Estimating the Price Move Needed to Increase a Volatility-Adjusted Position
Summary
The document asks how to estimate the price change that would make a risk-adjusted trading system add one share. The proposed procedure estimates annualized return volatility at the latest price, calculates the current position, then holds volatility fixed while calculating the price implied by a position one share larger. The difference from the live price is treated as the required move.
The central issue is whether holding risk constant gives a valid threshold. The document does not provide an answer or evidence validating the method; it presents the calculation as a question. In a system where volatility is recalculated from returns that include the hypothetical price, the target price and risk may depend on each other, so fixing risk at its current value could misstate the threshold. The result also depends on the specific position-sizing rule, capital and risk target. This is a useful problem framing for position sizing, but not a complete method or a demonstrated trading strategy.
Key ideas
- The proposed threshold is the difference between the current price and the price implied by a position one share larger.
- The calculation uses current annualized volatility for the target position.
- If volatility is recalculated using the hypothetical price, the risk estimate and target price may need to be solved together.
- The document poses the method as a question and does not establish that it is correct.
Tags
Full text
# What is the minimum price change required for a trading position increase of 1? # What is the minimum price change required for a trading position increase of 1? Suppose I have a trading system that calculates the daily risk adjusted position from the annualized risk, that is, the standard deviation of the returns of a stock over an arbitrary period of time. I would like to calculate the minimum price change (from the last closing price) required for the trading system to increase the position by 1 stock. Therefore, I thought that by finding the target price from a target position, which would be the last position added by a trade amount (in this case one), I will be able to find the respective price for that position and simply find the difference between that and the previous price. So far I have come up with the following: 1.) Append the price series with the last live price 2.) Calculate the annualized risk as mentioned above and keep note of the risk of the live price (let's call this risk `last_risk`) 3.) Calculate the risk adjusted position for the returns of the price series and keep note of the position of the live price (let's call this `last_position`) 4.) We want to find the minimum price change required for the position to increase by 1, therefore we append the risk adjusted position series with the value: `last_position + 1` 5.) We also append the annualized risk series with `last_risk`, so therefore we are using the same risk for this new target position as the one for the live price 6.) We then calculate the new resultant price series as follows: `new_price_series = (capital/risk_adj_position) * (target_risk/risk)` such that the capital is the amount of money available, and this is divided by the `risk_adj_position` which is a series containing the daily position (number of stocks) including the target one (`last_position + 1`) and this is multiplied by the `target_risk/risk`, where the `target_risk` is a value denoting the percentage of capital willing to be risked, and `risk` is a series containing the daily annualized risk values including the risk for the target position for which we want to find the respective price for. 7.) This will will output a price series that will also contain the price for the new target position 'last_position + 1' and the `minimum price change` is indeed obtained by finding the difference between this price and the previous price (the live price) Thing is, I am not sure if this method would be correct, namely because I am not confident that using the risk value of the live price for the target price is the right way to go. I only started delving into quantitative finance a couple of months ago so I apologise for any stupid misconceptions and errors, and I will appreciate any insight given. (P.S: Please note that Python is being used for coding the algorithm and Pandas and Numpy are used for data structure manipulation, etc (such as broadcasting of results) ) Thank you!
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