Get annualized volatility data from whatever source you prefer (even google probably works).
To get daily volatility from the annual volatility, just take
a = annualized volatility
a / sqrt (365) = d
#d is daily volatility
So for example, if Ether’s annual volatility is 75%
75 / sqrt (365) = 3.925679
Similar to options, where the fair price can be derived from the replicating portfolio, we will compare the LP position to “LVR” (see here for details).
Daily LVR in basis points can be calculated by taking
d = daily volatility
d ^ 2 / 8 = LVR
For example
d = 3.925679
3.925679 ^ 2 / 8 = 1.926369 basis points per day
Now, to calculate annual LVR we take LVR * 365, e.g.
1.926369 * 365 = 703.1248
Now divide by 100 to get the percentage since 1 basis points is 0.01%…
703.1248 / 100 = 7.031248%
Meaning that we must earn approximately 7.03% in fees (plus an unknown risk premium for smart contract risk) in order for LPing to be fairly priced.
To calculate expected fees, take
Pool fees in basis points * volume as a percent of AMM assets * time.
E.g., 30 basis point pool, daily volume is 11% of AMM assets in reserve, one year. Find fees
30 * 11 * 365 = 120,450
120,450 / 10^4 = 12.04%
#the 10^4 term undos the fact that the basis points should be 0.003 and the fees should be 0.11, you could also calculate as
0.003 * .11 * 365 = .12045, i.e. 12.045%
Now. we can also solve for volume as a percent of pool reserves by taking the basis fees (here I assume 30 BP fees) and time and solving for our LVR of approximately 7% plus a risk premium of 2%).
0.003 * z *365 = 0.09
#solve for z
z = 0.0821918
Thus, we can see that daily volume must be approximately 8% of AMM assets in reserve to justify LPing.