Talk:Return on investment/Archive 1

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Archive 1

The basis is always positive. Even if one is shorting a stock, the amount risked is positive. Only, in this case, the gain/losses have the opposite sign that they normally have.

In the presented definition, while V_f is the final value, V_b is the basis, which is not necessarily the initial value. For instance, the basis can be increased beyond the initial value by further investment during the preiod. (Sales during the fundamental period do not decrease its basis.)

If the full value of the additional investment in the fundamental period is not taken into account (as is sometimes done by using the modified Dietz approach within a fundamental period) then the general formula thus arrived at will not make economic sense, as can be easily seen in cases where the initial value is zero.

I haven´t added this because I don´t know if this is really useful (It´s a bit lengthy after all). Just an explanation for "Interestingly, to compensate for a negative ROI one needs a positive ROI that is higher in magnitude. For example, to recoup a 50% loss one needs to realize a 100% gain." It might be better to use R_tot+1 = (R₁+1) * (R₂+1). --Vulture

Total Return on Reinvestment (compound return):
Resoliving the defining term ...
 R = (V_f-V_b)/V_b
... to V_f:
 V_f = RV_b+V_b

 V_f1, V_f2     final value of investment 1 and 2
 V_b1, V_b2     basis of investment 1 and 2
 R₁, R₂, R_tot Return on investment 1, 2 and total return
Reinvesting final value of investment 1 as basis of investment 2:
 V_b2 = V_f1
 V_b = V_b1
(1) V_f1 = R₁V_b+V_b
    V_f2 = R₂V_f1+V_f1 with (1):
(2) V_f2 = R₁R₂V_b+R₁V_b+R₂V_b+V_b
    R_tot = (V_f2-V_b1)/V_b1 with (2):
         = (R₁R₂V_b+R₁+V_b+R₂+V_b+V_b-V_b)/V_b
Leading to a total return of:
(3)   R_tot = R₁R₂+R₁+R₂
To compensate (R_tot=0) we get with (3):
 R₁R₂+R₁+R₂ = 0
 R₂ = -R₁/(1+R₁)

The problems arise when it is not the case that V_b2 = V_f1, This arises when a portfolio makes a purchase at a known price in the middle of a day without pricing the rest of the portfolio at the time of the purchase. Especially if one desires a general and economically reasonable result that applies even in the case when V_b1=0. A related and more difficult problem arises when there is a transfer in the middle of the day between two sub-portfolios which comprise a total portfolio. It is then very difficult to provide an economically meaningful return of the total portfolio for the whole period as the weighted average of the returns of the sub-portfolios for the whole period. Trying to come up with a viable solution shows how difficult applying the apparently simple concept of "ROI" can become.

On another point, "Return on investment", is too narrow a name for this concept. The concept is not only applicable to financial investments. "Rate of Return" would be better. But I do not know why the original name of "Return" is still not best of all. Can someone enlighten me on this before I go ahead and change it back to "Return" in the general sense, rather than have the discussion just focus on "business" matters.