| Course | FIN-3210 Security Analysis and Portfolio Management |
|---|---|
| Module | Module 3 |
| Paper type | Written assignment 3: portfolio theory |
| Length | About 605 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | B.S.B.A. in Finance |
| Updated | October 2026 |
Free sample paper for FIN 3210 Module 3
Forty Percent Stocks Beat One Hundred: Portfolio Theory for a Two-Fund Household
Student Name
B.S.B.A. in Finance, Thomas Edison State University
FIN-3210: Security Analysis and Portfolio Management
Mentor Name
Month Day, Year
Forty Percent Stocks Beat One Hundred: Portfolio Theory for a Two-Fund Household
Problem 1: The Two Funds
Return averages out across the two funds; risk does not. With variance equal to wS²σS² + wB²σB² + 2wSwBρσSσB and a correlation far from 1, the mix is less risky than its parts. Bodie et al. (2017) define the frontier as the best expected return obtainable at every level of risk.
Moving from all bonds to 25 percent stocks raises expected return by 1.25 points while adding only about half a point of risk. Markowitz (1952) showed that this is the essence of diversification: when assets do not move together, combining them reduces risk for a given return.
| Stock fund | Bond fund | |
|---|---|---|
| Expected return | 10% | 5% |
| Standard deviation | 20% | 8% |
| Correlation | 0.2 | |
| Risk-free rate | 3% | |
| Stock weight | Expected return | Standard deviation |
| 0% | 5.00% | 8.00% |
| 25% | 6.25% | 8.54% |
| 50% | 7.50% | 11.49% |
| 75% | 8.75% | 15.52% |
| 100% | 10.00% | 20.00% |
Problem 2: The Minimum-Variance Portfolio
The mix with the lowest possible risk has a stock weight of (σB² − Cov) / (σS² + σB² − 2Cov), where the covariance is 0.2 × 0.20 × 0.08 = 0.0032. That gives wS = (0.0064 − 0.0032) / (0.04 + 0.0064 − 0.0064) = 8 percent. This portfolio has an expected return of 5.40 percent and a standard deviation of 7.84 percent, lower than the bond fund alone. Adding a small amount of risky stock reduces total risk.
Problem 3: The Optimal Risky Portfolio
The best risky portfolio for an investor who can also hold a risk-free asset is the one with the highest Sharpe ratio, the excess return per unit of risk. Using the standard formula for the tangency portfolio, the optimal stock weight is 40 percent.
The optimal portfolio offers more return per unit of risk than either fund alone. An investor wanting more return than 7 percent should not simply buy more stocks but, in theory, borrow at the risk-free rate to hold more of this portfolio.
| Portfolio | Expected return | Standard deviation | Sharpe ratio |
|---|---|---|---|
| Stock fund alone | 10.00% | 20.00% | 0.350 |
| Bond fund alone | 5.00% | 8.00% | 0.250 |
| Optimal risky portfolio, 40% stocks | 7.00% | 10.12% | 0.395 |
Problem 4: The Complete Portfolio
How much should the couple put in the optimal risky portfolio versus a risk-free money market fund? With a risk aversion coefficient of A = 4, the optimal fraction is y* = (E(rP) − rf) / (Aσ²P) = 0.04 / (4 × 0.1012²) = 0.977. The couple should put about 98 percent of their savings in the 40/60 risky portfolio and about 2 percent in the money market fund, for an expected return of 6.91 percent and a standard deviation of 9.88 percent. A more risk-averse investor, A = 8, would hold about half in each.
Problem 5: Pricing a Stock With the CAPM
Sharpe (1964) showed that in equilibrium, an asset's expected return depends only on its systematic risk, measured by beta. The couple owns shares of a utility with a beta of 0.6. If the market risk premium is 6 percent and the risk-free rate 3 percent, the CAPM gives an expected return of 3% + 0.6 × 6% = 6.6 percent. If analysts expect the stock to return 8 percent, it plots above the security market line and appears underpriced; if they expect 5 percent, it appears overpriced.
What the Problems Show
Diversification, not stock picking, is the free lunch of investing. The couple's best risky portfolio holds more bonds than stocks because the bond fund's low risk and low correlation make it valuable, and their personal risk tolerance, not the portfolio math alone, decides how much risk they take.
References
Bodie, Z., Kane, A., & Marcus, A. J. (2017). Essentials of investments (10th ed.). McGraw-Hill Education.
Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
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
Reading the FIN 3210 Module 3 assignment instructions
Module 3, Portfolio Theory, carries one of the eight FIN-3210 written assignments, which share 40 percent of the grade. Its material, together with Modules 1, 2 and 4, is also tested on the proctored midterm. Expect problems on portfolio expected return and standard deviation, the effect of correlation, the minimum-variance and optimal risky portfolios, the capital allocation line and the investor's choice of risky share, and the CAPM and security market line. The funds and household here are composites with round numbers; your problems will supply their own. Expect portfolio return and risk calculations for two assets, a discussion of the efficient frontier and CAPM problems that find required returns.
Inside the FIN 3210 Module 3 example
Problem 1 sets out the two funds and shows risk and return at five mixes, with Markowitz cited on why risk falls. Problem 2 computes the minimum-variance weights with the formula shown. Problem 3 finds the optimal risky portfolio and compares Sharpe ratios in a table. Problem 4 places the household on the capital allocation line using a risk aversion coefficient, and Problem 5 prices a stock with the CAPM and interprets an analyst forecast against it. A closing paragraph states the lesson in plain words. The CAPM results are compared with the expected returns given, to judge which assets look underpriced. A short paragraph explains why the market portfolio sits on the frontier.
Where the marks sit in the FIN 3210 Module 3 rubric
The two-fund portfolio set is graded on the full variance formula and a reasoned choice of mix. Mentors look for correct formulas and results for portfolio risk, the minimum-variance and optimal portfolios and the CAPM, along with explanations of what each result means. Distinguishing the optimal risky portfolio, which is the same for all investors, from the complete portfolio, which depends on risk aversion, shows a key understanding. Clear tables and stated formulas help the mentor award credit for each step. Mentors give credit for correct use of correlation in portfolio risk and for explaining why diversification lowers risk without lowering expected return proportionally.
FIN 3210 Module 3 help from the desk
Portfolio problems lose points for averaging standard deviations instead of computing portfolio variance, for forgetting the covariance term and for confusing the optimal risky portfolio with the investor's overall allocation. Write the variance formula out. Compute covariance from correlation. Compare Sharpe ratios to identify the best risky mix. Then use the investor's risk aversion to split money between it and the risk-free asset. A free first sample of your own FIN-3210 Module 3 problems is available on request. Use standard deviations and correlation together for portfolio risk; adding variances alone ignores diversification. Say what the efficient frontier means for the investor's choice, not only how it is drawn. Report the beta and required return of each stock in one table.
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FIN 3210 Module 3 questions, answered
Where can I find a free FIN 3210 Module 3 sample paper?
The two-fund household problem set above computes portfolio risk, the minimum-variance and optimal risky portfolios, the complete portfolio and a CAPM expected return.
Why does diversification reduce risk?
Because assets that do not move perfectly together offset some of each other's fluctuations, lowering portfolio variance.
What is the Sharpe ratio?
Excess return over the riskless rate per unit of standard deviation, or reward for each unit of total risk.
How do you find the optimal risky portfolio?
It is the combination of risky assets with the highest Sharpe ratio, where the capital allocation line touches the efficient frontier.
What does the CAPM say about expected returns?
Under the CAPM, a fund's expected return is the Treasury rate plus beta times the market's premium.