DEFINITION of Ad Infinitum
Ad infinitum is a Latin phrase meaning "to infinity" — in other words, forever. In finance, the term is associated with a perpetuity, in which the payments derived from an asset at fixed intervals are assumed to go on forever and ever, or ad infinitum. Contrary to conventional wisdom, some financial products have no maturity or expiration date. Thus, they're called perpetuities, and certain strings of cash flows are said to carry-on ad infinitum.
BREAKING DOWN Ad Infinitum
Payments received ad infinitum do indeed go on a very long time. But it's important to realize that, because of the time value of money, the present value (i.e., the value today) of those payments very far off in the future (say, 50 years from now) is negligible. Thus the present value of an ordinary annuity (i.e., one with a fixed end) of 50 years is not very much less than that of a perpetuity whose payments go on ad infinitum.
More general, the expression ad infinitum means "continue forever, without limit." So this definition can be adapted to a number of financial contexts characterized by a non-terminating process, a non-terminating repeating process, or a set of instructions to be repeated "forever." In mathematics, a sequence such as this is not uncommon. Thus, it's a natural extension to finance as markets have increasingly grown more computationally heavy. Especially in the area of economics. Investment strategies utilizing algorithms, machine learning and big data regularly turn to infinite loops which carry-on ad infinitum.
Within finance, and especially in the sale and marketing of investment products, ad infinitum can again come up but in a sarcastic or cynical context. For instance, many strategists who crave information but only get more of the same often lament the market hyper-analyzes certain trends 'ad infinitum.' For example, it wouldn't be uncommon to hear someone remark how certain cable news outlets are "talking about ETFs ad infinitum."