staking_frequency.ipynb

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  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculateSimpleInterest(currentTotal,deltaT,apy):\n",
    "    interest = currentTotal*apy/365*deltaT\n",
    "    return interest\n",
    "\n",
    "def compoundValue(currentTotal,deltaT,apy,fee):\n",
    "### currentTotal in coins. deltaT in days. apy in decimal. fee in coins.\n",
    "    interest = calculateSimpleInterest(currentTotal,deltaT,apy)\n",
    "    newTotal =  currentTotal+interest-fee\n",
    "    return newTotal\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulateTime(principal,deltaT,apy,fee,timeLength):\n",
    "    ### principal in coins. deltaT in days. apy in decimal. fee in coins. timeLength in years\n",
    "    compoundingEvents = int(timeLength/(deltaT/365.))\n",
    "\n",
    "    activeTotal = principal\n",
    "    for event in range(1,compoundingEvents+1):\n",
    "        activeTotal = compoundValue(activeTotal,deltaT,apy,fee)\n",
    "\n",
    "    #Account for interest gained during the final part of the time frame. Assumes you pull out at the end of the year no matter what.\n",
    "    fractionalEvent = timeLength/(deltaT/365)%1\n",
    "    #Approximating the end of the timeframe as getting a percentage of the growth over the next deltaT. Crude because it'll overestimate for small fractions but it should work.\n",
    "    activeTotal = activeTotal + fractionalEvent*calculateSimpleInterest(activeTotal,deltaT,apy)\n",
    "\n",
    "\n",
    "    return activeTotal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "vectorizedSimulateTime = np.vectorize(simulateTime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "The calculated total: 10.9986\nThe interest should be 1. It is: 1.0\nThe total should be: 10.9986 \n\nIf there's no interest and no fees: 10.0\nIf there's no fees: 11.0 \n\nApproximately continuous with no fees: 11.051709029363042 . Should be: 11.051709180756477\nThe difference:  -1.5139343467751587e-07  can be attributed to numerical error/continuous approximation error.\n"
     ]
    }
   ],
   "source": [
    "#Sanity checking formulas\n",
    "print(\"The calculated total:\", simulateTime(10,365,0.1,0.0014,1))\n",
    "print(\"The interest should be 1. It is:\", calculateSimpleInterest(10,365,0.1))\n",
    "print(\"The total should be:\", 10+1-0.0014,\"\\n\")\n",
    "\n",
    "print(\"If there's no interest and no fees:\",simulateTime(10,365,0,0,1))\n",
    "print(\"If there's no fees:\",simulateTime(10,365,0.1,0,1),\"\\n\")\n",
    "print(\"Approximately continuous with no fees:\",simulateTime(10,0.001,0.1,0,1), \". Should be:\", 10*np.exp(0.1*1))\n",
    "print(\"The difference: \",simulateTime(10,0.001,0.1,0,1)-10*np.exp(0.1*1),\" can be attributed to numerical error/continuous approximation error.\")"
   ]
  },
  {
   "source": [
    "# **EDIT THESE PARAMETERS**"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Optimal re-investing time: 45.763966147781346\nDue to approximations take this with a grain of salt. It's more useful to look at the graphs below.\n"
     ]
    }
   ],
   "source": [
    "### Maximum finding paremeters:\n",
    "principal = 50\n",
    "apy = 0.1\n",
    "fee = 0.004   # Important to include the total fees involved in the whole process including the redelegation of the reward\n",
    "\n",
    "timeLength=1 # Years\n",
    "\n",
    "# The minimum deltaT is the amount of time to accumulate 1 fee's worth of a token\n",
    "minimumDeltaT=fee/(principal*apy/365)\n",
    "\n",
    "# Negating function to find the minimum\n",
    "neg_simulateTime = lambda deltaT: -1*simulateTime(principal,deltaT,apy,fee,timeLength)\n",
    "brent_deltaT_o = opt.minimize_scalar(neg_simulateTime,bracket=(minimumDeltaT,timeLength))\n",
    "print(\"Optimal re-investing time:\", brent_deltaT_o.x)\n",
    "print(\"Due to approximations take this with a grain of salt. It's more useful to look at the graphs below.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "endpoint=timeLength*365\n",
    "x = np.linspace(minimumDeltaT,endpoint,num=2000)\n",
    "y = vectorizedSimulateTime(principal,x,apy,fee,timeLength)\n",
    "plt.plot(x,y)\n",
    "plt.xlim((-20,endpoint))\n",
    "plt.title(\"Coins vs deltaT\")\n",
    "plt.xlabel(\"deltaT (days)\")\n",
    "plt.ylabel(\"Coins\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.title(\"Zoomed in\")\n",
    "plt.xlabel(\"deltaT (days)\")\n",
    "plt.ylabel(\"Coins\")\n",
    "plt.xlim((-10,endpoint/4))\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.title(\"Zoomed in\")\n",
    "plt.xlabel(\"deltaT (days)\")\n",
    "plt.ylabel(\"Coins\")\n",
    "plt.xlim((-10,200))"
   ]
  },
  {
   "source": [],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}