Markowitz Portfolio Theory

• Returns that go up and down in tandem have positive correlation; those that move in opposite directions have negative correlations.

• For example, it is generally held that airline stocks and oil company stocks are both sensitive to the cost of oil, but react in opposite directions.

• When the cost of oil goes up airline stocks decline and oil company stocks rise. This is negative correlation. Using statistical data, modern portfolio theory develops coefficients of correlation to measure the way stocks move relative to each other.

(Scheangold,2001)

Practice

Variance

It is a measure of the variation of possible rates of return Ri, from the expected rate of return [E(Ri)]

Pi is the probability of possible rate of return (Ri)

Efficient Frontier

Definition of MPT

It is a trade-off between portfolio risk and portfolio return: the more risk an investor is willing to accept, the higher the expected return of the investment.

Expected Rates of return

portfolio investment

Individual investment

Modern portfolio theory

A theory on how risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward.

Markowitz(1952)

Correlation

Harry Markowitz first proposed modern portfolio theory in 1952. It believes that an efficiently combined set of stocks can create a portfolio that will have a lower risk than the average of the risk of the same stocks held separately (Schaengold, 2001).

Modern portfolio theory

Axioms of MPT

• The basis of investment decisions

• Investors have the same time horizon

• The investors are homogeneous

Diversification

• Refers to the reduction of risk by investing in more than one security.
• Don’t put all your eggs in one basket.
• Diversification results in reducing risk in portfolio.

Risk

• The risk or volatility of an individual asset is measured as the standard deviation of its return.
• Standard deviation can be employed to measure the risk or variability of returns of an asset because the standard deviation indicates how dispersed the actual returns are around the expected return .

(Aalberts and POON, 1996)

The Diversifiable risk

• Unsystematic risk, such as law suits, labor disputes, and the like, that are unique to the particular corporation..
• Can be reduced by investing in a portfolio because the risk is assumed to be random.

(Aalberts and Poon, 1996)

Non-diversifiable risk

• The market or systematic risk.
• This is the risk that includes changes in inflation and interest rates that affect the whole economy.
• The essence of proposing capital asses pricing model---only the market risk component of a security's total risk will be priced or compensated by the capital market, and the security may be a single stock or a well-diversified portfolio's
• (Aalberts and Poon, 1996)

Markowitz Portfolio Theory

Conclution

Limitations

Many assumptions in MPT are not always right in returns are normally distributed random variables, but a real life examination indicates this is often reality. For example, MPT assumes that asset far from true.

In many cases there are many large swings which invalidates the theory.

HowTheMarketsWorks.com (2014)

• Introduction
• Definition of MPT
• Practice
• Conclusion
• Reference

Introduction

Content of MPT

• Mean-Variance Model
• Efficient Frontier

Harry M. Markowitz.

Nobel prize winner 1990

The aim of MPT

To maximise return for any given risk level.

Reference

Aalberts, R.J. and Poon, P.S., (1996). The new Prudent Investor Rule and the modern portfolio theory: A new direction for fiduciaries. American Business Law Journal, 34(1), pp. 39.

HowTheMarketsWorks.com (2014) Modern Portfolio Theory (MPT) [online]. Available from: http://education.howthemarketworks.com/glossary/modern-portfolio-theory-mpt/ [Accessed 11th February 2014]

Investopedia (2013) Capital Asset Pricing Model - CAPM[online]. Available from: http://www.investopedia.com/terms/c/capm.asp [Accessed 11th February 2014]

Scheangold, D., (2001). Decade of change: Revising trust investment law to coordinate with modern portfolio theory. Tax Management Estates, Gifts and Trusts Journal, 26(6), pp. 258-266.

Vaclavik, M. and Jablonsky, J., (2012). Revisions of modern portfolio theory optimization model. Central European Journal of Operations Research, 20(3), pp. 473-483.

Markowitz, H(1952) Portfolio selection, Journal of Finance, 7 (1), 77-91.

David H. Bailey， arcos M. López de Prado，(2008). THE SHARPE RATIO EFFICIENT FRONTIER, Electronic copy available at: http://ssrn.com/abstract=1821643

Project Portfolio Selection: the Efficient Frontier Approach, Electronic copy available at:http://www.opttek.com/sites/default/files/pdfs/The%20Efficient%20Frontier.pdf