Abstract

In the book “The Man Who Solved the Market”, the author quotes Renaissance’s co-CEO Robert Mercer saying to a friend – “We’re right 50.75 percent of the time…but we are 100 percent right 50.75 percent of time…You can make billions that way”. This paper intends to provide a similar indicator or system, which is right a bit more than half the time. Drawing inspiration from physics, the paper investigates the applicability of basic principles of physics to arrive at a price prediction system (or indicator) for stocks. The system hence derived, named as “Tyche System”, shows strong performance during back-testing. The current paper also demonstrates the usage of Tyche system for – a) Market technicians who would like to get a heads-up about an impending technical event in a stock without scanning through the charts of thousands of stocks; and b) Hedge Funds, who would like to use their long-only portfolio for additional leverage to generate higher and un-correlated returns using the Tyche system.

Keywords: Physics, Newton’s Law, Hooke’s Law, Price Prediction, Stocks, market timing, un- correlated, Nifty, back tests, Hedge Funds.

Introduction

Capital markets play a vital role in economic growth as they provide funding access to companies in the primary market (issuance of new bonds or shares). To arrive at the funding cost for a company, price discovery becomes an important aspect and market participants often rely upon business fundamentals like earnings growth, and outlook to value a company. However, post primary issuance, secondary market trading of stocks is influenced by multiple factors like liquidity, size, earnings report, news flow, daily volatility, positioning and speculation by market participants etc.

While efficient market hypothesis states that asset prices reflect all available information (Fama, 1970), there is varying acceptance of the hypothesis and market participants have often relied upon fundamental / technical analysis for long-term investments / speculation, respectively. Technical analysis is viewed as an art or science of planting the stock information like price movements, trading volume and market scenario in the form of charts for the purpose of forecasting the future price trends. Increasingly, to improve trading edge, market participants are trying to create technical indicators based on simple physical systems. One such example is Elder Force (FI) which is calculated by multiplying the difference between the last and previous closing prices by the volume of the underlying, indicating a momentum shift towards strong buying or selling.

At the same time, some researchers are also studying stock market’s physical properties description based on Stokes’ law17, which is part of fluid mechanics and is a complex system. While physicist Jim Simons’ Medallion fund had posted c.39% CAGR returns (after fees) during 1988-2018 racing past peers18, large part of investment community still struggles to grapple with physics in finance. As a result, some of the existing technical indicators which are based on physical systems are yet to demonstrate if their unit (read unit of measurement) has any dimensional similarity with Physics and if they can be right more than half the time? With this backdrop, we start the next section with the building blocks of Tyche System.

Brief overview from Physics: Dimensional analysis & Newton’s law

Dimensional analysis offers a method for reducing complex physical problems to the simplest (that is, most economical) form prior to obtaining a quantitative answer. In physics there are five fundamental dimensions in terms of which the dimensions of all other physical quantities may be expressed. They are mass [M], length [L], time [T], temperature [θ], and charge. The accepted units are, respectively, the kilogram, the meter, the second, and the Kelvin or degree Celsius. These fundamental dimensions are essential to understand principles of physics including Newton’s Laws of Motion.

Newton’s first law (law of inertia) states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.

Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. If a body has a net force acting on it (in a direction – represented by vector in the equation), it is accelerated in accordance with the equation (in the direction of application of force). Conversely, if a body is not accelerated, there is no net force acting on it.

Mass (m – assuming constant) has a dimensional unit of [M1]

Distance (x) has a dimensional unit of [L1]

Velocity has a dimensional unit of [L1 T-1]

Acceleration is the rate of change of the velocity of an object with respect to time, its dimensional unit is [L1 T-2] and has a vector (or direction of acceleration).

While the unit of Force is Newton, dimensional analysis helps in breaking down Newton into fundamental dimensions:

Further, any equation in Physics is only valid if the dimension on the LHS (Left Hand Side) and RHS (Right Hand Side) of the equation are similar. Let us see this with an example of the first equation of motion:

The first equation of motion gives the relation between Velocity and Time

Here, v is the final velocity, u is the initial velocity, a is the acceleration and t is the time.

Dimensional analysis of LHS and RHS of equation 3:

Multiplication of dimensions leads to sum of the powers

Only physical quantities of the same nature having the same dimensions can be added

Defining the dimensions for stocks

Before we can talk about applying principles of classic mechanics in stock price prediction, we need to define what is stock market equivalent of [M], [L] and [T].

For a particular stock, at a particular time [T], we get the following two major data points – a) Price and b) Volume. Yes, traders and investors can argue that one can get variation of prices (close, high, low, avg. etc) and volumes (open interest, one day volume, 1 month volume, 30-day average etc.). However, intrinsically, it is Price [P], Volume [V] and Time [T] that are the defining variable of a stock.

What is Mass for a stock?

In physics, mass is a quantitative measure of inertia, it is the resistance that a body of matter offers to a change in its speed or position upon the application of force. When we talk about mass of a stock, market cap might be the first thought in a person’s mind. However, like physics, in stock market, mass of a stock can be viewed as that property of a stock that makes it difficult to change its price.

And it would be wrong to assume that market cap resists price movement because – a) not all outstanding shares are traded in a day, b) not all free float of a stock is traded in a day and, c) big market cap stocks can also easily demonstrate price high volatility at times.

Then what is mass for a stock? To answer this let us find out what are the properties of a stock that resist change in its price –

Daily traded volume of a stock – If daily average traded volume of a stock is 100,000 shares, then it would be very difficult to change the daily price of a share only by 1,000 shares etc.

Assuming daily traded volume of stock to be constant, what is the other factor that can resist price change of the stock? If a stock was trading at $20, 5 years ago, and is now trading at $25, then it would be more difficult to move the price of the stock now vs. 5 years ago as the investors will have to shell-out additional $5 to participate in the market. It also works the other-way round, if the stock is currently trading at $15 vs. $20 (5 years ago), it is easier to move the price of the stock as the investors will have to shell-out $5 less to participate in the market. So, price of a stock is also a property that resists further change in price of itself.

Since, we are using minimum unit of T = 1 day, we can define mass of a stock as daily turnover (i.e., average traded price * traded quantity in one day). As a result, dimensions of stock mass using Price [P], Volume [V] and Time [T] is:

Where 𝐶𝐶𝑡𝑡 is the mass of a stock at the end of day t, 𝑝𝑝(𝑎𝑎𝑣𝑣𝑎𝑎)𝑡𝑡is the average traded price of the stock on day t and 𝑣𝑣𝑡𝑡is the traded volume on day t.

What is velocity and acceleration for a stock? In physics, velocity of an object is the rate of change of its position with respect to a frame of reference and is a function of time. Similarly, velocity of a stock can be viewed as rate of change of its price.

In Physics, acceleration is the rate of change of the velocity of an object with respect to time. Similarly, acceleration of a stock can be viewed as rate of change of its velocity.

Applying Newton’s second law of motion in stocks

Using equation 1 and 2 to find out the dimension of Force in the stock market.

Using equation 7 and 9:

Since multiplication of dimensions leads to sum of the powers:

The RHS of Force on a stock in calculus format (using equation 7 and 9):

Since we are focusing on predicting one day price movement of a stock, we can calculate the acceleration in equation 13 as rate of change of velocity:

As a result, after using equation 13 and 14, we will have the value of force on the stock at the end of day t.

Applying Hooke’s Law to determine the likely price of the stock on t+1

Market participants have often talked about stock prices behaving as spring and oscillating at a particular vibration. As per William Gann – “Through the Law of Vibration every stock in the market moves in its own distinctive sphere of activities, as to intensity, volume and direction; all the essential qualities of its evolution are characterized in its own rate of vibration. To speculate scientifically it is absolutely necessary to follow natural law”.

Further, as per Hooke's Law the force needed to extend or compress a spring by some distance is proportional to that distance. The same is expressed mathematically as:

Where F is the force applied on the spring and ∆𝑀𝑀 is the displacement of the spring. And the negative sign indicating the displacement of the spring once it is stretched (k is spring constant).

We already have the value of Force from equation 13 and assuming that the force remains constant during t+1, we can find the likely change in price (∆𝑀𝑀 = 𝑝𝑝𝑡𝑡+1 − 𝑝𝑝𝑡𝑡) of the stock using equation 15. Further, the only other calculus variation that would lead to same dimension of force is:

Where, can be defined as (since we are focusing on one day movement):

As a result, we can use equation 13,14, 16 and 17 to find 𝑝𝑝𝑡𝑡+1:

As a result, with the help of Equation 19, we can try to predict share price of a stock (for the next day) with a reasonable degree of accuracy. However, it is quite possible that the value of force during t+1 can be materially different than that derived from equation 13. As a result, one should use the current system to build position in a stock towards market close (i.e., t) only if the predicted price for tomorrow (i.e., t+1) is with 1SD range of today’s price movement. However, if an investor deploys strong computation power during market hours, she might be able to dynamically find force (choice of her time frame) as per equation 13 and predict stock price within 1 unit of chosen time frame.

Back-testing of Tyche System

As part of back testing, Tyche was run on historical data spanning 1Apr’05 to 19Mar’21, across 50 stocks which are currently part of Nifty 50 Index (India). Result of Tyche back testing can be seen in Table 1. It is worth noting that Tyche was able to achieve 53% hit rate i.e., 53 out of 100 share price predictions made on “t” was achieved during “t+1”. The hit rate is favourable and should improve further, as and when Tyche is deployed for computations during market hours (then t will not be 1 day but can even be hours, minutes etc.). It is also important to note that on an average, Tyche generated only 166 trades per stock during the test period of 1Apr’05-19Mar’21.

Back testing conditions of Tyche for individual stocks:

• Tyche has the flexibility to go both long and short individual stocks.
• Tyche only looks for prediction of price movement greater than or equal to 1% or less than or equal to negative 1%.
• If the stock opens in the opposite direction vs. the predicted direction, there is no provision for Stoploss and Tyche takes loss on a closing basis
• If stock’s low during the day is above the predicted price (in case prediction was on the upside), Tyche does not book profit. Profit booking happens on a closing basis. Same is the case when Tyche predicted a decline and the high of the next day is lower than the predicted price, profit booking happens on a closing basis.

Table 1 Back testing result for Nifty 50 stocks (India) – Between 1Apr’05 to 19Mar’21

Tyche performance vs. Long-only stock portfolio

In the back testing period, the long only equal weighted stock portfolio (stocks from table 1) generated a 24% return CAGR with a maximum drawdown of 13.1% on 23Mar’20. In the back testing, 100% capital deployment happened in long only equal weighted stock portfolio. On the other hand, Tyche generated 15.9% return CAGR with money deployed in the market only for 75% of the test duration. Also, the maximum drawdown faced by Tyche was 8.4% on 16Nov’07. Unlike long-only stock portfolio which declined c.35% between last week of Feb’20 and last week of Mar’20, Tyche posted a gain of c.27% (Figure 3). Also, during Global Financial Crisis (from Sep’07 to Mar’09), long-only stock portfolio declined c.35%. However, Tyche posted a gain of c.122% in the same period (Figure 2).

It is important to note that Tyche has benefits of choosing from a vast pool of stocks (can be beyond the 50 stocks used in back testing) and this 15.9% return CAGR is after Tyche switched between Longs / Shorts and gyrated between various stocks (albeit on an equal weighted basis). However, it is important to note that as per Pareto chart (Figure 4), 80% of the time Tyche had less than equal to 3 holding (long / short) and yet generated 15.9% CAGR returns. As a result, Tyche is a good alert system for market technicians who would like to get a heads-up about an impending technical event in a stock without scanning through the charts of thousands of stocks.

How can Tyche assist long-only portfolio?

While Tyche can be a standalone system, but it would be wise to use Tyche along with long-only investment portfolio. Hedge Funds usually enjoy a strong relation with their prime brokers. This allows Hedge Funds to get cheap stock financing. Even if one assumes that the haircut on financing is 50% and the same is deployed in Tyche, return CAGR improves from 24% to 33.8% (excluding financing cost). At the same time, maximum drawdown on a day reduces from 13.1% earlier to 10.3%.

Table 2 Comparison between Long-only portfolio, Tyche and Long-only+ Tyche (at 50% haircut)

Figure 1 Portfolio value of Long only basket, Tyche System and Long only + Tyche System / portfolio (base of 100 as on 1Apr’05).

Figure 2 Tyche System / portfolio providing strong support to overall portfolio during the Global Financial Crisis (base of 100 as on 1Apr’05).

Figure 3 Tyche System / portfolio providing strong support to overall portfolio during Covid-19 market crash (base of 100 as on 1Apr’05).

Figure 4 Pareto Chart of Tyche: 80% of the time Tyche had less than equal to 3 holding (long / short) and yet generated 15.9% CAGR returns

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