# How does risk threshold work?

While Betoken's [Incentivized Meritocracy](https://github.com/Betoken/Whitepaper/blob/master/BetokenWhitepaper.md#introduction) can already deal with managers who don't make any investments but still redeem their [commissions](/docs/manage-the-fund/how-does-the-managers-monthly-commission-work.md) 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.


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