Formula to Balance Logarithmic or Continuously Compounding ?

[Aston08]

If I was interested in determining how to balance the rate of reinvestment of profits back into the original investment (to add to its compounding potential) while still growing the profit return on the investment.


How would I go about calculating something like that ?

 

[Ynaught?]

If I was interested in determining how to balance the rate of reinvestment of profits back into the original investment (to add to its compounding potential) while still growing the profit return on the investment.


How would I go about calculating something like that ?

I am not sure I totally understand what you are asking but I take a stab at an answer...

Where F = the final amount in the account, P = the principal invenstment, r = the rate of return per interest period, n = the number of interest periods, and A = additonal investment per insterest period, then:

F= P(1+r)^{n} + A((1+r)^{n} - 1)/n

 

[Aston08]

Ynaught -

It is pretty much the same concept as here. I just don't know how to do the calculations.

http://demonstrations.wolfram.com/HowMuchShouldIReinvestInABusiness/



The balance comes into play because the final price can never be determined up front and therefore creates 2 problems that need to be solved for:

1.) Continual reinvestment of profits will negatively impact the profitability of an investment in the short term but exponentially add to the profit potential in the long term.
2.) Withdrawal of accumulated profits will lock in profit from the investment, but harm the long term potential of the investment to compound.



Maximum Reinvestment Efficiency
Mathematically determining the most efficient way to reinvest the profits from a successful investment after the value of the investment has risen enough to cover the value of the initial risk and covering the future costs of risk thereafter, assuming a constant amount of risk is to be used during the life of the investment (i.e. no more than $300) .

Example –

• Starting Value = $30,000
• Account risk per trade = (1% of 30K = $300)
• Cost per Share = $100
• $ Risk per Share Using a 5% Protective Stop per Share = $100 x 5% = $5.00 (i.e. we can afford to lose $5 per share before we have to sell it)
• # Shares = $300 (Total Risk per Trade) / $5.00 (Maximum Risk per Share) = 60 Shares
• Commission Cost = $0.50 per Share each way ($0.50 to Buy & $0.50 to Sell = $1.00 Total)

Determine the following -
1. Amount of investment growth required for breakeven
2. Rate of reinvestment of profits to balance maximum profit and maximum rate of reinvestment
- a. Should not reinvest so heavily that investment is never profitable or invest so little that long term profit compounding potential is negatively affected – i.e. ideally 50%/50% Balance


1% Total Risk using 5% stop
Amount at Risk = $300
Purchasing Power = 60x Shares @ $100
Total Value of Position @ Entry = $6000
Value @ Exit = $6,900
Potential Profit = $900

If the stock rises 10% to $110 the value of the original investment is $6,600. Enough to cover the cost of the initial risk ($300) as well as the additional $300 risk to be reused to reinvest future profits without having to incur the original $300 every time.

1% Total Risk using 5% stop
Amount at Risk = $300
Total Value of Position @ Entry = $6,000
Purchasing Power = 60x Shares @ $100
Added additional 54 Shares @ $110
Totaling of 114 Shares @ Avg of $105
Total Cost of Position After Reinvesting Profit = $11,970
Value @ $115 Exit = $13,110
Potential Profit = $1,140