Monte Carlo
Monte Carlo simulation
In plain words
A Monte Carlo simulation imagines thousands of possible futures for a stock by replaying random chunks of its history. You see the range of its moves: what happens most often, and how far it can go.
A simulation, number by number
This is what a simulation looks like in PairScanner. The stock and the figures are fictional.
Click a number to learn its role
Chance of a rise52%of futures end higher
My role: count the futures that end above today. 52%: barely more than one chance in two, once the past trend is removed.
Fall of more than 10%31%of futures
My role: give the size of a bad scenario. Nearly one future in three loses more than 10% in a year.
9 times out of 10-38% to +62%at 1 year
My role: show the range of outcomes: nine futures out of ten land inside it. The wider it is, the choppier the stock.
Middle case+2%the median
My role: give the middle future: half the paths do better, half do worse.
Paths10,000blocks of 5 sessions
My role: tell you how many futures are drawn. 10,000 paths are enough for the figures to stay stable from one run to the next.
Horizon1 yearor 1 month, 3 months
My role: tell you how far ahead you look. The longer the horizon, the wider the range.
What PairScanner does
For every stock, PairScanner takes the daily returns of the last five years, cuts them into blocks of five sessions and draws them at random to build 10,000 paths, over 1 month, 3 months or 1 year.
By default, the past trend is removed: the simulation replays the stock's swings and volatility without assuming that its rise or fall of recent years will continue. A switch lets you keep it.
You see a fan of paths, green if they end higher and red otherwise, the bands where 9 futures out of 10 and 1 out of 2 land, and three numbers: the chance of ending higher, the chance of losing more than 10% and the 9-in-10 range. Same stock, same date: same result.
The idea in detail
Nobody knows a stock's future. But its past says a lot about how it moves: the size of its days, how often it falls, how long its choppy periods last.
A Monte Carlo simulation draws at random from that past to build thousands of plausible futures. Taken together, they show a distribution: the middle case, the common cases, the extreme cases.
Drawing blocks of several sessions rather than single days keeps the sequence of days: a choppy period stays choppy, as in real markets.
A worked example
For a fictional stock over one year, without the past trend: 52% of futures end higher, 31% lose more than 10%, and nine futures out of ten range from -38% to +62%. The middle case is +2%.
The reading: a choppy stock, almost as likely to rise as to fall, with a wide range. Enough to size a position knowingly.
Fictional example for teaching purposes. It is neither a signal nor a recommendation.
What research says
The bootstrap, introduced by Bradley Efron in 1979, estimates the distribution of a quantity by resampling the observed data. Hans Künsch extended it in 1989 to dependent series, such as stock returns, by drawing blocks of consecutive observations.
Dimitris Politis and Joseph Romano proposed the stationary bootstrap, with blocks of random length, in 1994. In finance, Phelim Boyle showed as early as 1977 that options can be valued by simulating thousands of paths of the underlying asset: the Monte Carlo method has been a standard tool ever since.
Sources
Studies cited on this page:
- Bradley Efron (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1), 1-26.
- Hans R. Künsch (1989). The Jackknife and the Bootstrap for General Stationary Observations. The Annals of Statistics, 17(3), 1217-1241.
- Dimitris N. Politis and Joseph P. Romano (1994). The Stationary Bootstrap. Journal of the American Statistical Association, 89(428), 1303-1313.
- Phelim P. Boyle (1977). Options: A Monte Carlo Approach. Journal of Financial Economics, 4(3), 323-338.
PairScanner promises no results. Educational content: neither investment advice nor a prediction; PairScanner places no orders.
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