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If the account is down 20%, what rate of return over the next year do we need to get to be even, in other words make back the 20% we lost? The rate of inflation in this case is zero.

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25% return as what you'd want to do is invert the 80% that is left to get the figure. Thus, just compute .8^-1=1.25 or 25%.

Now, to walk this through in a bit more detail for those that found the above to be a bit mystical:

  • Consider starting with $100 and we want to end with $100.
  • Now, the account goes down 20% which means that we are at $80 as 100*(1-.20)=80.
  • Now, to get an addition $20 back, we could take the fraction 20/80=1/4=.25 or 25% as you want to get a quarter back to get whole again.
  • +1 And after all this, if you ask someone what the average per annum rate of return was on your investment, the answer will be (-20% + 25%)/2 = +2.5%. Isn't math wonderful? – Dilip Sarwate Feb 11 '16 at 16:10

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