Analysis of the Stock Market Using Quantitative Approach Finance Essay

Quantitative finance started in the U.S. in the 1930s as some astute investors began using mathematical formulas to price stocks and bonds. Harry Markowitz's 1952 Ph.D. thesis "Portfolio Selection" was one of the first papers to formally adapt mathematical concepts to finance. Markowitz formalized a notion of mean return and covariances for common stocks which allowed him to quantify the concept of "diversification" in a market. He showed how to compute the mean return and variance for a given portfolio and argued that investors should hold only those portfolios whose variance is minimal among all portfolios with a given mean return. Although the language of finance now involves Ito calculus, minimization of risk in a quantifiable manner underlies much of the modern theory. In 1969 Robert Merton introduced stochastic calculus into the study of finance. Merton was motivated by the desire to understand how prices are set in financial markets, which is the classical economics question of "equilibrium," and in later papers he used the machinery of stochastic calculus to begin investigation of this issue. At the same time as Merton's work and with Merton's assistance, Fischer Black and Myron Scholes were developing their option pricing formula, which led to winning the 1997 Nobel Prize in Economics. It provided a solution for a practical problem, that of finding a fair price for a European call option, i.e., the right to buy one share of a given stock at a specified price and time. Such options are frequently purchased by investors as a risk-hedging device. In 1981, Harrison and Pliska used the general theory of continuous-time stochastic processes to put the Black-Scholes option pricing formula on a solid theoretical basis, and as a result, showed how to price numerous other "derivative" securities.

2.0 Fundamentals of Quantitative Analysis

Definition: Quantitative analysis is a process of disseminating financial data in order to make valid projections regarding the future performance of a corporation or market. Quantitative analysis of stocks is done purely based on numbers. In this type of analysis, the price trend of the stock is analyzed based on historical data using complex mathematical calculations and statistical modeling techniques. Quantitative Analyst: A quantitative analyst is a person who works in the financial markets developing and implementing mathematical models to assist the activities of traders and risk managers within investment banks, hedge funds and other financial institutions. Throughout the industry, such professionals are known as quants. Although the original "quants" were concerned with risk management and derivatives pricing, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance. An example is statistical arbitrage.

Differentiated Features: The quantitative analysis of stock is very different from fundamental analysis of stocks. Fundamental analysis considers the business, growth prospects and effectiveness of management to determine the value of the stock while quantitative analysis discounts all these factors. The analyst who believes in this technique think that all the above mentioned factors are very subjective and do not portray the exact picture since everyone can interpret these numbers in a different manner. The analysts who believe in quantitative analysis of stocks do not take into consideration the effectiveness of management, business or economy while doing this analysis. Quantitative analysis may also involve such characteristics as company liabilities, sales figures, trading trends, and alike. Unlike qualitative analysis, which may consider more uncertain factors like the quality of management, branding, and intrinsic value, quantitative analysis looks only at measurable facets. Thus, technical analysis, which employs mathematical models, would be considered part of quantitative analysis. A person who performs quantitative analysis is referred to as hybrid stock analyzed. This is because, he/she is characterized by the attributes of both fundamental and technical analyzed. Purpose: The purpose of quantitative analysis is to employ quantifiable attributes of a particular company in order to determine its security's or market's value. To do so, quantitative analysis practitioners gather and analyze data such as income statements, company assets, market share, and earnings records.

3.0 Techniques Used in Quantitative Analysis

Quantitative analysis in general is simply a way of measuring things. In quantitative analysis of stock, the behavior of a stock is analyzed using complex mathematical and statistical modeling equations. For analysts who specialize in quantitative analysis of a stock, the business or the management mean nothing to them. There is no regard for underlying business at all. All they look for are the numbers. For quantitative analysis, the number crunching is done through advanced computers now days. These people who do this are also called as quants. These quants will do analysis based on complex formula and will decide on sell versus buy option purely based on these equations and numbers. Some of the major considerations while doing quantitative analysis of stock are: Company size - First thing which the investors look at is the size of the company. This is usually done in term of capitalization or 'cap' in short. Broadly, the companies are divided into various caps depending upon their market. These are micro cap, small cap, mid cap and large cap. Smaller the cap, riskier is the company since it can go bankrupt very easily. But smaller companies have the chances to grow radically as well. Broadly, the guidelines of distinguishing these caps are:

Large cap - Tk. 1000 million or more.

Mid cap - Tk. 500 million to Tk. 1000 million.

Small cap -Tk. 250 million to Tk. 500 million.

Micro cap - Tk. 250 million or less.

4.0 Modus Operandi of Quantitative Analysis

4.1 Quantitative analysis with respect to trading equities generally includes the following research topics: Annual Reports Financial Statements (Earnings, Revenues, Etc.) Publicly Available Data General Economic Data General Econometric Data 4.2 Quantitative analysis with respect to funds involves evaluating statistical analysis of the trading manager's track record. These include:

A. Return Analysis

Compounded average rate of return Percentage of positive months Consistency Length of Track Record

B. Risk Analysis

Volatility Measures

Standard Deviation Monthly Standard Deviation Annual Standard Deviation Combined upside and downside standard deviation Downside Deviation only Sortino Ratio

Drawdowns

Maximum Drawdown Depth of Drawdowns Frequency of Drawdowns Time in any given Drawdown Recovery from a Drawdown

Reward to Risk

Average Return Divided by Maximum Drawdown (Total Return Minus Risk Free Rate of Return)/(The Total of All Drawdowns) (Average Return)/(Maximum Drawdown) Sharpe Ratio: (Average Rate of Return Minus Risk Free Rate of Return)/(Annual Standard Deviation) Treynor Ratio: : (Average Rate of Return Minus Risk Free Rate of Return)/(Degree of systematic Risk-AŽA²)

Reward to Assets Under Management

Evaluating all of the above measures as a manager increases assets under management The average rate of return since the manager first had 50% of their current assets under management.

5.0 Qualitative Analysis of Stock as Input to Quantitative Analysis of

Stock

Subjective, non-statistical oriented analysis - generally comes before Quantitative Analysis. Qualitative research is one of the two major approaches to research methodology in social sciences. Qualitative research involves an in-depth understanding of human behavior and the reasons that govern human behavior. Unlike quantitative research, qualitative research relies on reasons behind various aspects of behavior. Simply put, it investigates the why and how of decision making, as compared to what, where, and when of quantitative research. Hence, the need is for smaller but focused samples rather than large random samples, which qualitative research categorizes data into patterns as the primary basis for organizing and reporting results. Unlike quantitative research, which relies exclusively on the analysis of numerical or quantifiable data, data for qualitative research comes in many mediums, including text, sound, still images, and moving images. This sort of analysis is the most important for the following reasons: Stock market is in transition from poor form of efficient market to semi-strong form of efficient market; Most of the investors have inadequate knowledge of stock market; Most of the investors take investment decision on the basis of information being aired over the sky of the stock market without judgement; Most of the investors are willing to make capital gain; Most of the investors, especially small investors are vulnerable to stock market gambling/crisis originated from any source.

Non-statistical Qualitative analysis generally explores the following:

Sustainable competitive advantage Quality & Experience of Management Employee Morale & Loyalty Industry Competitors Strength of Research & Development Cyclicality of the Industry Actions towards Investors' interests Ability to achieve economies of scale General labor relations Quality and Positioning of Products Quality and Positioning of Services

6.0 Quantitative Analysis-Selection of Security to Buy or Sell

An investor or Fund Manager can create "An Equity Desk"- a set of some stocks which has the potential to grow at a good pace over a period of time. This analysis is an attempt to rank the selected stocks and help an investor decide which among the lot is the best and the worst stock to invest at the current market prices. Basically, this is a quantitative analysis of a set of stocks, based purely on their fundamentals. The 'TED' methodology can be used on any portfolio to determine the best and the worst. The study has taken 11 blue chip stocks for analysis as follows:

All the 11 stocks will be analyzed based on -

P/E Ratio Return on Equity Last 4 years CAGR Sales Growth Last 4 Years CAGR Profit Growth Market Cap P/BV Ratio Debt to Equity Ratio Dividend Yield Last 4 Years CAGR dividend per share growth Dividend Payout Ratio Basically, we will be looking at parameters typically used by both "growth" and "value" investors.

Ranking Methodology:

All the 11 stocks are ranked based on each parameter - say P/E Ratio to begin with. A stock with the lowest P/E Ratio gets the highest 11 points, while a stock with the highest P/E Ratio gets the lowest 1 point. Similarly, for other parameters like ROE, market-cap etc, each stock is awarded between 1 point and 11 points depending on where it stands compared to each other. The scores are added at the end, and the stocks are ranked from 1 to 11.

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