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CMT Association

Conquest Tech Olympiad 2026 · Finance track

Lesson 2 of 7

Prices, returns, and total-return indexes

Learning goal

Turn prices into returns, compound weekly returns correctly, and read an index that starts at 100 and includes dividends.

Explanation

A return is the percentage change in value. If something is worth 100 and becomes 105, the return is 5%.

Return = (new value / old value) − 1

The challenge uses weekly data. Daily returns are combined (compounded) into weeks. Each week ends on the last trading day of that Monday-to-Friday week.

Compounding means each week's return applies to the new value, not the original one. A gain of 10% followed by a loss of 10% does not return you to the start. The second percentage applies to a different base.

An index is a number that tracks a group of assets. Here, each series is turned into an index that starts at 100. This makes comparison easy. If an index shows 130, it is up 30% since the start. If it shows 85, it is down 15%.

A dividend is a cash payment a company makes to its shareholders. A price index ignores dividends. A total-return index includes them, as if reinvested. Total return shows what an owner truly earned. Every index in the challenge is a total-return index.

CAGR (compound annual growth rate) is the steady yearly growth rate that would turn the start value into the end value:

CAGR = (V_end / V_start)^(52 / weeks) − 1

The 52 is the number of weeks in a year.

Worked example

An index starts at 100. Weekly returns: +2%, −1%, +3%.

  • Week 1: 100 × 1.02 = 102.00
  • Week 2: 102.00 × 0.99 = 100.98
  • Week 3: 100.98 × 1.03 = 104.01

The total return is 4.01%, not 4% (2 − 1 + 3). The difference is compounding.

Dividends: a stock's price rises from 100 to 105 and it pays 2 in dividends. The price return is 5%. The total return is (105 + 2) / 100 − 1 = 7%.

CAGR: an index grows from 100 to 150 over 260 weeks (five years). CAGR = 1.5^(52/260) − 1 = 1.5^0.2 − 1, which is about 8.4% a year.

Self-check

  1. An index starts at 100. Week 1: +10%. Week 2: −10%. What is the value after week 2?

    Show the answer

    Answer: 100 × 1.10 = 110; 110 × 0.90 = 99. The second percentage applies to a larger base.

  2. Why does the challenge use total-return indexes and not price indexes?

    Show the answer

    Answer: A total-return index includes dividends. It shows what an owner really earned. A price index leaves dividends out and understates the return.

  3. An index grows from 100 to 121 over 104 weeks. What is the CAGR?

    Show the answer

    Answer: 121 / 100 = 1.21. 104 weeks is two years, so the exponent is 52/104 = 0.5. 1.21^0.5 = 1.10. CAGR = 10%.