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Search for the Holy Grail 尋找必勝之道. Lecture 3 April, 2014. Science as an investment tool. Pythagoras Theorum.
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Search for the Holy Grail尋找必勝之道 Lecture 3 April, 2014
Pythagoras Theorum In mathematics, the Pythagorean theorem—or Pythagoras' theorem—is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation: C2 = A2 + B2
Dodecahedron • 十二面體
In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα, dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces, but usually a regular dodecahedron is meant: a Platonic solid. It is composed of 12 regular pentagonal faces, with three meeting at each vertex, and is represented by the Schläfli symbol {5,3}. It has 20 vertices, 30 edges and 160 diagonals. Its dual polyhedron is the icosahedron, with Schläfli symbol {3,5}.
Isaac Newton Law of Universal Gravitation • Explains why earth revolves around the sun
Einstein as an investment tool Einstein & Relativity
Special Relativity • 1905 • Speed of light = Distance/Time • E = MC2 • When the speed of light is constant, then time is relative.
General Relativity 1916 • Why the universe exists like now, • Stars and galaxies • Gravity and Light • Black hole • G = 8 T
Blair Hull • Math genius, who developed successful principles to win at Black Jack • Three factor model to analyze stocks • Which became the model for computerized stock trading • Goldman Sachs bought Hull’s company for US$500 million in 1999 • People and machines – key to success
Goldman Sachs • Alynikov stole source code for program trading in 2009 • Sentenced to 8 years in prison in 2010 • Now released on bail on appeal • Awaiting new trial
Black Scholes • Black-Scholes/ Black-Scholes-Merton: Mathematical model of financial market • Contains derivative investment instruments • Black-Scholes Formula: theoretical estimate prices of European style options • Derived stochastic partial differential equation- Black-Scholes equation • Governs price of option
Main idea of derivation was to protect option by buying and selling • No arbitrage opportunity (no riskless profits) • Borrow and lending cash with risk-free interest rate • Ability to buy and sell any amount, or partial, of stock • Do not require fees/costs • Dividend is not paid by underlying security • Stock price is followed by geometric Brownian motion
Values for a call price c or put price p are: Where: Here, log denotes the natural logarithm, and: s = the price of the underlying stock x = the strike price r = the continuously compounded risk free interest rate t = the time in years until the expiration of the option σ = the implied volatility for the underlying stock Φ = the standard normal cumulative distribution function.
Variables • Δ delta measures the change in price of option when underlying stock changes • Γ gamma measures the sensitivity of delta • Νvega measures the volatility of option • Θ theta measures the time valueρ rho measures change in interest rate
Program trading 程式買盤 • Black Scholes option model • Blair Hull Model • Algorithm trading
High frequency trading Use the quickest computer to get the best possible prices Use Algorithm to detect the best trading strategy Use inside information to beat the market On 18.9.2013, Bernanke surprised the market by announcing delaying tapering at 2 pm. Traders in Chicago got the news one millisecond ahead of everybody else. Use the time to buy substantial amounts of gold future and made a killing. They used military laser which allows them to input orders a millisecond faster than their competitors. Fiber optic is not fast enough, where every millisecond counts. Reuters paid University of Michigan to get information on consumer sentiment 20 minutes ahead of announcement and sell the information to high paying customers.
Strategies • 1. Detect price differences in different exchanges • 2. Phantom trade: inputting large orders, creating a false market; orders will disappear when others want to buy • 3. Front running: Detecting large orders and then front run your orders to lock in minute profit, which accumulates.
Artificial intelligence • Futurists predict that in ten years, many human tasks will be done by DROIDS. • In 50 years, machines can think and replace human beings. • In securities trading, machine has already replaced human beings.
Loneliness of a stock broker • Machine replacing human
