# Options trade - statistically expected return calculation?

I am calculating expected return for composite option strategies based on event probabilities provided by the broker. For example, consider the following spread On the left hand side we see:

• maximal possible return $$R_{max}=\25$$
• probability of max return $$P_{Rmax}=0.84$$
• maximal possible loss $$L_{max}=\225$$
• probability of max loss $$P_{Lmax}=0.089$$
• expected commission $$C=2\times \3=\6$$ (times two, expecting the same on exit)

So basically, I am parametrizing all outcomes by taking a range on the real line $$x\in(0,1)$$ corresponding to outcome probabilities. On that range I construct a function as follows:

$$f(x)=\begin{cases} R_{\max }-C & x1-P_{\text{Lmax}} \end{cases}$$

which linearly interpolates between max return and max loss assigning them the corresponding probability regions. Here a plot of $$f(x)$$: which basically visualizes the weight distribution of returns or losses based on respective probabilities. Now I take the expected overall % return/loss on risk to be given by the integral

$$I=\frac{\int_0^1 dx f(x)}{L_{max}+2C}$$

In the example above, the expected % return/loss on risk turns out to be $$I=-0.052$$, which means one can expect to lose on average about $$5.2\%$$ of risked capital after a large number of such trades. (Very bad proposition.)

Is the above approach sound, or can you suggest a better way to calculate average expected return?

One thing that makes me skeptical, is that overall Profit Probability is stated by the broker to be $$85\%$$, while function $$f(x)$$ crosses the x-axis at about $$0.84$$ which is a slight deviation. Based on this I suspect that the above approach is not very precise?

Also, note that the function $$f(x)$$ basically mimics the spread in this case and simply maps the outcomes onto the range $$x\in (0,1)$$. However, the stated probabilities for the outcomes are generated by the broker in the same fashion for any complicated composite strategies. Do you think this calculation may be less reliable for a more complicated strategy?

EDIT

The problem is very visible in the following setup: The overall Profit Probability in this case is stated by the broker to be 41%, while constructing function $$f(x)$$ as above produces the weight curve which crosses the x-axis at around $$0.675$$ instead of $$0.41$$, suggesting that there is definitely something wrong with the approach. How would one improve upon it?