Done book

reading/001_Quantitative_Trading/README.md

@@ -2,6 +2,10 @@
 
 [pdf](./Quantitative_Trading_Ernest_P_Chan.pdf)
 
-total pages=204
+I will be loosey reading through this book. Many of the concepts will be gone into more rigour in other textbooks.
 
-**Currently reading:** chapter 1, page 117
+## Post read notes
+
+Not alot of math, but math that did show up was hand wavy.(Seems like the book assumes you understand certain concepts)
+
+Main takeaway is use Kelly formula for sizing positions.

reading/001_Quantitative_Trading/notes.ipynb

@@ -13,7 +13,10 @@
    "id": "b13688b9",
    "metadata": {},
    "source": [
-    "## Main Takeaways"
+    "When loss of money occurs, rationality is often the first victim.\n",
+    "\n",
+    "As long as financial markets demand instant liquidity, however, there will always be a profitable\n",
+    "niche for quantitative trading."
    ]
   },
   {
@@ -47,6 +50,18 @@
     "## Definitions"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "8ec7516e",
+   "metadata": {},
+   "source": [
+    "**Defn** Information Ratio (Sharpe ratio):\n",
+    "\n",
+    "$$\\text{Information Ratio} = \\frac{\\text{Average of Excess Returns}}{\\text{Standard Deviation of Excess Returns}}$$\n",
+    "\n",
+    "$$\\text{Excess Returns} = \\text{Portfolio Returns} - \\text{Benchmark Returns}$$"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "7aab1f0d",
@@ -60,18 +75,6 @@
     "- ***slippage*** - The difference between the price that triggers the trading signal and the average execution price of the entire order"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "8ec7516e",
-   "metadata": {},
-   "source": [
-    "**Defn** Information Ratio (Sharpe ratio):\n",
-    "\n",
-    "$$\\text{Information Ratio} = \\frac{\\text{Average of Excess Returns}}{\\text{Standard Deviation of Excess Returns}}$$\n",
-    "\n",
-    "$$\\text{Excess Returns} = \\text{Portfolio Returns} - \\text{Benchmark Returns}$$"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "865b04b1",
@@ -86,6 +89,14 @@
     "- ***regime shift*** - Situation when the financial market structure or the macroeconomic environment undergoes a drastic change so much so that trading strategies that were profitable before may not be profitable now"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "076ad86c",
+   "metadata": {},
+   "source": [
+    "- ***Risk-Adjusted returns*** - "
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "a845580c",
@@ -163,7 +174,9 @@
     "- Liquidity cost\n",
     "- Opportunity cost\n",
     "- Market Impact\n",
-    "- Slippage"
+    "- Slippage\n",
+    "\n",
+    "Try to combine all of these into a \"one way transaction cost\" (onewaytcost)"
    ]
   },
   {
@@ -214,6 +227,227 @@
    "source": [
     "## Money and Risk Management"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "41ddff80",
+   "metadata": {},
+   "source": [
+    "### The Kelly Formula"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "169dc996",
+   "metadata": {},
+   "source": [
+    "Let $F^*$ be the optimal fractions of your equity that you should allocate to each of your $n$ strategies by a column vector $F^* = (f_1^*, f_2^*, \\dots, f_n^*)^T$\n",
+    "\n",
+    "Let $C$ be the covariance matrix such that matrix element $C_{ij}$ is the covariance of the returns of the $i^\\text{th}$ and $j^\\text{th}$ strategies.\n",
+    "\n",
+    "Let $M = (m_1, m_2, \\dots, m_n)^T$ be the column vector of mean returns of the strategies, where $m_i$ is a one-period, simple(uncompounded), unlevered return.\n",
+    "\n",
+    "Given our optimization objective and the Gaussian assumption, Dr. Thorp has shown that the optimal allocation is given by\n",
+    "\n",
+    "$$F^* = C^{-1}M$$\n",
+    "\n",
+    "If we assume that the strategies are all statistically independent, the covariance matrix becomes a diagonal matrix, with the diagonal elements equal to the variance of the individual strategies. This leads to an especially simple formula\n",
+    "\n",
+    "$$f_i = \\frac{m_i}{s_i^2}$$\n",
+    "\n",
+    "This is the famous Kelly formula as applied to continuous finance as opposed to gambling with discrete outcomes, and it gives the optimal leverage one should employ for a particular trading strategy.\n",
+    "\n",
+    "As a practical procedure, this continuous updating of the capital allocation should occur at least once at the end of each trading\n",
+    "day. In addition to updating the capital allocation, one should also\n",
+    "periodically update F* itself by recalculating the most recent trailing mean return and standard deviation. What should the lookback\n",
+    "period be and how often do you need to update these inputs to the\n",
+    "Kelly formula? These depend on the average holding period of your\n",
+    "strategy. If you hold your positions for only one day or so, then as a\n",
+    "rule of thumb, I would advise using a lookback period of six months.\n",
+    "Using a relatively short lookback period has the advantage of allowing you to gradually reduce your exposure to strategies that have\n",
+    "been losing their performance. As for the frequency of update, it\n",
+    "should not be a burden to update F* daily once you have written a\n",
+    "program to do so."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "270f0944",
+   "metadata": {},
+   "source": [
+    "Model risk simply refers to the possibility that trading losses are\n",
+    "not due to the statistical vagaries of the market, but to the fact that\n",
+    "the trading model is wrong\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b6709290",
+   "metadata": {},
+   "source": [
+    "the one golden rule in risk management is to keep the size of your portfolio under control at all times\n",
+    "\n",
+    "Do not succumb to either despair or greed"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a6edc9d9",
+   "metadata": {},
+   "source": [
+    "# Mean-reverting versus Momentum strategies"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "63f1028e",
+   "metadata": {},
+   "source": [
+    "Security prices are either mean reverting or trending. Otherwise they are random walking and trading will be futile. \n",
+    "\n",
+    "- ***Mean reverting***: Prices tend to return to an average (mean) over time\n",
+    "- ***Trending***: Prices move persistently in one direction. Momentum builds and continues.\n",
+    "\n",
+    "Sometimes (usually) a security is both mean reverting and trending."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "084a3a0b",
+   "metadata": {},
+   "source": [
+    "## Stationarity and Cointegration\n",
+    "\n",
+    "- ***cointegrated***: Most stock price series are not stationary—they exhibit a geometric random walk that gets them farther and farther away from their starting (i.e., initial public offering) values. However, you can often find a pair of stocks such that if you long one and short the other, the market value of the pair is stationary, then the pair of stocks are cointegrated\n",
+    "\n",
+    "If a price series (of a stock, a pair of stocks, or, in general, a portfolio of stocks) is stationary, then a mean-reverting strategy is guaranteed to be profitable, as long as the stationarity persists into the future (which is by no means guaranteed)\n",
+    "\n",
+    "**Cointegration Is Not Correlation**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a60d882c",
+   "metadata": {},
+   "source": [
+    "## Factor Models"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2d21e3c0",
+   "metadata": {},
+   "source": [
+    "- ***Factor returns***: The common drivers of stock returns\n",
+    "- ***Factor exposures***: The sensitivities to each of these common drivers\n",
+    "- ***Specific return***: Any part of a stock’s return that cannot be explained by these common factor returns is deemed a specific return\n",
+    "\n",
+    "Each stock’s specific return is assumed to be uncorrelated to another stock’s."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e48e218",
+   "metadata": {},
+   "source": [
+    "## Exit Strategy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e61edcb1",
+   "metadata": {},
+   "source": [
+    "- A fixed holding period\n",
+    "- A target price or profit cap\n",
+    "- The latest entry signals\n",
+    "- A stop price\n",
+    "\n",
+    "The mean reversion of a time series can be modeled by an equation called the Ornstein-Uhlenbeck formula. See page 163 for more info.\n",
+    "\n",
+    "The properties of the Ornstein-Uhlenbeck formula can inform us about the exit strategies.\n",
+    "\n",
+    "If you believe that your security is mean reverting, then you also have a ready-made target price—the mean value of the historical prices of the security, or µ in the Ornstein-Uhlenbeck formula.\n",
+    "\n",
+    "Target prices can also be used in the case of momentum models if you have a fundamental valuation model of a company. But as fundamental valuation is at best an inexact science, target prices are not as easily justified in momentum models as in mean-reverting models.\n",
+    "\n",
+    "Exiting a position based on running an entry model also tells us whether a stop-loss strategy is recommended"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eb884fe5",
+   "metadata": {},
+   "source": [
+    "## High Frequency Trading Strategies"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22ad0ba8",
+   "metadata": {},
+   "source": [
+    "Requires low level programming and alot of reasources to consider viable"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9c8eeee5",
+   "metadata": {},
+   "source": [
+    "## Other topics / notes\n",
+    "\n",
+    "- Markov regime switching / hidden Markov models\n",
+    "- Kalman filter\n",
+    "- neural networks\n",
+    "\n",
+    "Empirical studies have found that a portfolio that consists of low-beta stocks generally has lower risk and thus a higher Sharpe ratio"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bdd23956",
+   "metadata": {},
+   "source": [
+    "- Mean-reverting regimes are more prevalent than trending regimes.\n",
+    "- There are some tricky data issues involved with backtesting mean-reversion strategies: Outlier quotes and survivorship bias are among them.\n",
+    "- Trending regimes are usually triggered by the diffusion of new\n",
+    "information, the execution of a large institutional order, or\n",
+    "“herding” behavior.\n",
+    "- Competition between traders tends to reduce the number of\n",
+    "mean-reverting trading opportunities.\n",
+    "- Competition between traders tends to reduce the optimal holding period of a momentum trade.\n",
+    "- Regime switching can sometimes be detected using a dataminingx approach with numerous input features.\n",
+    "- A stationary price series is ideal for a mean-reversion trade.\n",
+    "- Two or more nonstationary price series can be combined to form a stationary one if they are “cointegrating.”\n",
+    "- Cointegration and correlation are different things: Cointegration\n",
+    "is about the long-term behavior of the prices of two or more\n",
+    "stocks, while correlation is about the short-term behavior of\n",
+    "their returns.\n",
+    "- Factor models, or arbitrage pricing theory, are commonly used\n",
+    "for modeling how fundamental factors affect stock returns linearly.\n",
+    "- One of the most well-known factor models is the Fama-French\n",
+    "Three-Factor model, which postulates that stock returns are\n",
+    "proportional to their beta and book-to-price ratio, and negatively\n",
+    "to their market capitalizations.\n",
+    "- Factor models typically have a relatively long holding period and\n",
+    "long drawdowns due to regime switches.\n",
+    "- Exit signals should be created differently for mean-reversion versus momentum strategies.\n",
+    "- Estimation of the optimal holding period of a mean-reverting strategy can be quite robust, due to the Ornstein-Uhlenbeck formula.\n",
+    "- Estimation of the optimal holding period of a momentum strategy can be error prone due to the small number of signals.\n",
+    "- Stop loss can be suitable for momentum strategies but not reversal strategies.\n",
+    "- Seasonal trading strategies for stocks (i.e., calendar effect) have\n",
+    "become unprofitable in recent years.\n",
+    "- Seasonal trading strategies for commodity futures continue to\n",
+    "be profitable.\n",
+    "- High-frequency trading strategies rely on the “law of large numbers” for their high Sharpe ratios.\n",
+    "- High-frequency trading strategies typically generate the highest\n",
+    "long-term compounded growth due to their high Sharpe ratios.\n",
+    "- High-frequency trading strategies are very difficult to backtest\n",
+    "and very technology reliant for their execution.\n",
+    "- Holding a highly leveraged portfolio of low-beta stocks should\n",
+    "generate higher long-term compounded growth than holding unleveraged portfolio of high-beta stocks."
+   ]
   }
  ],
  "metadata": {