(Weighted?) Average CAGR (Compound Annual Growth Rate) Equation

Question

What’s the equation to calculate the average CAGR (Compound Annual Growth Rate) for all investment purchases where the holding durations (number of days since purchase date) and purchase cost (compounding from) vary?

Notes/Thoughts:

1. Is this a weighted average equation? If so, what should be included in calculating the weight percentages for each CAGR? 
2. How to calculate those weights when they don’t all start at the same date (different compounding durations)? 
3. Since 30% CAGR increases exponentially more than 15% CAGR, does that mean the weights have to be calculated with an exponential equation?
4. A purchase in 2021 with a lower amount purchase cost and higher CAGR would contribute less to the total invested than a purchase in 2010 with a larger amount purchase cost and a slightly lower CAGR. The more recent purchase (lower amount in current value) that contributes less toward the overall growth should have less importance in calculating the average.
5. A purchase of ETF VUG in 2011 has a CAGR of approx 16.5%. The VUG non weighted average CAGR of continuous purchases since 2011 came out to be around 24.93%. What equation for calculating the weights for each CAGR would get the CAGR average closer to that 16.5% putting more of an importance on longer compounding durations of larger purchase amounts?

Example of problem to solve: What is the equation to calculate the average of all CAGR percentages (Column O) in the spreadsheet screenshot shown below?

Answer 1

That’s a great question, and yes, what you’re describing should be treated as a weighted average CAGR, not just a plain average.

When you have multiple investments with different durations and purchase sizes, the fairest way to find the overall CAGR is to weight each individual CAGR by its starting investment value (the cost basis), not by its percentage or time. That’s because CAGR already accounts for how long each position has been compounding the “duration” is already baked into it.

So the most direct way to combine them is this:

∑ ( wi x ri )

∑ wi

where

1. ri = individual CAGR for investment i (as a decimal),
2. wi​ = purchase cost or invested amount (shares × purchase price).

That keeps larger, older positions dominant as they should be, and prevents a small recent high-CAGR position from skewing the total.

If you want something even more exact, the mathematically pure way is to compute the total current portfolio value and solve for the single CAGR that would turn your total invested amount into that total value over the weighted average holding time. That’s:

1/ ‾t

Portfolio CAGR = ( ∑i current value i )

( ∑i cost basis i ) - 1

where tˉ is the time-weighted average (in years) across all positions, usually weighted by cost.

But in most practical cases, weighting each individual CAGR by the invested cost gives a realistic “average CAGR” that lines up with your intuition longer, larger holdings drive the number more than small, recent ones.

Summary



Here's the clean, general equation you can use in math form, in Excel, or in any financial model.

Average = CAGR i ∑ ( CAGR i x Purchased Shares i x Purchased Price Per Shares i )

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∑ ( Purchased Shares i x Purchase Price Per Share i