portfolio selection by harry markowitz

Assignment

on

PORTFOLIO SELECTION

by

HARRY MARKOWITZ

Name Prashanth premchand banu

Student ID A4018183

RISK MANAGEMENT ASSIGNMENT --MODERN PORTFOLIO THEORY

Modern portfolio theory, or MPT, is a popular investment theory which suggests that

investors can maximise returns and minimise risk by carefully selecting different

types of assets in their portfolio. The theory is considered as a mathematical

formulation of the concept of diversification in investing.

Modern portfolio theory was introduced in 1952 by Harry Markowitz, then a student

in the University of Chicago. The theory became very popular because at that time

there was no mathematical method to quantify risk and MPT offered a solution. For

his contribution to the finance, Markowitz received a Nobel prize in 1990.

In its simplest form MPT provides a framework to construct efficient portfolios by

selection of the investment assets, considering risk appetite of the investor. MPT

employs statistical measures such as correlation and co variation to quantify the effect

of the diversification on the performance of portfolio.

For most investors, the risk they take when they buy a stock is that the return will be

lower than expected. In other words, it is the deviation from the average return. Each

stock has its own standard deviation from the mean, which MPT calls "risk".

The risk in a portfolio of diverse individual stocks will be less than the risk inherent in

holding any one of the individual stocks (provided the risks of the various stocks are

not directly related).

Consider a portfolio that holds two risky stocks:

One that pays off when it rains

Another that pays off when it doesn't rain.

A portfolio that contains both assets will always pay off, regardless of whether it rains

or shines. Adding one risky asset to another can reduce the overall risk of an all-

weather portfolio.

Modern Portfolio Theory proposes that it’s possible to construct a portfolio of

investments that maximizes returns and minimizes risk by diversifying investments

among uncorrelated assets.

LSBF Risk Management assignment 2


There are two key assumptions inherent in MPT:

1. Investors Are Rational: This means that investors, collectively, will be correct

in their economic and financial assumptions on average. In other words,

market moves are always rational and based on the fundamental economic and

corporate realities of the moment.

2. Efficient Market Hypothesis: Those who subscribe to this view believe that all

information relevant to a stock is priced into it at a given point in time. In

other words, the stock price is reality.

MPT models an asset’s return as a normally distributed random variable, defines risk

as the standard deviation of return, and models a portfolio as a weighted combination

of assets so that the return of a portfolio is the weighted combination of the assets’

returns. By combining different assets whose returns are not correlated, MPT seeks to

reduce the total variance of the portfolio. MPT also assumes that investors are rational

and markets are efficient.

Although MPT is widely used in practice in the financial industry and several of its

creators won a Nobel Prize for the theory, in recent years the basic assumptions of

MPT have been widely challenged by fields such as behavioural economics, and

many companies using variants of MPT have gone bankrupt in various financial

crises. MPT is a mathematical formulation of the concept of diversification in

investing, with the aim of selecting a collection of investment assets that has

collectively lower risk than any individual asset. This is possible, in theory, because

different types of assets often change in value in opposite ways. For example, when

the prices in the stock market fall, the prices in the bond market often increase, and

vice versa. A collection of both types of assets can therefore have lower overall risk

than either individually.

It often requires investors to rethink notions of risk. Sometimes it demands that the

investor take on a perceived risky investment in order to reduce overall risk. That can

be a tough sell to an investor not familiar with the benefits of sophisticated portfolio

management techniques. Furthermore, MPT assumes that it is possible to select stocks

whose individual performance is independent of other investments in the portfolio.

But market historians have shown that there are no such instruments; in times of



market stress, seemingly independent investments do, in fact, act as though they are

related.

Likewise, it is logical to borrow to hold a risk-free asset and increase your portfolio

returns, but finding a truly risk-free is very complicated. Government-backed bonds

are presumed to be risk free, but, in reality, they are not. Securities such as gilts and

U.S. Treasury bonds are free of default risk, but expectations of higher inflation and

interest rate changes can both affect their value.

The conventional interpretation of MPT is based on finance research through the mid-

1960s. By that standard, buying and holding the market portfolio and letting it ride is

the embedded wisdom. But research over the last several decades tell us that risk and

return are more complicated, which implies doing something other than holding the

unmanaged market portfolio. In the long run, the broad market portfolio is still likely

to perform as theory predicts and generate middling to slightly above middling returns

for relatively little risk compared with the various efforts to beat this index.

Another assumption of MPT is that investors accurately understand what returns are

possible. This is often not the case and is why many investors often need help from

money managers. Professionals are more likely to understand real-world limitations

of Modern Portfolio Theory.

Conclusion

Even though MPT has evolved into a major theory in finance and it is commonly used

by research analysts and portfolio managers as a tool to monitor risk and return

characteristics of a portfolio, some serious criticisms have also evolved to challenge

the very basic assumptions of MPT, especially after the findings in the field of

behavioural economics. For example, the theories that markets are efficient and all

investors are rational have been proved wrong by behavioural economists as well as

the success of outstanding investors. Also other assumptions such as the correlations

between asset classes are constant and all investors have access all available

information are also wrong in many cases. Further, MPT does not take into account

the impact of taxes and trading costs on portfolio returns. Moreover, the reliance of

MPT on past performance to project expected returns is not always reliable since as

everyone knows past performance is no guarantee of future results. A portfolio's

success rests on the investor's skills and the time he or she devotes to it. Sometimes it



is better to pick a small number of out-of-favour investments and wait for the market

to turn in your favour than to rely on market averages alone.

Reference

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

2. Gupta, Francis, Markowitz, Harry M.Fabozzi, Frank J. (2002) The Legacy of Modern Portfolio Theory THE JOURNAL OF INVESTING Fall 2002

3. Risk glossary (2006) "Modern portfolio theory", Available from http://www.riskglossary.com/link/portfolio_theory.htm [19/06/2006]

4. Andrei Shleifer: Inefficient Markets: An Introduction to Behavioral Finance. Clarendon Lectures in Economics (2000)

External links

1. http://www.investopedia.com/articles/06/MPT.asp

2. http://www.capital-flow-watch.net/tag/modern-portfolio-theory/

3. http://www.articlesbase.com/investing-articles/modern-portfolio-theory-an-

introduction-2105870.html#ixzz0t5RMm3Fp

4. http:/en.wikipedia.org/wiki/Modern_portfolio_theory


http://en.wikipedia.org/wiki/Modern_portfolio_theory

http://www.capital-flow-watch.net/tag/modern-portfolio-theory/

http://www.investopedia.com/articles/06/MPT.asp

portfolio selection by harry markowitz

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