I have been thinking about this problem for a little while and I think it is a multivariable calculus problem. I am currently studying calculus and I would like to see how someone would solve this.
Say you invested \$100 in the stock market. If the market goes up 20% you profit $20. Due to volatility, your investment would be up some days and down others. What if you invested a portion of your money and saved a portion to buy on the days the market goes down and sell once the market has recouped - "buying the dip."
For the sake of argument, we can assume that the invested funds will appreciate $x$ percent in any given time period ($t$) and that the value of those funds will depreciate at least by $y$ percent $n$ times a year.
trying to work out this problem is driving me down an ever more complex rabbit hole. The way I am going about this is to assume that the "dips" are evenly spaced within the time period and are uniformly 10% declines.
\$100 -> \$110
\$99 -> \$108
$10 x 11.111% = 0.11111
99 + 9 + 0.11111 + 10 = 118.11111
(principle) + (profit) + (profit from dip) + (reserve for buying dips)
If you made a 11.111% profit from each dip then it would take a little over 18 profitable dips to make up for the $2 of lost profit from having a portion of funds in cash.
How do I translate this into a calculus problem?