Learn portfolio risk by changing one thing
Published 9 September 2026 · Three exercises · About 25 minutes
For students, investment clubs and curious investors: predict what will happen, move one control, then explain the result. Each exercise uses round, hypothetical inputs and shows its workings. No account is needed.
EXERCISE 1 · DIVERSIFICATION
Two risky assets can make a calmer mix
Invest half in Asset A and half in Asset B. Each has 15% annual volatility. Keep those weights and volatilities fixed, then change how closely the assets move together.
Portfolio volatility: 10.61% a year.
Volatility measures fluctuations, not the worst possible loss. The zero-volatility result at −1 is a mathematical special case, not a reliably available investment.
Show the formula and model answer
Variance = (0.5 × 15)² + (0.5 × 15)² + 2 × 0.5 × 0.5 × 15 × 15 × correlation. Take the square root for volatility. At +1 it is 15%; at 0 it is 10.61%; at −0.5 it is 7.5%. Diversification changes risk even when each asset's own risk is unchanged.
EXERCISE 2 · ALLOCATION AND RISK
A fifth of the money can carry more than a fifth of the risk
For this hypothetical exercise, equities have 15% volatility, Bitcoin has 45%, and their correlation is 0.2. These are round teaching inputs, not Portfolio Lab's current forecasts or a recommended allocation.
Portfolio volatility: 16.38%
Bitcoin's share of variance risk: 38.3%
Share of money
Share of variance risk
Show the model answer
At 20% Bitcoin, portfolio variance is 268.2 percentage-points squared. Bitcoin contributes 102.6 of that, or 38.3%. Its contribution includes half the cross-asset covariance term. These are variance contributions, not predicted losses or probabilities. The allocation you choose and the risk it contributes answer different questions.
EXERCISE 3 · WITHDRAWALS
Same returns. Different order. Different money left.
Start with 100,000 money units. One path earns +20% then −20%; the other earns −20% then +20%. Withdraw the same amount at each year end. Ignore fees, taxes and inflation to isolate the effect.
| End of year | Gain first | Loss first |
|---|---|---|
| 1 | 115,000 | 75,000 |
| 2 | 87,000 | 85,000 |
Difference after two years: 2,000.
Show the model answer
At a 5,000 annual withdrawal, the gain-first path ends with 87,000; the loss-first path with 85,000. With no withdrawals, both end with 96,000. An arithmetic average of 0% does not mean the starting money is preserved: 1.2 × 0.8 = 0.96. Early losses matter more when money is being withdrawn.
A ready-to-use lesson
- Give learners two minutes to predict each result before touching the controls.
- Spend five minutes on each exercise. Ask which inputs stayed fixed and which changed.
- Have pairs reproduce one answer with a calculator or spreadsheet, using the formulas and worksheet.
- Finish by asking what the examples leave out: changing correlations, uncertain forecasts, transaction costs, taxes and liquidity.
The worksheet and model answers may be reproduced with attribution to Portfolio Lab. Use fictional portfolios in group discussions. The exercise is independent educational material, not an accredited course or professional qualification.
Read further and try real data
The SEC's guide to asset allocation and diversification explains the underlying idea. FINRA's retirement portfolio guide discusses managing investments and withdrawals.
Then explore historical correlations, retirement simulations, or the app's methodology.
Teaching pack questions
Do students need an account?
No. All three exercises, the worksheet and model answers are public. A free account is needed to save and compare personal analyses in the workstation.
Are these current investment forecasts?
No. These are explicitly hypothetical teaching inputs chosen so the answers can be independently reproduced. They are not recommended allocations or current market assumptions.
Can I use the exercises in a class or investment club?
Yes. You may share the link and reproduce the Portfolio Lab worksheet with attribution. The page includes three exercises, model answers and a suggested lesson structure.
Educational examples only. Hypothetical inputs are not forecasts or investment advice. All exercises run in your browser.