# 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!