I Fell In a 10 Foot Hole…How Far Do I Have To Climb to Get Out?

If you fall into a 10 foot hole, you have to climb 10 feet to get out. That simple physical rule doesn't work for portfolios. I have written a few times about the asymmetry of loss and gain in portfolios (Asymmetry, Which Way is Up). The basic concept is that risk is not equal to a commensurate amount of reward. For example, if I lose 25% of my $100 million fund, then I will have to be up by 33% the following year to be back to break even. Because of this asymmetry, it is critical to calculate risk for every investment and avoid potential loss that does not give a more than adequate level of reward.

Because I spend so much time talking about this concept (and I'm not good with math in my head), I was looking for a quick way to calculate the reward I need to break even after a loss. After writing out the formula and then refining it, I came up with a simple formula:

 

For example:

As you can see, the sum of each fraction is 100%, so it is very easy to compose the formula. The only problem is I still have to do math in my head. So I then tried to create a ratio, but I realized after plotting it out, that it is logarithmic (see chart below) and above my pay grade.

Although the BreakEvenReturn formula definitely makes the math easier, does anyone know a simple way to perform the calculation? Or at least point me to a quick way to turn fractions into percentages in my head.