Labs/Paths/Investment Management 101
Curated learning path
Beginner
3 hr · 7 labs

Investment Management 101

Foundations to Performance Evaluation

The canonical Investment Management curriculum, taught through hands-on tools instead of dense textbook chapters. Risk and return, diversification, optimal portfolios, equilibrium pricing, and risk-adjusted performance evaluation — in one connected journey.

Undergrad / MBA / CFA Level I / curious self-learners.

By the end you will…
Compute risk and return for any asset or portfolio using probabilistic and historical data.
Build optimal portfolios using the Markowitz mean-variance framework.
Apply the CAPM and Security Market Line to spot mispriced assets.
Evaluate any portfolio's performance using Sharpe, Treynor, Jensen, and M².
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The journey

7 stops · 3 hr of focused work · Beginner

1
Stop 1 · 25 min · Risk & Return
Risk & Return Statistics
Compute E(r), σ², σ, Sharpe, skew, kurtosis from probabilistic or historical data.
The two numbers that drive every decision: expected return and variance.
Open lab →
Worked example
Probabilistic E(r) and σ for a single stock — Bull/Base/Bear scenarios.
ScenarioProbabilityReturnP × rP × (r − μ)²
Bull0.30+25%+7.5%0.0058
Base0.50+10%+5.0%0.0001
Bear0.20−15%−3.0%0.0098
E(r) = 9.5% σ² = 0.0157 σ = 12.5%
2
Stop 2 · 20 min · Risk & Return
Correlation Matrix
Visualize how assets co-move; quantify diversification benefit.
Bridge from single-asset stats to multi-asset co-movement.
Open lab →
Worked example
Correlation matrix — diversification benefit comes from low/negative ρ.
StocksBondsGold
Stocks1.00−0.120.05
Bonds−0.121.000.18
Gold0.050.181.00
Stocks ↔ Bonds is negative — classic diversifier pair.
3
Stop 3 · 25 min · Portfolio Construction
Two-Asset Portfolio
Sliders for weights and correlation; see how σ shifts.
Two-asset portfolios make the diversification math visible.
Open lab →
Worked example
60/40 stocks-bonds with ρ = −0.2
σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂
= 0.6²(0.20)² + 0.4²(0.10)² + 2(0.6)(0.4)(−0.2)(0.20)(0.10)
σ_p = 12.0% (vs naive 16% if added linearly)
4
Stop 4 · 30 min · Portfolio Construction
Efficient Frontier
Multi-asset Markowitz mean-variance optimization with tangency portfolio.
Markowitz mean-variance optimization, the CML, and the tangency portfolio.
Open lab →
Worked example
Efficient frontier with tangency portfolio (T) and minimum-variance (M).
MTRfσ (vol) →↑ E(r)
5
Stop 5 · 25 min · Asset Pricing Models
CAPM Calculator
Live β regression, expected return via Capital Asset Pricing Model.
Equilibrium pricing: what return should the asset earn given its β?
Open lab →
Worked example
AAPL with β = 1.20, Rf = 4%, market premium = 6%
E(r) = Rf + β·(Rm − Rf)
= 4.0% + 1.20·(10.0% − 4.0%)
E(r) = 11.2%
6
Stop 6 · 25 min · Asset Pricing Models
Security Market Line
Plot the SML; find under and overpriced assets via Jensen's α.
Plot the cross-section. Above the line = positive Jensen's α.
Open lab →
Worked example
Security Market Line with three sample stocks plotted.
JNJAAPLTSLAβ →↑ E(r) %α > 0 (above SML)α < 0 (below SML)
7
Stop 7 · 30 min · Performance Measurement
Sharpe / Treynor / Jensen
Compute every major risk-adjusted return ratio side-by-side.
Risk-adjusted return measurement — Sharpe, Treynor, Jensen, IR, M².
Open lab →
Worked example
Sample fund vs benchmark — see who actually delivered after risk.
Sharpe
0.92
vs 0.71
Treynor
0.082
vs 0.064
Jensen α
+1.8%
vs —
Info Ratio
0.42
vs —

Apply what you learned

Real-world scenarios that pull together the path. Each links back to the Labs you just used.

Case Study

Building a $10K starter portfolio for a 25-year-old

Maya is 25, earns a stable salary, and just finished an emergency fund. She has $10,000 to invest with a 30+ year horizon. Walk through the path: her risk score lands her in 'Aggressive' (70% stocks / 15% bonds / 10% alternatives / 5% crypto). Run the Two-Asset lab on a stock/bond core to see how diversification cuts σ from ~18% to ~13%. Plot the Efficient Frontier on SPY+AGG+GLD and pick the tangency portfolio for the maximum Sharpe. Apply CAPM with β=1.0 and a 6% premium → an 10% expected return. Over 30 years that compounds the $10K to roughly $175K (real terms, before fees) — the textbook power of long-horizon compounding combined with mean-variance optimization.

Case Study

Why my fund manager underperformed: a Sharpe-Treynor postmortem

Active fund 'Alpha Growth' returned 11.2% annualized vs the S&P at 10.5% — sounds like alpha. But the fund's σ was 22% (vs benchmark 16%) and β was 1.4. Run the numbers: Sharpe = (11.2 − 4) / 22 = 0.33 vs benchmark Sharpe = (10.5 − 4) / 16 = 0.41. The fund actually underperformed risk-adjusted. Treynor = (11.2 − 4) / 1.4 = 5.1% vs benchmark 6.5% — same story. Jensen's α = 11.2 − [4 + 1.4 × (10.5 − 4)] = −1.9%. Three different measures, one verdict: the manager added beta exposure but no skill. Use the Performance Lab to spot this trap before paying 1.5% in fees.

Case Study

Indonesia ETF vs S&P 500 for an Indonesian investor

An Indonesian investor weighs SPY (USD-denominated S&P 500) against an IDX-listed Indonesia broad-market ETF. SPY's 10y annualized return is ~12% in USD; IHSG's is ~6.5% in IDR. But IDR has depreciated ~3% per year against USD, so SPY's return in IDR terms is ~15%. Risk-free rate in Indonesia (BI 7DRR) is 6% vs US 4%. Run CAPM with the local market premium for each, then compute Sharpe on IDR-denominated returns: SPY's currency-adjusted Sharpe is ~0.55, IHSG ~0.10. Lesson: home-bias costs Indonesian investors a lot. The Asset Allocation Wizard's Indonesia mode handles this currency layer automatically.

Free for any classroom or self-study use. Each Lab works standalone too — this path is one suggested ordering of the foundations.