Educational material from 
What you will learn
- Calculate market capitalisations and weights at the period’s start.
- Calculate a weighted change under an explicitly stated rule.
- Explain why different indices can measure different things.
Prepare two index groups for 45 minutes
Spend five minutes on the table, ten on starting weights, ten on ending index values, ten on comparison and ten on an individual two-company problem. One group uses market-capitalisation weights and another uses equal weights. Both set the starting index to 100. All companies and prices are invented for the activity.
Assume unchanged share counts, no dividends or fees, and no stock splits during the period. Market capitalisation here is share count multiplied by price. Starting weights must be used for this period’s return calculation. Neither group may switch to ending weights after seeing the price outcomes.
If the table does not fit, scroll it sideways.
| Company and share count | Starting price | Ending price |
|---|---|---|
| A, 10 shares | SEK 100 | SEK 110 |
| B, 100 shares | SEK 20 | SEK 18 |
| C, 200 shares | SEK 10 | SEK 11 |
Student worksheet: build two starting allocations
Calculate each starting market capitalisation and add them up. Divide each company’s value by the total for the first group’s weights. The second group uses one third for each company. Write down both allocations and check they add to one whole index before calculating the changes.
Starting values are SEK 1,000 for A and SEK 2,000 each for B and C, totalling SEK 5,000. Market-capitalisation weights are therefore 20%, 40% and 40%. Price changes are +10%, −10% and +10%. Students now use the same three changes in both calculations so that only the weighting rule differs.
Answer key: 102 versus approximately 103.33
The market-capitalisation-weighted change is 0.20 × 10 + 0.40 × (−10) + 0.40 × 10 = 2%. The index moves from 100 to 102. Check against aggregate ending capitalisation: 1,100 + 1,800 + 2,200 = SEK 5,100, which is two percent above 5,000.
With equal starting weights the change is (10 − 10 + 10) / 3 ≈ 3.33%, making the ending index approximately 103.33. B has greater influence in the first index than the second. The difference identifies which measure was used; it does not prove that one method always produces better future results.
If the table does not fit, scroll it sideways.
| Rule | Period change | Ending index |
|---|---|---|
| Market-capitalisation weighted | +2% | 102 |
| Equal starting weights | ≈ +3.33% | ≈ 103.33 |
Teacher prompts: inspect the rule before comparing
As an optional extension, define a simple price-weighted index as the sum of ending prices divided by the sum of starting prices, multiplied by 100. This gives (110 + 18 + 11) / (100 + 20 + 10) × 100 ≈ 106.92. This is our simplified rule; it does not describe every adjustment in a named real index.
Ask students which company influences the price-weighted measure most and why share count is absent there. Assess whether each answer states starting weights, the period and the total used. Finish by distinguishing an index as a measure from a fund that tries to follow it. Investiq’s calculation lessons provide further practice; this task does not mean users can create or trade indices in the app.
Try it yourself
Two fictional companies have starting market capitalisations of SEK 800 and SEK 1,200. Prices change −5% and +10%, with no other events. Find the change with market-capitalisation weights and with equal starting weights.
Show the solution and explanation
Market-capitalisation weighting gives +4%. Equal starting weights give +2.5%.
Starting weights are 800 / 2,000 = 40% and 1,200 / 2,000 = 60%. 0.40 × (−5) + 0.60 × 10 = 4; (−5 + 10) / 2 = 2.5.
Check your understanding
Why use starting weights when weighting the period’s price changes?
They describe the allocation before the outcome. Ending weights describe another time and do not produce the same calculation.
Are an index and an index fund the same thing?
No. An index is a defined measure; an index fund holds assets and tries to follow an index under its strategy.
Practise with virtual money
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More activities on this topic
Ownership, funds and stock indices
Sources and examples
The sources support the factual explanations. Calculations and exercises were created for this lesson. Amounts and price changes are invented unless stated otherwise.
This material is educational and does not recommend securities to buy. A simulated result does not guarantee a future result.
