Computed 401K RoR differs from broker's information

Question

I have a 401k through Fidelity and have recently started being more active in the market. I was haphazardly selecting funds that seemed to do well but apparently wasn't the most advantageous due to their expense ratios. So I decided to rebalance and from here do a lookback each year on performance.
To make sure I understand the RoR calculation, I looked at my statement from 31 Dec 2019 to 31 Dec 2020:
 - Beginning balance:          $27,222.92
 - Employee Contributions:    +$6,853.54
 - Employer Contributions:    +$3,909.74
 - Exchange In:                $34,661.77
 - Exchange Out:              -$34,661.77
 - Fees/Credits:              -$11.83
 - Change in Market Value:    +$8,334.29
 - Ending Balance:             $46,308.66
 - Vested Balance:             $46,308.66
 - Dividends/Interest:         $1,189.54

Below that is a block that says my Personal RoR was 22.7%, however I cannot come up with that RoR on my own.
As I understood it, to compute the RoR I would use the following formula:
(((End Balance - Total Contributions) / Start Balance) - 1) * 100
(((46,308.66 - 10,763.28) / 27,222.92) - 1) * 100 = 30.57%

What am I doing wrong in my calculation? According to Fidelity, its computed like this.

D Stanley · Answer

What am I doing wrong in my calculation?

You're not considering the timing of all of those activities. If your contributions all happened at the beginning of the year, then you'd need a lower return to get a change in market value of $8,334 than if they all happened at the end of the year.
Your calculation basically calculates the return of the initial balance, which is similar to saying that the contributions were all made at the end of the year. Since some of your contributions happened earlier, they contributed more to the net return, so your actual rate of return is lower.
I have no idea how your broker calculates it, but one way to calculate the performance of an underlying investment with varying cashflows is to use time-weighted return. Essentially you take the relative change (e.g. 1.02 for a 2% gain) of all periods in between cash flows, multiplying them to get the overall change (subtracting 1 to get return).
Another way is Money-weighted return, which is essentially just taking the IRR of all cashflows over the year.
Neither of those is an easy calculation to do by hand, but if you line up the inflows/outflows and beginning/end values for each period in excel then the calculations are much easier.

Computed 401K RoR differs from broker's information

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