Let's consider two stocks with the following prices for a three days period:
Stock 1:
day 1: 100
day 2: 105
day 3: 110
Stock 2:
day 1:100
day 2:100
day 3:110
The increase percentage each time for stocks 1 and 2 are respectively:
Stock 1: [5% , 4,761904761904761904761904762%]
Stock 2: [0% , 10%]
When I average the two stocks increase percentage, I get:
Avg Stock growth: [2,5% , 7,38095238095238095238095238%]
The problem is when I try to compute back the price of both stock combined together, with an initial price of 100, to reflect the scenario of investing equally in both stocks:
Day 1: 100
Day 2: 102.5 (100 + 100*2.5%)
Day 3: 110.0654761904761904761904762 (102.5 + 102.5*7,38095238095238095238095238%)
The end result does not add up to 110 but to 110.06 (...) which is not something I expected.
I'm not sure what I'm doing wrong here. Note that I'm using python to compute results
When taking average of the two stocks increases, you should also consider the investment ratio by value between the two stocks.
After day 2, the investment ratio is no longer $1:1$ as in day 1, but becomes $105:100 = 21:20$. Then when taking weighted average of the stock increases from day 2 to day 3,
$$\begin{align*} \text{Weighted avg stock growth} &= \frac{21\cdot \frac{110-105}{105} + 20\cdot \frac{110-100}{100}}{21+20}\\ &= \frac{(110-105)+(110-100)}{105+100}\\ &\approx 7.317\% \end{align*}$$
This matches the combined portfolio growth from day 2 to day 3:
$$\begin{align*} \text{Portfolio growth} &= \frac{\frac12 (110+110)-\frac12 (105+100)}{\frac12 (105+100)}\\ &= \frac{110-102.5}{102.5}\\ &\approx 7.317\% \end{align*}$$