The Chapter 8 homework assignment is below. Click here to go directly to the instructions, format rules, and examples.
Portfolio overview (Investopedia): Steps to Build an Optimal Portfolio
The checklist is the “inputs.” The risk profile below turns those inputs into a real portfolio plan.
Write a 6–8 line “Client Investment Policy Statement” (IPS): objectives, risk tolerance, horizon, constraints.
This IPS drives the strategy and portfolio design.
Click each profile. Inside, you’ll see recommendations aligned to the same checklist items.
Class note: These are educational “security type” examples (not personal financial advice). Real recommendations require client-specific details.
Strategy = “how we choose what to buy” + “how we control risk.”
Strategy must match the IPS: a short-horizon, risk-averse client should not be in a high-volatility, concentrated growth portfolio.
Use diversification + correlations to build a portfolio with the “best” risk/return tradeoff for the client.
Turn weights into real trades: buy the right dollar amounts, at reasonable costs, with basic safeguards.
Portfolios drift. Rebalancing keeps risk aligned with the IPS and prevents “accidental” overexposure.
You are here: Homework Assignment
Submit ONE page per team. This is your “mini portfolio report.” Keep it clean + readable. Tables may be small. Bullet points are fine.
Use this format. If your submission is too general, revise it to match these examples.
Many teams accidentally write definitions instead of a client plan. That version is too general to grade.
Why this matches: high bond/cash share reduces drawdowns and supports monthly withdrawals; small equity sleeve fights inflation.
Dividend + high-quality bond (mostly passive): diversified funds, low fees, scheduled rebalancing (no frequent trading).
Why this matches: stocks drive growth; bonds/cash reduce volatility; international + REIT add diversification.
Passive indexing: diversified index funds + low fees + scheduled rebalancing fits a beginner and long horizon.
Why this matches: mostly equities for growth; small bond/cash sleeve helps rebalancing and avoids forced selling.
Index core + small growth tilt: broad index funds first; limited tilts with caps (risk control).
Reminder: Classroom exercise (not personal financial advice).
MPT is a framework to maximize expected return for a given level of risk through diversification and correlation management.
Markowitz (1952): risk is portfolio variance/standard deviation; correlations are essential.
While watching, listen for: correlation, efficient frontier, and why adding an asset can reduce risk.
Watch for: highest return for given risk and why diversification bends the curve.
E[Rp] = Σ wi · E[Ri]
Example (3 stocks): w1*r1 + w2*r2 + w3*r3
σp2 = Σ wi2 σi2 + ΣΣ 2 wiwj ρij σiσj
Correlation terms drive diversification benefits.
σp = √( w1²σ1² + w2²σ2² + 2w1w2ρ12σ1σ2 )
If ρ is low/negative, risk drops sharply.
Click a correlation value to see how two stocks move. Blue = Stock 1 • Green = Stock 2
ρ12 = σ12 / (σ1 · σ2)
σ12 = ρ12 · σ1 · σ2
Translation: covariance is just “correlation × σ1 × σ2”.
Expected Return
E[Rp] = w1r1 + w2r2 + w3r3
Standard Deviation
σp = √( w12σ12 + w22σ22 + w32σ32 + 2w1w2ρ12σ1σ2 + 2w1w3ρ13σ1σ3 + 2w2w3ρ23σ2σ3 )
Expected Return
E[Rp] = Σ wiri (i=1..8)
Standard Deviation
σp = √( Σ wi2σi2 (i=1..8) + ΣΣ 2wiwjρijσiσj (all i<j) )
Let Σ be the 8×8 covariance matrix and w be the 8×1 weight vector.
Portfolio variance: σp2 = wᵀ Σ w
Portfolio stdev: σp = √(wᵀ Σ w)
In Excel: build the covariance matrix, then use MMULT to compute wᵀΣw.
E[Ri] = Rf + βi(E[Rm] − Rf)
βp = Σ wi βi
Weighted average of component betas.
The SML shows the required return for each level of systematic risk (beta). Points above the line look “cheap” (higher return for their beta); points below look “expensive”.
In class: if two stocks have similar expected returns, prefer the one with lower β — unless you intentionally want more market exposure.
In class: work the question first. Then click Show solution to check your work.
Goal: achieve the best investment results (low risk, high return) using Modern Portfolio Theory. You have $10,000. How should you allocate funds among three stocks (A, B, C) to create an “optimal” portfolio?
| Year | Stock A | Stock B | Stock C |
|---|---|---|---|
| 1 | 10% | 4% | 12% |
| 2 | 5% | 6% | 5% |
| 3 | 4% | 8% | 7% |
| 4 | 7% | 10% | 8% |
| 5 | 1% | 5% | 14% |
Required steps: (1) mean & risk (σ) for each stock, (2) correlations (3 pairs), (3) set up portfolio mean & risk, then find an “optimal” allocation.
✅ When finished, click here: Jump to ICE 1 Solution
Your page already includes the MPT mini-app below that reproduces the logic. In class, you can grade: correct means, σ, correlations, and a sensible weight set that improves Sharpe or lowers σ for similar return.
Uses the ICE 1 inputs by default (A,B,C). Generates many portfolios, draws the cloud + the efficient frontier curve, and highlights the minimum-variance and max Sharpe portfolios.
| Mean Return (%) | Std Dev (%) | |
|---|---|---|
| Stock A | ||
| Stock B | ||
| Stock C |
| Pair | ρ |
|---|---|
| A–B | |
| A–C | |
| B–C |
| Type | wA | wB | wC | E[Rp]% | σp% | Sharpe |
|---|---|---|---|---|---|---|
| Click “Generate Frontier”. | ||||||
| # | wA | wB | wC | E[Rp]% | σp% | Sharpe |
|---|
You have two risky assets: Stock A and Stock B. Compute the portfolio’s expected return and standard deviation.
| Expected Return | Std Dev (σ) | |
|---|---|---|
| Stock A | 8% | 20% |
| Stock B | 12% | 30% |
Portfolio weights: wA = 60%, wB = 40%
Correlation: ρAB = 0.20
Steps: (1) E[Rp] = wA·EA + wB·EB, (2) σp = √(wA²σA² + wB²σB² + 2wAwBρσAσB)
E[Rp] = 0.6(0.08) + 0.4(0.12) = 0.096 = 9.6%
σp2 = (0.6²)(0.20²) + (0.4²)(0.30²) + 2(0.6)(0.4)(0.20)(0.20)(0.30)
= 0.36(0.04) + 0.16(0.09) + 0.48(0.20)(0.06) = 0.0144 + 0.0144 + 0.00576 = 0.03456
σp = √0.03456 = 0.1859 ≈ 18.6%
Notice: both stocks are risky, but σp (18.6%) can be less than a weighted average of σ’s because ρ is not 1.
Use CAPM to compute the required return for three stocks.
| Input | Value |
|---|---|
| Risk-free rate, Rf | 3% |
| Expected market return, E[Rm] | 11% |
| Stock | Beta (β) |
|---|---|
| WMT | 0.70 |
| AAPL | 1.10 |
| NVDA | 2.30 |
Formula: E[Ri] = Rf + β(E[Rm] − Rf)
Market risk premium = E[Rm] − Rf = 11% − 3% = 8%
WMT: 3% + 0.70(8%) = 3% + 5.6% = 8.6%
AAPL: 3% + 1.10(8%) = 3% + 8.8% = 11.8%
NVDA: 3% + 2.30(8%) = 3% + 18.4% = 21.4%
Interpretation: Higher β → higher required return because the stock carries more systematic (market) risk.
You build a 3-asset portfolio. Compute: (1) the portfolio beta βp, and (2) the portfolio required return using CAPM.
| Asset | Weight | Beta (β) |
|---|---|---|
| WMT | 40% | 0.70 |
| AAPL | 40% | 1.10 |
| NVDA | 20% | 2.30 |
| Input | Value |
|---|---|
| Risk-free rate, Rf | 3% |
| Expected market return, E[Rm] | 11% |
Formulas: βp = Σ wiβi and E[Rp] = Rf + βp(E[Rm] − Rf)
βp = 0.40(0.70) + 0.40(1.10) + 0.20(2.30) = 0.28 + 0.44 + 0.46 = 1.18
Market risk premium = 11% − 3% = 8%
E[Rp] = 3% + 1.18(8%) = 3% + 9.44% = 12.44%
Interpretation: the portfolio is slightly more aggressive than the market (βp > 1), so its required return is slightly above the market’s required return.
We will complete the term project using the dedicated project page. Please use the link below.
Topics: risk vs return, standard deviation, correlation, diversification, beta, CAPM, Security Market Line.
If you use outside tools, always cite the ticker + your date range.