# How to handle annualizing returns over short time interval leading to huge annualized return?

When calculating the annual return of an investment (as (1 + return in %)^(365/days)-1) over a very short time period - say 2 days - my annual return explodes due to the exponential term, which I think can later on when calculating average annual returns over few investments lead to a huge bias in the average return as the average is sensitive to outliers. This might be a bit misleading. If I would use a normal linear transformation to calculate the net annual return ((return in %*days)/365), the annual return would not explode as much for a short time interval. What is the usual way to handle these cases? Still using the exponential transformation or something else? Thanks a lot!

• If you make only a relative handful of short-term loans in a year, you should use whatever method produces the most reasonable numbers. – RonJohn Aug 29 '19 at 3:34
• Are you including all of the days with 0% return in your average? Are you calculating the simple average or the geometric average? – Charles Fox Sep 9 '19 at 23:38
• @CharlesFox Assume the NPV of the returns of an investment is 1020 and the NPV of my costs of this investment is 1000. The net return is 20. Assume the investment was over 2 days. If I annualize my return now using the exact exponential formula, my annual net return explodes. Using the imprecise linear formula, the net return does not explode as much. – sh_student Sep 11 '19 at 4:27
• @sh_student, are you keeping cash available to make these short term investments? If so, are you considering the overall strategy? If you make \$20 in two days and earn 0% in your checking account for 363 days, would you be happy with the outcome? Is your measurement consistent with your goals? – Charles Fox Sep 11 '19 at 19:00
• @CharlesFox Assuming I could reinvest my returns from the investment at a rate of my cost of capital (so I won't win/loose any amount over the remaining time of the year), how would my net annual return be calculated mathematically correctly? – sh_student Sep 12 '19 at 3:40