Frequently Asked Questions In Quantitative Finance

(Kiana) #1
Chapter 2: FAQs 51

What is Modern Portfolio Theory?


Short Answer
The Modern Portfolio Theory (MPT) of Harry Markowitz
(1952) introduced the analysis of portfolios of invest-
ments by considering the expected return and risk
of individual assets and, crucially, their interrelation-
ship as measured by correlation. Prior to this investors
would examine investments individually, build up port-
folios of favoured stocks, and not consider how they
related to each other. In MPT diversification plays an
important role.

Example
Should you put all your money in a stock that has low
risk but also low expected return, or one with high
expected return but which is far riskier? Or perhaps
divide your money between the two. Modern Portfolio
Theory addresses this question and provides a frame-
work for quantifying and understanding risk and return.

Long Answer
In MPT the return on individual assets are represented
by normal distributions with certain mean and standard
deviation over a specified period. So one asset might
have an annualized expected return of 5% and an annu-
alized standard deviation (volatility) of 15%. Another
might have an expected return ofโˆ’2% and a volatility of
10%. Before Markowitz, one would only have invested in
the first stock, or perhaps sold the second stock short.
Markowitz showed how it might be possible to better
both of these simplistic portfolios by taking into account
the correlation between the returns on these stocks.

In the MPT world ofNassets there are 2N+N(Nโˆ’1)/ 2
parameters: expected return, one per stock; standard
deviation, one per stock; correlations, between any two
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