Math Challenge-Exercise.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "casual-importance",
   "metadata": {},
   "source": [
    "# Balancer Simulations Math Challenge - Basic Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "laughing-disclosure",
   "metadata": {},
   "source": [
    "This is a series of exercises to gain intuition for the core algorithm in Balancer Pools: the Value Function, and invariant V."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "spoken-corporation",
   "metadata": {},
   "source": [
    "**Exercise:** We'll work on Step 1 questions in our working session on May 25 in teams of 2, facilitated by @Octopus and @akrtws.  \n",
    "**Challenges:** Step 2 will be homework assignments, submitting at least one challenge solved is mandatory for successful participation!  \n",
    "Here's the notebook with challenges: https://github.com/TokenEngineeringCommunity/BalancerPools_Model/blob/fcb67145e8b0f8a1843fe3c6921dbb5a7085938e/Math%20Challenges-Advanced.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sublime-polish",
   "metadata": {},
   "source": [
    "## Exercise:   \n",
    "Let's set up a pool.  \n",
    "\n",
    "We have 100 Token A and 100 Token B, with equal weights.  \n",
    "The price definition in our pool is constraint by the\n",
    "Invariant V in Balancer Pools. \n",
    "\n",
    "a_bal = balance of token A  \n",
    "b_bal = balance of token B  \n",
    "a_weight = weight of token A  \n",
    "b_weight = weight of token B   \n",
    "\n",
    "The weights in this pool are equal for both tokens.\n",
    "For now, we don't have a swap fee."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "thirty-ecuador",
   "metadata": {},
   "source": [
    "# Q1.1: \n",
    "What's the initial spot price of token A in token B?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "forced-surgery",
   "metadata": {},
   "source": [
    "# Q1.2:\n",
    "Now let's assume a series of 99 swaps. With every swap, **1.0 token A is bought from the pool, against token B**.  \n",
    "\n",
    "**a) Create a table \"buy_A\"** with\n",
    "\n",
    "    the token A balances (swap by swap)\n",
    "    the token B balances (swap by swap) - that are constraint by the value function. \n",
    "\n",
    "**b) What do you notice in general?**\n",
    "Write down your findings (in words).\n",
    "\n",
    "**c) How much would Alice have to pay in token B when buying the first 1.0 token A?**\n",
    "Write down your findings (in words). Compare with the initial Spotprice."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abandoned-chicken",
   "metadata": {},
   "source": [
    "# Q1.3:\n",
    "\n",
    "Now let's assume a series of 99 swaps in the opposite direction. We start again with the original state: We have 100 Token A and 100 Token B.   \n",
    "With every swap, **1.0 token B is bought from the pool, against token A**.\n",
    "\n",
    "Create a table **'buy_B'** with\n",
    "\n",
    "    the token A balances (swap by swap)\n",
    "    the token B balances (swap by swap) - that are constraint by the value function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "composite-multimedia",
   "metadata": {},
   "source": [
    "# Q1.4:\n",
    "\n",
    "a) What are the new balances of token A and token B after 90 swaps token A (in) for B (out)?\n",
    "\n",
    "b) How much would Alice have to pay in token A in case she wants to buy the 91st token B? "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "commercial-client",
   "metadata": {},
   "source": [
    "# Q1.5:  \n",
    "Now create a graph (use plotly or similar), and draw the full curve for this series of both kinds of swaps - the AMM curve."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "about-comparison",
   "metadata": {},
   "source": [
    "# Q1.6:\n",
    "Take this plot, and mark \n",
    "- the initial price in Q1.1 (starting price)\n",
    "- the new price in Q1.4 (after 90 swaps)\n",
    "\n",
    "Side note: Why is it actually not appropriate to call this a \"price\". What would be a better name?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fourth-newspaper",
   "metadata": {},
   "source": [
    "# Q1.7:\n",
    "Formulate a \"rule of a thumb\", how do swaps effect the price?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "voluntary-wisdom",
   "metadata": {},
   "source": [
    "## Additional questions:\n",
    "\n",
    "**Q1.8:** Buying A) 99 tokens at once vs. B) buying 99x 1 token\n",
    "Is there a difference in terms of the number of tokens you have to swap in? Is it \"more expensive\" to swap 99 times?\n",
    "**Answer: no, there's no difference - you pay the same amount no matter if you buy 1 at a time or 99 at once. Intuition: you are moving on the SAME curve, no matter if you take a huge leap, or walk in small steps.**\n",
    "\n",
    "**Q1.9:** Swap fees for buying 99 tokens at once vs. buying 99x 1 token\n",
    "Again, does it matter in terms of the total amount of tokens (change in balance+ fees) you have to pay?\n",
    "\n",
    "\n",
    "**Q1.10:** Price changes and position at the curve\n",
    "For a relative change in price, does it matter where we are at the curve? ( @mark richardson | bancor explained it very nicely, you might want to watch the recording again, will share it by tomorrow)\n",
    "\n",
    "**Q1.11:** Price changes, position at the curve and unequal weights\n",
    "What's the effect of weights on this? If weights are not equal, and we want to move prices, does it matter where we are at the curve?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "consecutive-savage",
   "metadata": {},
   "source": [
    "## Solution Q1.9 - by @AngelaKTE (Twitter @akrtws)\n",
    "Swap fees for buying 99 tokens at once vs. buying 99x 1 token Again, does it matter in terms of the total amount of tokens you have to pay/send to the pool?\n",
    "\n",
    "**Answer: Yes, is does matter. With fees, it's more expensive to buy 99 x1 tokens.**"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "relative-legislation",
   "metadata": {},
   "source": [
    "![Bildschirmfoto%202021-06-30%20um%2011.38.52.png](attachment:Bildschirmfoto%202021-06-30%20um%2011.38.52.png)"
   ]
  },
  {
   "attachments": {
    "Bildschirmfoto%202021-06-30%20um%2014.58.01.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "limiting-winner",
   "metadata": {},
   "source": [
    "![Bildschirmfoto%202021-06-30%20um%2014.58.01.png](attachment:Bildschirmfoto%202021-06-30%20um%2014.58.01.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "large-investing",
   "metadata": {},
   "source": [
    "# Now, let's consider weights!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "medical-merit",
   "metadata": {},
   "source": [
    "We continue with the value function V = a^w_a*b^w_b  \n",
    "where  \n",
    "a = balance of token asset A  \n",
    "b = balancer of token asset B  \n",
    "w_a = weight of token asset A  \n",
    "w_b = weight of token asset B  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "premier-denver",
   "metadata": {},
   "source": [
    "# Q2.1:  \n",
    "Write down the value function for the pool in Q1.1!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vanilla-immigration",
   "metadata": {},
   "source": [
    "# Q2.2:\n",
    "Let's got back to your initial balances in Step 1 in the pool:  \n",
    "100 tokens A  \n",
    "100 tokens B  \n",
    "\n",
    "How do you need to change the weights in order to land at a **price of  \n",
    "4 tokens A : 1 token B**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cubic-scanner",
   "metadata": {},
   "source": [
    "Provide the new value function!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compact-dietary",
   "metadata": {},
   "source": [
    "# Q2.3:\n",
    "Create a graph showing the new AMM Curve in Q2.2  \n",
    "Compare to the graph in Q1.4 - how does a change in weights change the graph?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rural-guarantee",
   "metadata": {},
   "source": [
    "# Q2.4:\n",
    "Compare token prices in this pool.  \n",
    "How much would Alice have to pay in case there are only 2 tokens left in the pool  \n",
    "    **a) buy 1.0 token A for token B**  \n",
    "    **b) buy 1.0 token B for token A**   "
   ]
  }
 ],
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