I need help developing a mathematical equition that I will use to evaluate some of the financial portfolios I invest in. The end goal is to determine the probability that my portfolio will reach my maximum allowed drawdown. This will help me add and remove assets to my portfolio to get the best balance.
Overview
Assume you have a graph that plots the performance of your financial portfolio. The graph plots equity (in dollars) on the x-axis and time (in days) on the y-axis. Also, assume that it is possible to enter into a portfolio at any day along the equity curve.
The end goal is to determine out of the total number of days you could enter into your financial portfolio, how many of those days would cause you to reach your maximum drawdown if you stay in the portfolio until the current day. Consider the following example:
Starting Balance: $10,000
Maximum Drawdown: $1,000 or 10% of capital
Hypothetical Portfolio Performance: Day1-2%, Day2-3%, Day3-(-%20), Day4(-25%), Day5(1%), Day6 -(-2%)
Entering on Day 1
Starting with a balance of $10,000, on Day2 my balance would be at $10,200. On Day3 it would be $10,506. On Day4 it would be $10,294.80. On Day5 it would be $7,721.10 at which point I would have dropped below my maximum drawdown of $1,000. I can thus conclude that entering on Day 1 would be considered a bad day to enter.
Entering on Day 5
Starting with a balance of $10,000, on Day6 my balance would be at $10,100. On Day7 it would be $9,898. Because the drawdown is not more than $1,000 I can conlude that entering on Day 5 would be a good day to enter.
I would then do this for everyday of data I have so far and determine the ratio of good days to bad days.
Summary
I’m a very visual learner so I need to create an IF/THEN statement that can be graphed. Essentially, my mathmatical calculation needs to help me locate the good days and the bad days. I can then use IF/THEN statements to color code those good days and bad days on a chart.
I’ve outlined the components that I think I need to do this affectively below but don’t really know how to go from here.
Constants
e(i) = my initial capital investment ($)
R = the amount of capital I’m willing to risk, % terms
D(R) = the amount of capital I’m willing to risk, $ terms
Variables
d = date
d(i) = date my account becomes active
e(d(i) + x) = equity at a given date after d(i) ($)
x
Statement
If e(i) - e(d(i) + x) < D(R) then d(i) = good day
If e(i) - e(d(i) + x) ≥ D(R) then d(i) = bad day