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Take an example of two mutual funds: A and B.
For simplicity, following are assumptions:

  • Both funds always perform exactly same (same fall or same growth depending the direction of market).
  • Let us neglect Taxes and Fees.
  • Assume unrealized gain as realized gain to make it easy to compare two cases below.

I invested amount 100 in fund A 1 year back as lump sum. No further investment. Today, that 100 is grown to make total amount 200. This makes annualized returns of 100%.

Now, consider two cases:
Case 1) Withdraw all amount from fund A and invest it in fund B. Additionally, invest another 200 in fund B. Total becomes 400.
Case 2) Keep amount in fund A as is. Invest another 200 in fund B. Both funds have 200 now.

Which case from above two will deliver better returns in following scenarios:

  1. Both funds raise by 100% in next 1 year.
  2. Both funds fall by 50% in next 1 year.

I am not good in mathematics so I base my thinking on purchase price of units. If I am thinking correctly, Case 2 will deliver better returns in both the scenarios because I have purchased the units in fund A at far lower rates. If I sell them today and immediately buy units of fund B for entire amount, my purchase price becomes higher.

Is my understanding correct? Can someone please explain mathematics behind this?

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  • Your entire understanding of what investment in a mutual fund means, what gains are in a mutual fund, the difference between unrealized and realized gains and what that implies in terms of taxes, which you are determined to ignore, is incorrect. There is no point in explaining the "mathematics behind this" when one needs to start from whether 2+2 equals 4 or it is possible that 2+2 equals 5 for large values of 2 (or small values of 5) Oct 9 at 20:30
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If there are no taxes because these are retirement accounts, and there are no fees.; then there is no difference between the options..

Doubling $400 gives you $800 as does doubling two piles of $200 each. The same thing is true iif it drops 50%. $400 becomes $200 no matter how many piles it is divided into.

Taxes and fees will change the math.

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