MT422 Unit 5 Beta and CAPM Analysis Example

Course	MT422 Portfolio Management
Unit	Unit 5
Paper type	Beta and CAPM analysis
Length	About 940 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 5

Above or Below the Line Depends on the Window: An MT422 Unit 5 Beta and CAPM Analysis of a Freight Broker

[Student Name]

Purdue University Global

MT422: Portfolio Management

Unit 5 Beta and CAPM Analysis

[Instructor Name]

[Date]

The freight broker, its prices and its sixty monthly returns are composite, as are the analyst target and the supplied 4.2 percent risk-free rate and 5.5 percent market premium; the regression statistics are internally consistent, and the sources cited are real.

What this part is doingPreviewing the split-window result in the lead tells the grader the analysis will not treat one beta as exact.

The Data

The analysis uses sixty monthly total returns for the composite freight broker and for a broad U.S. stock index over the same five years. The stock's returns have an annualized standard deviation of 26.54 percent, against 15.75 percent for the index. Monthly returns are used because five years of annual data would give only five points, far too few to estimate a slope. Each return is regressed as an excess return over the monthly Treasury bill yield, so the slope measures how the stock's return above bills moves with the market's return above bills.

The Regression

The full-period regression of the stock's excess returns on the index's excess returns gives a beta of 1.38. When the market's excess return rises by one percentage point in a month, the broker's tends to rise by about 1.38 points. The standard error of the estimate is 0.13. The R-squared is 0.67, meaning about two thirds of the variation in the stock's monthly returns moves with the market, and one third is specific to the company.

These figures fit together. R-squared equals beta squared times the market's variance divided by the stock's variance: 1.38 squared, times 0.1575 squared, divided by 0.2654 squared, gives 0.67. Two standard errors either side of 1.38 give a rough 95 percent range for the true beta of 1.13 to 1.63.

Two Windows

Splitting the sixty months into two halves of thirty gives a beta of 1.05 for the first and 1.67 for the second. The broker's sensitivity to the market rose sharply. A plausible reason, for a freight broker, is that the second half included a freight recession, when spot rates and shipment volumes fell together with the wider economy, so the stock moved more closely with the market. Each half-window beta has a wider error band than the full estimate because it rests on half the data, so part of the gap may be noise; still, the difference is large enough to matter for the conclusion.

The same stock looks fairly priced, cheap or expensive depending on which thirty months produced its beta.

What this part is doingNaming the window effect in a single line prepares the reader for the conclusion's caution.

Expected Return From the Target

The stock trades at 36.40. An analyst target for one year from now is 40.10, and the expected dividend is 0.54. The expected holding-period return is the target price minus today's price plus the dividend, divided by today's price: 40.10 minus 36.40 plus 0.54, or 4.24, divided by 36.40, which is 11.65 percent. This is a forecast, and it is only as good as the target behind it.

What the Model Requires

In the model Sharpe (1964) developed, a stock is paid only for its market risk: bills set the floor, and on top of it the stock earns its beta multiplied by the premium the whole market offers over bills. Taking the case's 4.2 percent bill rate and 5.5-point premium, the full-period beta requires 4.2 plus 1.38 times 5.5, or 11.79 percent. On the first-half beta it is 9.98 percent, and on the second-half beta 13.39 percent.

The premium in this formula is the market's expected return minus the risk-free rate. Using the market's total expected return in its place, for example 9.7 percent instead of 5.5, would inflate every required return by about 1.38 times 4.2 points.

The CAPM result is not a forecast of what the stock will earn. It is the return its market risk requires. Comparing the two tells an analyst whether the forecast offers enough to justify the risk.

On the Security Market Line

Plotted on a security market line that runs from 4.2 percent at a beta of zero with a slope of 5.5, the stock's forecast of 11.65 percent sits 0.14 points below the line at the full beta. At the first-half beta it sits 1.67 points above the line, and at the second-half beta 1.74 points below.

Sensitivity

The conclusion depends on two choices. One is the window: the full beta places the stock just below the line, the early beta well above it and the late beta well below. The other is the premium. At a premium of 4.5 percent, the full-period required return falls to 10.41 percent and the stock sits above the line. At 6.5 percent, it rises to 13.17 percent and the stock sits well below.

Blume (1971) found that estimated betas tend to move toward one over time, which is why some services report an adjusted beta that weights the raw estimate two thirds and one third toward one. For the broker, that gives about 1.25 and a required return of 11.10 percent, which would put the stock slightly above the line.

What the Analysis Shows

The broker's forecast return is close to what its market risk requires, and whether it lies slightly above or below the line depends on the beta window, the premium and whether the beta is adjusted. None of those choices is obviously right. Fama and French (2004) concluded that the CAPM's empirical record is weak, with returns explained poorly by beta alone, which is a further reason not to read a 0.14-point gap as a verdict. The model frames the question; it does not settle it.

What this part is doingEnding on what the model can and cannot settle keeps the analysis on pricing rather than on a trade.

References

Blume, M. E. (1971). On the assessment of risk. Journal of Finance, 26(1), 1-10. https://doi.org/10.1111/j.1540-6261.1971.tb00584.x

Fama, E. F., & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25-46. https://doi.org/10.1257/0895330042162430

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x

The Purdue Global MT422 Unit 5 instructions

For MT422 Unit 5, a stock's beta is estimated, compute its required return under the capital asset pricing model and compare it with an expected return. Instructors expect the regression described: the period, the return frequency, the index and whether excess returns were used. Beta should come with its standard error or another sign of how precise it is. The expected return usually comes from a price target and dividend, and it should be labeled a forecast. Required return starts from the bill rate and adds beta's share of the market premium, which must be the market's excess over bills, never its total return. Plotting the stock against the security market line is common, and the strongest analyses test how sensitive its position is to the window and the premium.

How this MT422 Unit 5 example is built

In this sample the data section explains why sixty monthly returns are used and why returns are taken in excess of bills. The regression section reports beta, its standard error and R-squared, and shows that the three figures fit together. Splitting the window gives two different betas, with a reason a freight broker's sensitivity might rise, under a highlighted line on fair, cheap or expensive. The expected return is built from the target and dividend. The required return section, after Sharpe, works the full-beta case and warns about the total-return error. The stock is placed on the line under each beta. Sensitivity tests the premium and a Blume-adjusted beta, and Fama and French frame the conclusion that the model poses the question rather than answering it.

Where the points sit in the MT422 Unit 5 rubric

CAPM analyses are typically graded on a documented beta estimate, a correct required return, a clear distinction between required and expected returns and a tested conclusion. Treating the CAPM figure as a forecast is the confusion graders flag most often. Rubrics check the premium next, since using the market's total return inflates every required figure. Credit goes to a beta with its period, frequency, index and standard error. Showing how the beta changes across windows demonstrates judgment. Testing the stock's position against several premiums earns more than a single verdict. Recommending a purchase moves outside the question and loses marks. A regression table and a security market line chart with the stock marked under each beta make the result easy to audit.

MT422 Unit 5 help: mistakes that cost points

The most frequent weak analysis copies a beta from a website with no period, frequency or index, so it cannot be checked. Another common error plugs the market's expected total return into the formula where the excess return belongs. Students often present one beta as exact, ignoring its error band. Some compute only the required return and never compare it with an expected return. Others spot the stock above or below the line and stop. Many end by telling the reader to buy or sell. Before submitting, rerun your required return with the premium one point higher and one point lower. If the stock moves to the other side of the line, your conclusion should say the result depends on that assumption.

Get an MT422 Unit 5 example written to your instructions

Working from a named stock rather than a composite one? Give the ticker, the window and the index the Unit 5 prompt specifies, and a free first MT422 beta and CAPM analysis follows within 24-48h, regression shown, inputs bracketed with sources and the verdict tested against the rubric's questions. Composite data works equally well. 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 5 questions, answered

Where should the risk-free rate and market premium come from?

The risk-free rate usually comes from a Treasury yield with its date, and many sections name the maturity they want. The premium is a judgment; published surveys and historical averages give ranges rather than one figure. Stating both with sources, and showing how the conclusion changes across a plausible premium range, reads far better than a single unexplained number.

Is a beta from a financial website acceptable?

Sometimes, if the site's method is named: the period, the return frequency and the index used. Many instructors prefer an estimate the student runs, because website betas differ from one another for exactly those reasons. Running the regression also produces the standard error, which a quoted figure never shows and which strengthens the interpretation.

What does it mean if the stock plots above the security market line?

Its expected return exceeds what its beta requires, which the model reads as underpricing. That conclusion is only as strong as the expected return, the beta and the premium behind it, so the better analyses test each. A gap smaller than the uncertainty in those inputs is usually described as no clear mispricing at all.

Where can I find a free MT422 Unit 5 sample paper?

This page carries the complete MT422 Unit 5 analysis, estimating a composite freight broker's beta from sixty months and testing it against the CAPM.

Why do the two half-window betas differ in the MT422 Unit 5 sample?

The later thirty months likely included a freight downturn that tied the broker's returns more closely to the market, lifting beta from 1.05 to 1.67.