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Total return vs CAGR

Total return is one holding-period sum: price change plus income, over the start. A $100 holding that ends at $105 and pays $3 returns 8 percent. CAGR is a different object, the yearly root on two balances. $10,000 to $18,000 over 6 years is 10.29 percent a year.

 Total returnCAGR
Formula(P1−P0+D)/P0(P_1 - P_0 + D) / P_0. Income is added once.(Vt/V0)1/t−1(V_t / V_0)^{1/t} - 1. Two balances and a clock.
Teaching sheet$100 to $105 with $3 of income is 8 percent: 5 percent from price, 3 percent from income.$10,000 to $18,000 over 6 years is 10.29 percent a year. A different object.
IncomeA separate DD added once. The ending price stays $105. The $3 is the 3 percent yield.No income column. If the cash is still in the account, it is already inside VtV_t.
TimeOne window, however long it was. The 8 percent is not a yearly rate unless that window was a year.The years are the exponent. The same two values over fewer years print a higher yearly rate.
A loss in the window$50 to $40 with $2 of income is -16 percent. The $2 did not cancel the fall.A root on two balances can be negative when VtV_t is below V0V_0. That is a different sheet.
What it is notA CAGR. Do not paste the $100 holding onto a multi-year root.A one-period split. Do not read 10.29 percent a year as the 8 percent total return.
On this page

One period is not a yearly root

Total return is the holding-period return: what the price did, plus what the holding paid, over what you started with.

HPR=P1−P0+DP0\text{HPR} = \frac{P_1 - P_0 + D}{P_0}

On a $100 start, a $105 finish and $3 of income, price change is 5 percent and income yield is 3 percent. Total return is 8 percent. That 8 percent is one window. It is not a yearly rate unless the window was a year.

CAGR is a different object. It is the annualised return that reproduces an ending value over tt years:

CAGR=(VtV0)1t−1\text{CAGR} = \left(\frac{V_t}{V_0}\right)^{\frac{1}{t}} - 1

On $10,000 growing to $18,000 over 6 years, the multiple is 18000/10000=1.818000/10000 = 1.8. The sixth root is 1.10292357. Subtract 1 and the CAGR is 10.29 percent a year. Grow $10,000 at that rate for 6 years and you land on $18,000.

Do not paste the $100 holding onto that 6-year root. They are two teaching sheets. How total return works owns the 8 percent. How the CAGR formula works owns the 10.29 percent.

Income is added once, or it is already in the end

Income enters the two formulas in different places.

On the $100 sheet, $3 of income is added once, as DD. The ending price is still $105. The 3 percent income yield is a separate term. A second sheet starts at $50, ends at $40, and pays $2: total return is -16 percent. The $2 did not cancel the price fall.

CAGR has no income column. It sees two balances and a clock. If the income was received and still sits in the account, it is already inside VtV_t. If you take the income out, the ending value is lower and the root is lower. There is no separate DD to add after the root.

The total return calculator is the one-period split. The CAGR calculator is the yearly root. The total return explorer holds the start still and lets you drag the finish. This is educational material, not financial advice.

Worked examples

\$100 to \$105 with \$3 of income

A holding starts at $100, ends at $105, and pays $3 of income in the window. What is total return?

  1. Price change: (105−100)/100=0.05(105 - 100) / 100 = 0.05, which is 5 percent.
  2. Income yield: 3/100=0.033 / 100 = 0.03, which is 3 percent.
  3. Total return: (105−100+3)/100=0.08(105 - 100 + 3) / 100 = 0.08, which is 8 percent.

Total return is 8 percent. Price change is 5 percent. Income yield is 3 percent. That 8 percent is one window, not a CAGR.

\$50 to \$40 with \$2 of income

A holding starts at $50, ends at $40, and pays $2. What is total return?

  1. Price change: (40−50)/50=−0.2(40 - 50) / 50 = -0.2, which is -20 percent.
  2. Income yield: 2/50=0.042 / 50 = 0.04, which is 4 percent.
  3. Total return: (40−50+2)/50=−0.16(40 - 50 + 2) / 50 = -0.16, which is -16 percent.

Total return is -16 percent. Price change is -20 percent. Income yield is 4 percent. The $2 of income did not cancel the price fall.

\$10,000 to \$18,000 over 6 years

An investment was worth $10,000 at the start and $18,000 six years later, with nothing paid in and nothing taken out. What annual rate is that?

  1. Divide the ending value by the starting value: 18000/10000=1.818000 / 10000 = 1.8. The money grew to 1.8 times its starting size.
  2. Take the 6th root, which is the same as raising to the power 1/61/6: 1.81/6=1.102923571.8^{1/6} = 1.10292357.
  3. Subtract 1: 1.10292357−1=0.102923571.10292357 - 1 = 0.10292357, which is 10.29 percent a year.
  4. Check it by growing the money back up: 10000×1.102923576=1800010000 \times 1.10292357^{6} = 18000.

The CAGR is 10.29 percent a year. $10,000 compounding at that rate for 6 years lands on $18,000. That yearly root is a different object from a one-period total return.

Common questions

Is total return the same as CAGR?

No. Total return is one window. On the first sheet that is 8 percent from $100 to $105 with $3 of income. CAGR is the yearly root that reproduces an ending value over tt years. The CAGR teaching sheet is $10,000 to $18,000 over 6 years, which is 10.29 percent a year.

Does income go into CAGR?

Only if it is still inside the ending value. CAGR has no separate income term. The total-return sheet adds $3 once on top of a $105 finish. If you want that income in a CAGR, it has to be in VtV_t already.

Can I read the 8 percent as a yearly rate?

Only if that holding period was a year. The formula does not know the dates. An 8 percent window over six months is not 8 percent a year, and it is not the 10.29 percent CAGR on the other sheet.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.