Simulating Mean-Reversion Trades to Estimate Turnover and Drawdowns
Summary
The question asks how volatility might inform the number of round trips and the chance that a one-unit strategy loses more than a chosen amount. The response recommends simulating price paths, applying the entry and exit rules to each path, and summarizing the resulting trade counts with an average or median. It describes geometric Brownian motion as one possible price-generation model, using drift, volatility, time steps, and random shocks.
For loss confidence estimates, the response suggests examining simulated price quantiles, connecting this to value at risk. That is only a starting point: a terminal-price quantile does not by itself measure the strategy’s maximum underwater loss or account for its entry, exit, and position rules. Results depend on assumptions such as the price process, drift, sampling interval, and transaction costs, none of which are calibrated in the note. The proposed simulation should therefore run the actual strategy and calculate its pathwise trade count and drawdown directly before using quantiles to describe risk.
Key ideas
- Simulate many price paths and run the full trading rule on each path to estimate round-trip counts.
- Geometric Brownian motion offers one model for generating price paths from drift and volatility assumptions.
- Use simulated path outcomes to estimate loss probabilities at a selected confidence level.
- Terminal price quantiles alone do not capture the strategy’s maximum drawdown or trading mechanics.
- Estimates depend on model assumptions and should account for costs and position constraints.
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Full text
# How to calculate number of round trips given volatility? # How to calculate number of round trips given volatility? Suppose we know stock price volatility is normally distributed with mean = 0 and annual volatility say 20%. Let's assume markets never close and we can trade at 1 second intervals. Let's assume stock at $t_0$ is \$100. How to estimate the number of round trips in a given time period (day, month,...) with a basic strategy of opening a trade $x$ standard deviations away from \$100 and closing it at \$100? We can have a max open position of 1 unit, so basically this trades around stock at $t_0$. Then how to estimate with $x\%$ confidence that we will not be underwater more than $y$ dollars with this basic strategy? I've never seen this type of problem expressed before but it has practical implications for what I am trying to do. I'm not sure what I'm getting myself into, if this is a hard problem or not, if it is some recommended stuff to look into will be helpful. ## Answer by Varun Divakar (score 1) https://quant.stackexchange.com/a/43296 To approximate the number of transactions based on volatility you will need to make many simulations and run your trading strategy in all the simulations and then take the average or the median as an approximation. To make the simulations you can use the Random Walk approach. You can use GBM equation to create a Random walk simulation as shown below: A Geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. To simulate the stock prices we can use the SDE or Stochastic Differential Equation of St (a stochastic process). SDE===> dSt = 𝛍St dt + 𝞼St dWt Where, St is a stochastic process 𝛍 is the percentage drift 𝞼 is the percentage of volatility Wt is a Weiner’s process or Brownian motion If you want to link this equation to a stock data then you can think of St as the stock price at time step t, 𝛍 as the average daily return and 𝞼 as the average daily volatility of the stock. Let us try to simulate the stock prices from the above equation by expanding it further using the Ito’s interpretation. St = St-1* exp((𝛍-(𝞼^2/2))*t + 𝞼*Wt) Where, St is stock price at time t St-1 is stock price at time t-1 𝛍 is the mean daily returns 𝞼 is the mean daily volatility t is the time interval of the step Wt is random normal noise These simulations are very useful when one is interested in finding the VaR or the expected shortfall for a particular stock with a certain degree of confidence. This exactly what your question is. To calculate the VaR you just need to take the lower x% percentile price(p) of all the simulated prices. This should give you the confidence-x and price p associated with it. For a given confidence value, you can get the price associated with it.
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