Why does a 28 percent stock make a 14 percent stock steadier? Correlation of 0.13 is the answer this MT422 two-asset portfolio problem for Unit 3 works out. Searches like "mt 422 unit 3 assignment example", "mt422 unit 3 sample" and "mt422 unit 3 example" land here.
What a finished MT422 Unit 3 two-asset portfolio problem looks like
Three pages, one table and one curve. Covariance between the two stocks comes to 0.00533 from six paired years, and dividing by the product of their deviations gives the correlation of 0.13. The table then runs eleven weightings from all chain to all RV maker. At 20 percent RV maker the portfolio's deviation is 13.51 percent, below the chain's 14.45 alone and far below the 17.20 a weighted average of the two deviations would suggest. The minimum-variance mix, solved by formula, holds 17.3 percent in the RV maker for 13.48 percent risk and an 8.61 percent expected return. Risk stays under the chain's own level until the RV share passes about 35 percent. A final panel reruns the 30/70 mix at correlations of plus one, zero and minus one.
How a MT422 Unit 3 example is structured
The problem builds the portfolio formula piece by piece so the covariance term can be seen doing its work. Covariance is computed first from paired deviations, then converted to a correlation, because the correlation is the figure readers can interpret. The two-asset variance formula is written with both squared-weight terms and the cross term, and one weighting, 20/80, is substituted in full. The table and curve follow, plotting expected return against deviation for every weighting, with the minimum-variance point labeled. The formula for that point is derived rather than found by trial, then checked against the table. A sensitivity panel isolates correlation as the only input changing. At plus one the 30/70 mix carries 18.57 percent risk, at zero 13.19, and at minus one 1.65, which shows the gain belonged to correlation rather than to the number of stocks held.
Covariance before correlation
Paired deviations over six years give 0.00533, and the conversion to 0.13 is shown with both standard deviations substituted.
The cross term written out
At 20/80 the variance formula carries two squared-weight terms and twice the weighted covariance, reaching 13.51 percent risk.
Minimum variance by formula
17.3 percent in the RV maker, 13.48 percent deviation and an 8.61 percent expected return, confirmed against the table's nearest rows.
Where the benefit runs out
Beyond roughly 35 percent in the RV maker, the combined position becomes riskier than the chain held on its own.
Correlation isolated
Plus one, zero and minus one applied to the same 30/70 mix, producing deviations of 18.57, 13.19 and 1.65 percent.
Where marks go in MT422 Unit 3
Portfolio deviation computed as a weighted average of the two deviations is the error these problems exist to catch, and it turns 13.51 into 17.20. The cross term is the next thing graders inspect: dropping the factor of two, or using correlation where covariance belongs, gives a number that looks plausible and is wrong. Historical means used as expected returns should be labeled as such, since six years say little about the future. Papers that find the minimum-variance weight by scanning the table, without the formula, typically lose method credit even when the answer is close. Interpretation carries weight too. Claiming a diversification benefit from holding two stocks, without saying it depends on their correlation, misses the sensitivity panel's point, and treating a 35 percent cap as guidance for an actual investor reads beyond the problem.
Get a 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.
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.