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.
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.