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:
- Both funds raise by 100% in next 1 year.
- 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?