You will be able to read a Value at Risk figure and explain why expected shortfall says more about bad days.
Banks report a figure to their regulators every day that sounds like exactly what Marcus wants: how much they could lose. It's called Value at Risk, and fund risk reports quote it too. For his own account, it would turn "my portfolio is volatile" into "in a bad month I could lose about S$13,000". That is a sentence he can plan around. It also has a hole in the middle that a lot of people fell through in 2008, and you need to see both.
Value at Risk, or VaR, is the loss you would not expect to exceed on a given share of days or months, over a given period. A one-month 95% VaR of S$13,000 means that in 95 months out of 100, you'd expect to lose less than S$13,000, or gain. In the other 5, you'd expect to lose more.
Three choices define any VaR figure: the confidence level, usually 95% or 99%; the period, such as one day or one month; and the method. Always check all three before you compare two figures.
The simplest method for your own account is historical. You take your actual past returns, sort them from worst to best, and read off the line where the worst 5% begins.
Here is Marcus's version, with made-up figures. He has 60 monthly returns for his portfolio, five years' worth. Five percent of 60 is 3, so the 95% VaR sits at his third-worst month. Sorted, his five worst months were minus 11.2%, minus 8.0%, minus 6.4%, minus 5.1% and minus 4.8%. His one-month 95% VaR is 6.4%. On a portfolio of about S$202,000, that's about S$12,900.
Spreadsheet percentile functions such as PERCENTILE interpolate between neighbouring months, so they can give a somewhat different figure from counting. Neither is wrong. Pick one method, write it down and keep it.
VaR tells you where the bad months begin. It says nothing about how bad they get past that line. A portfolio whose worst 5% of months all lose about 7% and one whose worst 5% include a month of minus 30% can have identical VaR.
That's the hole. The losses that do the real damage sit beyond the VaR line, in exactly the region the number ignores. Before the 2008 crisis, many banks reported modest VaR figures based on calm years, and the losses they then took were many times larger.
Expected shortfall, also called conditional VaR, answers the question VaR skips: when a month is bad enough to cross the line, how bad is it on average? You take the losses at or beyond the VaR line and average them.
For Marcus, that means his three worst months: minus 11.2%, minus 8.0% and minus 6.4%. Their average is about 8.5%, or about S$17,300 on his portfolio. So his summary becomes: "In about one month in twenty, I should expect to lose at least S$12,900, and when that happens, the average loss is about S$17,300."
Bank regulators moved in the same direction. The Basel Committee's market risk rules for banks, known as the Fundamental Review of the Trading Book, replaced VaR with expected shortfall as the main measure for market risk capital.
There's another way to estimate VaR, and it shows why the historical method is worth the effort. The parametric method assumes returns follow a bell curve. You take the average monthly return and subtract 1.645 standard deviations, the cut-off for the worst 5% of a normal distribution.
Marcus's 60 months have a made-up average of 0.5% and a standard deviation of 3.3%. The bell curve says his 95% VaR is 0.5 minus 1.645 times 3.3: about minus 4.9%, or about S$10,000. His actual history put it at 6.4%, and his worst month at 11.2% would be a once-in-many-decades event if returns really followed a bell curve. Real returns have fat tails, as lesson 2.1, Volatility: what standard deviation captures and what it misses, showed. A bell curve model flatters the risk exactly where it matters most.
Historical VaR and expected shortfall are built entirely from the months in your window. Five calm years produce small numbers, and the next crisis isn't in them yet. Nothing in the method warns you about that.
Two habits help. Use the longest history you can get, ideally one that includes at least one serious fall such as 2008 or early 2020; for holdings you haven't owned that long, an index that tracks them is a reasonable stand-in. And treat the figures as a floor for what a bad month looks like, never as a ceiling. Lesson 11.6, Stress test against past crises and made-up shocks, adds the other half: deliberately running your portfolio through scenarios worse than anything in your data.
For the activity, take at least 60 monthly returns for your portfolio, from your returns tab or from index data for your holdings, sort them, and find the third-worst month and the average of the worst three.
Calculate monthly historical Value at Risk and expected shortfall at 95% for your portfolio from at least five years of data.
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