Risk Exposure

When X+Y0X+Y\neq0, the system has risk exposure because of the constant price fluctuation.

At any given moment tt, we have the state of a derivative StS_t, the sum of total long positions XtX_t, the sum of total short positions YtY_t and the current price index ItI_t. Assuming that we have a new price It+1I_{t+1} at the moment t+1t+1, then the risk exposure VexposureV{exposure} can be calculated as follows:

Vexposure=((Xt+Yt)(It+1It))V_{exposure}=\sum\Big((X_t+Y_t)*(I_{t+1}-I_t)\Big)
  • XtX_t is always positive and YtY_t is always negative.

Consider that It+1ItI_{t+1}-I_t from external markets is unpredictable and cannot be controlled, the only way to reduce the risk exposure is to restrict the value of Xt+YtX_t+Y_t.

Obviously, if Xt+Yt=0X_t+Y_t=0, the risk exposure will not increase at moment tt.

Thus, the hAMM system reaches a balanced state (i.e. X+Y=0X+Y=0), which is so called "risk exposure closed".

Naked Position

At any moment, the value of X+YX+Y means the "unhedged" or "naked" position NN of a certain derivative at that moment:

N=X+YN=X+Y

When N=0N=0, the sum of total long positions equal to the sum of total short positions, and there are no naked positions.

When N>0N>0, the sum of total long positions are greater than the sum of total short positions, and the naked positions are long positions.

When N<0N<0, the sum of total short positions are greater than the sum of total long positions, and the naked positions are short positions.

VexposureV_{exposure} can be simplified as follows:

Vexposure=(Nt(It+1It))V_{exposure}=\sum\Big(N_t*(I_{t+1}-I_t)\Big)

It can be concluded that:

When N=0N=0, no matter how the index was fluctuated, the net profit/loss of all positions equals zero, and the net loss of the system will not increase.

When N0N\neq0, if the sign of It+1ItI_{t+1}-I_t and NN are the same (i.e., naked positions and the index fluctuation has the same direction), the net loss of the system may increase.

Thus, the balanced state of hAMM system equals to "zero naked position":

N=X+Y=0N=X+Y=0

The key to achieve the balance of hAMM system is to restrict naked position.