Question

Discuss briefly the concept of CAPM and APT in terms of modern portfolio theory?

Answer 1

Capital Asset pricing model:

As per CAPM model:
Re= Rf+(Rm-Rf)B

Re= required rate of return.
Rf= Risk-free rate.
Rm = Return on market.
Rm-Rf =Market Risk Premium.
B = Beta, systematic risk.

How each of them is determined/estimated?

Risk-free rate (Rf) is the rate of return an investor expects to earn from an investment which carries zero risk.

Rm return on market: it is determined by the overall return on the market. For example: S&P500 Index in the USA, Nifty in India.

Beta that is systematic risk is determined by: Rate of change of stock return to the rate of change of market return. It is the sensitivity of stock return to Market return.

Arbitrage pricing theory:

arbitrage pricing theory is a multifactor asset pricing model.

It is a very useful model for analysing portfolios from a value investing perspective.

Both CAPM & APT are similar in the sense that, they both focus on systematic risk only.

APT criticize CAPM on the ground that true market portfolio required under CAPM does not exist.

APT takes many factors into consideration Like using macroeconomic factors or fundamental factors like ROE, P/E Ratio, the market capitalisation of the company.
APT is not specific in terms of the number of factors or which factors.

As it is a multifactor model- the more the factors the more useful it is.

Modern portfolio theory relationship with CAPM & APT.

1. Modern portfolio theory assumes that investors are rational.
2. They want to maximize the utility of their portfolio.
3. According to modern portfolio theory utility is a positive function of return and negative function of risk.
4. To calculate portfolio with maximum utility, we calculate the coefficient of variation.
5. Coefficient of variation is standard deviation divided by the return of the portfolio.
6. Lower the coefficient of variation, the better, the lower the unit of risk per unit of return.
7. The portfolio with a lower coefficient of variation in the pool of portfolio- lies on efficient Frontier.
8. So a portfolio on efficient Frontier gives the lowest amount of risk per unit of return.
9. That's why we invest in the portfolio on efficient Frontier rather than portfolio below the Efficient Frontier (inefficient portfolio/all other possible portfolios).
10. Also as investors are rational invest in a diversified portfolio i.e market portfolio, where unsystematic risk is gone. What is left is a systematic risk. Only systematic risk is relevant in the world of Capital asset pricing model and arbitrage pricing model. Systematic risk is captured by beta.
11. If the investor is able to use the CAPM and APT to perfectly optimize the portfolio's return in comparison to its risk, it will exist on efficient Frontier.