How does risk threshold work?

While Betoken's Incentivized Meritocracy can already deal with managers who don't make any investments but still redeem their commissions every month (AKA freeloaders), it does so too slowly to disincentivize managers from freeloading. Thus, we have introduced a mechanism we call Risk Threshold to better handle freeloaders.

The Risk Threshold mechanism measures the amount of risk each manager has taken in a cycle, and only gives them the full commission amount if the risk they've taken exceeds a certain threshold.

Formula

We measure the risk a manager has taken using the formula:

$$Risk = \sum_{i\in Investments} Duration(i) \times Stake(i)$$

And the threshold we have chosen for each manager is:

$$Threshold = KairoBalanceAtCycleStart \times (3 \text{ days})$$

The proportion of the full commission that each manager will receive is:

$$min(1, \frac{Risk}{Threshold})$$

Example

Say at the beginning of a cycle Alice has 100 Kairo and Bob has 10 Kairo.

Alice stakes 50 Kairo in an investment for 7 days, Bob stakes 1 Kairo in an investment for 15 days and 2 Kairo in another investment for 5 days.

The risk Alice has taken is:

$50\times7=350$

and her risk threshold is:

$100 \times 3 = 300$

so she will receive the full commission amount.

The risk Bob has taken is:

$1 \times 15 + 2 \times 5 = 25$

and his risk threshold is:

$10 \times 3 = 30$

so he has not exceeded the risk threshold, and will receive

$\frac{25}{30} = 83.33%$

83.33% of the full commission amount.