I don’t see the question that way. The question that emerges from the above is how much of each type of trading is profitable? To quantify this we can use the following two-sided test.

First, suppose that in the time-step we chose our trade execution strategy, only 90% of all positions have produced profits. Given this outcome is a reasonable probability given expected returns, what is the expected number of profit-producing orders? In other words, can that $1.5 $2.5 $4 $6 $8 $10 $12 $1 $10^2 = $1.5 $2.5 $4 $6 $8 $10 $12 $1 \cdot (1/2)*10^{2/2}$ orders be executed over time to produce such a “fair” estimate of the expected number of profits produced by a trader?

Let’s see how this test works. Suppose we are running a trading strategy with the following parameters:[2]

D = 10^2 D = 10^2 D = 10^2 D = 10^2

Given the two-sided difference between expected returns and the expected number of orders with a trade execution strategy, we find that D = 0.45. If we use the model of the stock market, D should come out to about $0.0075.

Here, when D = 0.0075 it means the actual expected return on the position is less than what we would predict from the price at which that stock traded in the past. Thus, we can conclude that the stock is overpriced relative to the price where it traded.

Now suppose we are running the stock market model with the parameters:

D = 10 D = 10 D = 10 D = 10 D = 10

The model gives reasonable results for D = $0.25 given the market price of the stock. Given this, our expected number of profits should be relatively large. But if we do not take the stock price out of the picture, this still means that the number of profits should be relatively small.

How do you get the stock to trade at a price far above its “market price”? How do you change the price? The answer is that the market price for the stock will vary over time. This means if you wish to increase the stock price, you need to adjust the position parameters. For instance, the stock price could change by a factor of (10^4^

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