Drawdowns and the underwater plot

Let’s say we have a time series of portfolio returns, in percentages:

portReturns <- ts(rnorm(30)) #randomly generated 'returns'
portReturns #show the first handful of 'returns'

## Time Series:
## Start = 1 
## End = 30 
## Frequency = 1 
##  [1]  0.67616342  0.07398030 -0.61932880  0.21041818 -0.76346086
##  [6] -0.82951638  1.57191386  0.08774548  0.02411848  1.01011886
## [11] -0.77200624  0.39298838  1.96212242 -0.66670138 -0.04075096
## [16] -0.89394127  0.26163506  0.74785858 -1.20744080  1.13539527
## [21] -0.68981343  0.70767474  1.45024932  0.67600472 -0.99920754
## [26] -1.71959460 -0.70442081  0.11580595 -0.20839502 -0.44757219

Let’s plot them:

plot(portReturns, main='returns')

We see the typical whitenoise-like pattern.

Now let’s find the cumulative sum of those returns, which will show the change in the value of our portfolio over time:

portReturnsCumu <- ts(cumsum(portReturns))
plot(portReturnsCumu, main = 'Cumulative returns/Portfolio value')

Let’s visually find when the portfolio reaches it’s maximum value, before losing value, for the first time. Then find when it recovers from that trough. That period of loss after a peak, is a period of drawdown.

Let’s make it easy to identify these periods by plotting a line, showing the running max value reached by the portfolio:

plot(portReturnsCumu, main = 'Cumulative returns/Portfolio value with Running Max')

portReturnsCumuMax <- cummax(portReturnsCumu)
lines(portReturnsCumuMax, col='red')

Whenever the value of the portfolio (black line) is below the running max (red line), that is a period of drawdown

Now that we can find drawdowns visually, how do we compute them, so we can plot them on their own?

portDrawdowns <- portReturnsCumuMax - portReturnsCumu

everything <- data.frame(portReturnsCumuMax,
                        portReturnsCumu,
                         portDrawdowns) 
                         
colnames(everything) <- c('Portfolio Running Max Value','Portfolio Value', 'Drawdown')

head(everything)

##   Portfolio Running Max Value Portfolio Value  Drawdown
## 1                   0.6761634       0.6761634 0.0000000
## 2                   0.7501437       0.7501437 0.0000000
## 3                   0.7501437       0.1308149 0.6193288
## 4                   0.7501437       0.3412331 0.4089106
## 5                   0.7501437      -0.4222278 1.1723715
## 6                   0.7501437      -1.2517441 2.0018879

It’s just subtraction: Column 1 - Column 2 = Drawdown

Now lets plot the drawdowns on their own:

plot(portDrawdowns, main = 'Drawdowns')

You’re probably noticing that these are positve values. Drawdowns are positive. In order to turn this into an underwater plot, we simply reflect the drawdowns across the x-axis:

plot(-portDrawdowns, main = 'Underwater plot')

From what I’ve read, a trader named Jack Schwager thought this way of presenting the info better emphasized that we’re dealing with reductions in portfolio value, than did plotting positive values.

What kinds of questions can this chart help us answer?

“What was the longest period of loss for this portfolio?” (Duration)
- “How long might I find myself waiting for the portfolio to recover to a previous peak?”
- “Do we have the patience/liquid capital to wait that long?”
“What was the largest drawdown for this portfolio?” (Magnitude)

Noteworthy:

“Drawdowns present a significant risk to investors when considering the uptick in share price needed to overcome a drawdown. For example, it may not seem like much if a stock loses 1%, as it only needs an increase of 1.01% to recover to its previous peak. However, a drawdown of 20% requires a 25% return to reach the old peak. A 50% drawdown, seen during the 2008 to 2009 Great Recession, requires a whopping 100% increase to recover the former peak.” -https://www.investopedia.com/terms/d/drawdown.asp#:~:text=A%20drawdown%20refers%20to%20how,a%20measure%20of%20downside%20volatility.

Noteworthy:

The drawdowns show the loss in value since the last peak, not overall loss in portfolio value