Arbitrage Pricing Model Case Study

Introduction

In financial markets, we often hear the target price, outperform the market, and underperform the market. DO you know how to calculate the target price? We should not just estimate, the target price can also be calculated.

This paper will introduce 3 models, it is the Capital Asset Pricing Model (CAPM), Arbitrage pricing theory (APT) and Three Factor Model, and discuss the usefulness and the problems. Here is the history of CAPM and APT.

The Capital Asset Pricing Model (CAPM), it was developed by four economists - John Lintner (1965a, b), Jan Mossin (1966), William Sharpe (1964), and Jack Treynor (1962), William Sharpe also received the 1990 Nobel Prize in the economic science for this work and make the financial economy has a

It expands portfolio theory and helps us to calculate the unexpected risk of asset. As long as we know the risk-adjusted expected return of the asset, we can assess the asset's price as correct. Although CAPM allows us to determine the rate of return required for any risky asset to determine its price, but CAPM is actually used primarily to evaluate common stock.

Use the CAPM it may requires some assumptions, including the following:

There is risk-free asset so that investors can lend or borrow at a risk-free rate of return. Investors agree on the expected rate of return and probability of these returns. Investors attempt to construct efficiency frontier portfolios. Market are I equilibrium and price are efficient. Investors plan for one identical holding period. Investors do not pay tax or transaction costs to trade. Investors have homogeneous expectations regarding the probability distribution of risk and return of the available securities.

Risk-Free Rate

And the risk-free rate assumptions are important to CAPM. The risk-free assets must: The rate of return has not changed and zero variance. The rates of return have zero correlation with all other risky

Markowitz uses variability of expected returns as a reasonable measure for risk. This is called the variance, which can be calculated by a formula.

“The variance often turns out to be a large number but can be rationalized to a simpler version to work with by taking the square root of the variance. The result is the standard deviation.”

Standard Deviation of a Portfolio

The standard deviation of the portfolio is a linear proportion of the risk of the risk-free and risky assets. Because of the zero variance and zero correlation characteristics of the risk-free asset, the risk of a portfolio which includes a risk-free and risky asset will only be a linear proportion of the standard deviation of the risky asset portfolio. Capital Market Line

The concave curve is the efficient frontier. The figure above illustrates the impact of introducing risk-free assets on the capital markets. The risk-free asset creates new possibilities in forming a new risk-return tradeoff. By combining the risk-free asset with a portfolio of risk assets (i.e. any point on the efficient frontier), portfolios with a new set of risk-return tradeoffs. For instance, combining rf and M with different proportions will give great portfolios on the line segment rf - M. this process is known as capital allocation, i.e., allocation of investment funds between the risky and risk-free