Question

Markowitz theory, CAPM, and Multi-factor models, if you have the option of choosing between two stocks for investing, how would you use AI/ML to decide between the two? Please explain your answer with an example.

Answer 1

1) Markowitz theory that investors could design a portfolio to maximize returns by accepting a quantifiable amount of risk. In other words, investors could reduce risk by diversifying their assets and asset allocation of their investments using a quantitative method.

With a well-balanced and calculated portfolio, if some of the assets fall due to market conditions, others should rise an equal amount in compensation, according to MPT.

Markowitz demonstrated that, by taking a portfolio as its whole, it was less volatile than the total sum of its parts.

To begin with, Markowitz assumed that most investors are, in their hearts, risk-averse. That means they are more personally comfortable with less risk, and nervous and anxious with increased risk. This also translates into the belief that it is better to not lose money than to find or gain it.

So, given a choice between a higher return possibility with greater risk, and a lower return possibility with less risk, most people will naturally prefer the portfolio with the least risk, even if it means a lower return.

2) Capital Asset Pricing Model

The CAPM allows investors to quantify the expected return on an investment given the investment risk, risk-free rate of return, expected market return, and the beta of an asset or portfolio. The risk-free rate of return that is used is typically the federal funds rate or the 10-year government bond yield.

An asset's or portfolio's beta measures the theoretical volatility in relation to the overall market. For example, if a portfolio has a beta of 1.25 in relation to the Standard & Poor's 500 Index (S&P 500), it is theoretically 25 percent more volatile than the S&P 500 Index. Therefore, if the index rises by 10 percent, the portfolio rises by 12.5 percent. If the index falls by 10 percent, the portfolio falls by 12.5 percent.

CAPM Formula

The formula used in CAPM is: E(ri) = rf + βi * (E(rM) - rf), where rf is the risk-free rate of return, βi is the asset's or portfolio's beta in relation to a benchmark index, E(rM) is the expected benchmark index's returns over a specified period, and E(ri) is the theoretical appropriate rate that an asset should return given the inputs.

3)Multi-factor model is a financial model that employs multiple factors in its calculations to explain market phenomena and/or equilibrium asset prices. The multi-factor model can be used to explain either an individual security or a portfolio of securities. It does so by comparing two or more factors to analyze relationships between variables and the resulting performance

And

• Multi-factor portfolios are a financial modeling strategy in which multiple factors, macroeconomic as well as fundamental and statistical, are used to analyze and explain asset prices.
• The portfolios can be constructed using various methods: intersectional, combinational, and sequential modeling.