Assume, I lend someone money against a certain fee or interest (charged at the day the loan gets repaid). The loan defaults and I get no fee or interest back. Hence, I have a return of -100% as all my starting capital is lost. How do I annualize this return? As I want to compare it with other annualized returns from other investments. I don't have an investment period to annualize the -100% over. Like when using the little inaccurate formula (return*365)/days . The "days" are missing to annualize my -100 %. Is there a best practice how to annualize complete losses to compare them with other annualized returns?
If your return for say, one month, is
r = -100 % your future value on investment
FV = a (1 + r) = a (1 - 1) = 0
and the annualised return is
(1 + r)^12 - 1 = 0^12 - 1 = -100 %
If your total return is
t years then
q is your annualized return. You can calculate it with
The exact calculation of
t depends on how exactly the investment works. If you are open for business every day then it could be
days/365, or you may need to adjust for holidays and business days. It doesn't really matter how you measure time so long as you measure it in the same way as whatever benchmark you're comparing to.
If you have no time horizon, you cannot calculate an annualized return because there is no meaningful annualization to do.
t would approach infinity and therefore
q would approach 0. In reality, what you say makes no sense. The loan must have had some sort of maximum term, otherwise your debtor could in theory repay it after 100 or 1000 years, in which case the money you "lent" was not a loan, but a gift. If there was a max term, that max term is
I am not sure of your purpose, but you could consider taking it out of your annual returns and instead show it as “Default ratio”, hence leaving the non-defaulted loans in your return-calculations and then keeping a separate measure for default-ratio.
But this of course depends on the purpose.