## Formula for a financial instrument

Hi,

I am looking for a common and simple formula that would govern the value of a hypothetical financial instrument. Imagine that the hypothetical financial instrument's value is determined by the academic performance of a student. It would have to reward both consistent high performance and progress over time.

The formula would have to have the following properties:

Y = rate of return
X = absolute score
Z = change in score over a period of time

1) Rate or return (Y) is a function of both absolute score (X) and change in score (Z)

2) The financial instrument would reward performance both in absolute terms and in terms of change. For example, if a student begins the year below average and makes progress throughout the year then the financial instrument should have a positive payout. If a student begins and ends the year as a strong student, that too should have a positive payout.

3) The inverse should have lower payouts. That is, if a student begins and ends the year as a low performer, he should have a low or negative return; and if a student begins the year as a strong student but ends it as a week student, then he should have negative or low returns.

4) Lastly, the formula should accommodate different levels of risk tolerance. That is, lets say I want to use this for a low-risk class, then the payout would be between 0% and 5% with an average of 2.5%. On the other hand, if it were for a high-risk class, I would want to make the variability around the rate of return bigger (e.g., -95% to +100% with an average of 2.5%.

Thank you for any help you can provide. Also, if you can tell me where and how the formula you recommend is being used today in real-life, that would be very helpful.

Kindly,
Jon