Quantitative Analysis
Quantitative analysis is a branch of financial analysis that focuses on using data and mathematical techniques to inform investment decisions. Harry Markowitz pioneered modern quantitative analysis with his introduction of Modern Portfolio Theory in the early 1950s.
Guide to Quantitative Analysis

Alpha measures how much an investment outperforms or underperforms a benchmark. Beta is a measurement of an investment’s volatility and is one measurement of an investment’s risk.
Learn More: Alpha vs. Beta: What's the Difference? 
Both ratios exist to try and quantify the riskadjusted return of an investment. The primary difference between the two is that the Sharpe Ratio measures an investment’s performance against the riskfree rate of return, the Treynor ratio measures it versus equity markets more broadly.

You calculate the beta of an investment by taking the covariance between the return of a specific investment and broader market return and then dividing that by the variance of broader market returns.

A Sharpe Ratio over 1 indicates that an investment has a higher riskadjusted return than the riskfree rate of return. The higher it is over 1 is how much better a riskadjusted rate of return it has.
Learn More: What Is a Good Sharpe Ratio?

Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model (CAPM) is a mathematical model that seeks to illustrate a very simplified version of the relationship between risk and return on investments. Because of its simplicity, CAPM can’t precisely predict investment returns, but it can provide a good analytical baseline to understand capital markets.

Alpha
Alpha is a term used to refer to how much an investment outperforms the broader market. It is represented by the greek letter of the same name, α, in equations.

Beta
Beta is the term used to refer to the relative volatility of an investment versus that of the market as a whole. This can be used as a tool to measure the riskadjusted return of the investment and is represented by the greek letter of the same name, β, in equations.

Sharpe Ratio
The Sharpe Ratio is a method for measuring the riskadjusted return of an investment. It does this by comparing the investment to the riskfree rate of return over a certain time period.

Modern Portfolio Theory (MPT)
Invented by Harry Markowitz and first published in 1952, MPT is one of the first quantitative analysis frameworks. MPT was made to help an investor choose investments that will match their risk tolerance.

Quantitative Analysis (QA)
Quantitative analysis broadly refers to using mathematical models and measurements to understand various topics. In investing it refers more specifically to a method of investment analysis that focuses on using mathematical and statistical models.

Fama and French Three Factor Model
The Fama and French Three Factor Model, often referred to as just the Fama and French Model, is an expanded version of the CAPM model. Instead of just looking at the systematic risk of a portfolio, it adds size and value premiums as additional variables to the model.

Treynor Ratio
The Treynor Ratio is a method for measuring the riskadjusted return of an investment. It does this by measuring an investment’s risk and return against that of the broader market.