method points that scanning a table does not. A correlation panel showing how the benefit disappears at plus one demonstrates understanding. Overreaching from six years to investment advice loses interpretation marks. A labeled return-against-risk chart lets the grader see the bend at a glance.

MT422 Unit 3 help from the desk

Many weak solutions take the portfolio's deviation as the weighted average of the two deviations, which removes the very effect the problem tests. Others drop the factor of two in the cross term, or multiply weights by correlation instead of covariance. Students often read the minimum-variance weight off a coarse table rather than solving for it. Historical means are sometimes presented as reliable forecasts. Interpretation frequently claims that holding two stocks always reduces risk, ignoring correlation. Before submitting, recompute your portfolio deviation at a correlation of plus one. It should equal the weighted average of the two deviations exactly. If it does not, your formula has an error, and finding it there is far easier than finding it in the eleven-row table.

Get an MT422 Unit 3 example written to your instructions

Two assets named in the Unit 3 prompt, plus their return history or a given correlation, are what a first custom MT422 portfolio problem needs; it is free, lands in 24-48h and shows the cross term, the minimum-variance weight and a curve, formatted to the rubric. Real tickers work if the section wants them, with the data period stated. 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 3 questions, answered

What if my two assets have a high correlation?

Then the diversification gain is small, and an honest answer reports that instead of hunting for a benefit. Above a certain correlation, equal to the lower deviation divided by the higher one, the minimum-variance mix holds none of the riskier asset at all. Stating that threshold turns a disappointing result into a correct and complete one.

Are six annual observations enough for a correlation?

For a classroom problem it is common, but a careful answer admits that correlations from six points are unstable and could look quite different over another period. Some sections supply longer monthly series for this reason. Naming the limitation in one sentence costs nothing and shows the result is understood as an estimate rather than a fact.

Do I need to draw the curve?

Most rubrics for this kind of problem reward a plot of expected return against standard deviation, because the bend in the curve is the diversification effect made visible. A spreadsheet chart is fine. Label the minimum-variance point and both single-stock ends, and state the correlation used so the shape can be checked.

Where can I find a free MT422 Unit 3 sample paper?

You can read the complete MT422 Unit 3 problem here, combining two composite stocks with a 0.13 correlation and solving for the minimum-variance mix.

What happens to the 30/70 mix in the MT422 Unit 3 sample at a correlation of minus one?

Its deviation falls to 1.66 percent, nearly riskless, against 18.58 percent at plus one, with the same stocks, means and deviations.