You will be able to measure maximum drawdown and recovery time and explain why they matter more to behaviour than volatility.
Ask Marcus about risk and he won't mention standard deviation. He'll tell you about the two years after his first year, when his investments, measured without his deposits, stayed below the high they had reached. New money kept the balance growing, which hid the problem from his app but not from him, and around the middle of that stretch he caught himself searching for "should I sell everything". That is the risk investors feel, and it has its own measures.
A drawdown is a fall from the highest value reached so far to a later value, measured in percent. Maximum drawdown is the largest such fall over the whole history you're looking at.
To calculate it, you need a value series, such as month-end values of a total return index or of your account with cash flows stripped out. Add a column that tracks the running peak: the highest value so far. In the next column, divide each value by the running peak and subtract one. That column is the drawdown at each date. Its lowest number is the maximum drawdown.
Here is a made-up world equity fund. It peaks at an index value of 100, falls over nine months to 66, and then climbs back. Its maximum drawdown is 66 divided by 100, minus one: minus 34%.
Data frequency matters. Marcus's portfolio, measured only at year-ends, shows a maximum drawdown of 18%, his one bad calendar year. Measured monthly, the same history shows a deeper fall in the middle of that year, because markets don't time their lows for 31 December. Use monthly data at least. Fund factsheets that report drawdown from yearly figures are understating it.
A fall needs a bigger gain to recover. After a 34% fall, the fund is at 66, and getting back to 100 needs a gain of 100 divided by 66, minus one: about 52%. A 50% fall needs a 100% gain. Marcus's 18% year needed a gain of about 22% to recover.
This is the same arithmetic as the geometric mean trap in lesson 1.1, seen from a different side. It's why deep drawdowns do so much long-term damage, and why two funds with similar volatility can leave investors in very different places if one has a habit of falling hard.
Two well-known episodes give the scale. US shares, measured by the S&P 500, fell more than half from their 2007 peak to their low in March 2009. Japan's Nikkei 225 peaked at the end of 1989 and didn't close above that level again until early 2024, more than three decades later. Both are price index figures without dividends, which shorten the wait somewhat in total return terms, but neither is a rounding error.
The depth of a fall is half the experience. The other half is how long it lasts. Time under water counts the periods from a peak until the value first gets back above it.
For the made-up fund above, the fall took nine months and the climb back to 100 took another 22. It spent 31 months under water. For Marcus's yearly series, measured without his deposits, the portfolio sat below its year-one high for two year-ends running.
Time under water is the measure that predicts behaviour. Most investors can sit through a sharp fall that recovers in a few months. A long stretch below the old high, with no clear end, is when people abandon their plans, often near the bottom. Behavioural Finance: why you make the money mistakes you make covers the psychology in lesson 6.5, Your calm-day risk tolerance is not your crash tolerance. Your job here is to know the number before you live through it.
Maximum drawdown records the single worst moment. Time under water records the longest stretch. Neither tells you how much of the history was spent in pain. The ulcer index, developed by Peter Martin in the 1980s, combines depth and duration into one figure.
It is the square root of the average of the squared drawdowns. Squaring makes deep drawdowns count far more than shallow ones, and averaging over every period means long drawdowns count more than brief ones.
A small made-up example. A fund's drawdowns at seven quarter-ends were 0%, minus 8%, minus 19%, minus 26%, minus 15%, minus 6% and 0%. Square each, average the seven squares, and take the square root: about 13.9. A second fund fell harder at first, to minus 20% and minus 26%, then recovered faster, with drawdowns of 0, minus 20, minus 26, minus 10, minus 2, 0 and 0. Its ulcer index is about 13.0. Same worst point, less time spent deep in the hole, a lower score.
In a spreadsheet the ulcer index is one formula over your drawdown column: the square root of the average of the squared values. Use monthly data, and calculate it over the same window for everything you compare.
Drawdown, time under water and the ulcer index all go on your risk dashboard in lesson 2.8, Build a risk dashboard for your portfolio and two benchmarks. For the activity, pull ten years of month-end values for your portfolio and for a world equity index, both in SGD, and build the running peak and drawdown columns for each.
Find the maximum drawdown and time under water for your portfolio and a world equity index over the last ten years.
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