Return on Investment/Talk

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.

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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 = (Vf-Vb)/Vb
 ... to Vf:
  Vf = RVb+Vb

  Vf1, Vf2     final value of investment 1 and 2
  Vb1, Vb2     basis of investment 1 and 2
  R1, R2, Rtot Return on investment 1, 2 and total return
 Reinvesting final value of investment 1 as basis of investment 2:
  Vb2 = Vf1
  Vb = Vb1
 (1) Vf1 = R1Vb+Vb
     Vf2 = R2Vf1+Vf1 with (1):
 (2) Vf2 = R1R2Vb+R1Vb+R2Vb+Vb
     Rtot = (Vf2-Vb1)/Vb1 with (2):
          = (R1R2Vb+R1+Vb+R2+Vb+Vb-Vb)/Vb
 Leading to a total return of:
 (3)   Rtot = R1R2+R1+R2
 To compensate (Rtot=0) we get with (3):
  R1R2+R1+R2 = 0
  R2 = -R1/(1+R1)