No Pain No Gain: The Lake Ratio

I liked Prashanth's recent article on drawdowns. Leaving aside definitions we ponder over few things related to drawdowns in this post.

The sun setting at Lake Washington. Photo taken by Deepak from Houghton Beach Park in 2022

There is some form of direct correlation between drawdowns in equity curves and pain suffered by investors/traders. The questions presented below are situations where you have to chose one of the two options which you feel is less painful. Assume this is the equity curve of your portfolio which begins it fall from value N at time t to some lower value at a future time. In one situation recovery is also shown.

Simply note down which is a preferred Experience A or B (less painful for you).

First try to answer each of these three questions impulsively. Then give each of these questions a few minutes of thought. Also try to recall real drawdowns you have witnessed in your equity curve before. Are you confident about the options you have chosen? 

Sensex as the equity curve

When the equity curve falls there are two things a) speed of fall that is in how much time it fell from the current value to the lower value and b) the extent of fall that is from the start value to the lowest value in the fall. The latter is referred to as the Maximum Drawdown (if the start value is the all time high of past).

During the Covid crash of March 2020 the speed of fall was swift and as I recall it was the fastest drop the Sensex had ever seen. The pain was like a sharp swift cut from a Japanese chef's knife. But going back to Harshad Mehta's crash of 1992 the pain was spread over years.

Enter the Lake ratio

When the equity curve drops below its previous high and stays below it for a certain duration we say that we are under water. And we continue to be under water till we reach a new peak. The time spent in the lake is one parameter and the other factor is how deep does the lake go. This in some way denotes the total value of pain suffered. Though I believe the surface of the bottom of the lake also matters - a swift drop, then a gentle recovery vs a gradual drop, then a steep recovery. Both will have different values of pain. 

Using Maximum Drawdowns alone leaves a few things unanswered in terms of pain.

Here is the Lake formation on a log chart of Sensex since inception. Data from BSE. Please click to expand the chart.

In summary 3 factors matter:

1. Speed of fall

2. Extent of fall

3. Speed of recovery to previous high

Volume of water could be the same in the lake but basis these factors the pain could be very different.

'In the stock market, the most important organ is the stomach. It's not the brain.' - Peter Lynch