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What are the main meanings of Portfolio theory
by 趙永祥, 2017-03-07 19:50, 人氣(1381)

     What are the main meanings of Portfolio theory

The theory that holds that assets should be chosen on the 
basis of how they interact with one another rather than how 
they perform in isolation. According to this theory, an optimal 
combination would secure for the investor the highest possible 
return for a given level of risk or the least possible risk for a given 
level of return. Although individual investors can use some of the 
ideas of portfolio theory in putting together a group of investments, 
the theory and the literature relating to it are so complex and 
mathematically sophisticated that the theory is applied primarily 
by market professionals. 

Also called modern portfolio theory.


portfolio theory

 the study of the way in which an individual investor may theoretically achieve the 
maximum expected return from a varied PORTFOLIO of FINANCIAL SECURITIES that has attached to it a given level of RISK.

Alternatively, the portfolio may achieve for the investor a minimum amount of risk 
for a given level of expected return.Return on a security comprises 
plus or minus any 
or loss from holding the security over a given time period. 
The expected return on the collection of securities within the portfolio is the 
weighted average of the expected returns on the individual INVESTMENTS 
that comprise the portfolio. The important thing, however,is that the risk attaching 
to a portfolio is less than the weighted average risk of each individual investment. 



As part of the continuing series on Modern Portfolio Theory, we will providing weekly updates to track our model portfolio’s performance.  As illustrated below, we will be tracking the performance of three portfolios.

Two of these portfolios will be optimized based on the theory of mean variance optimization (Markowitz’s Modern Portfolio Theory) and one is allocated based on a traditional approach of a mix between equity and debt.  At the beginning of each week we invest $1,000 based on the allocation of the three portfolios and compare the results at the end of trading on Friday.  Check back often to see how the optimized portfolio’s fared!

Portfolios that will be compared based on performance and risk/reward.  Based on Markowitz's modern portfolio theory (mean variance optimization)

Portfolios that will be compared based on performance and risk/reward. 

Based on Markowitz’s modern portfolio theory (mean variance optimization)

For an easy-to-follow guide for building the optimized portfolios in R based on Markowitz’s Modern Portfolio Theory (mean variance optimization), please refer to Chapter 5 in the series.

Portfolio Composition

The table below summarizes the three tracking portfolios, as of May 28, 2013, using data from the past two years.

PortfolioSPYEFAIWMVWOLQDHYGStd.DevExp.Returnsharpe
Optimized – Short Selling &amp No Max0.87-0.13-0.22-0.330.620.180.00350.00060.18
Optimized – No Shorting &amp 75% Max0.15-0.00-0.00-0.000.750.100.00320.00030.10
Traditional0.300.200.150.100.150.100.01060.00030.03

As can be quickly gleamed from the table, both optimized portfolios have a much higher Sharpe Ratio.  The Sharpe Ratio is the portfolio’s return over its standard deviation and can be used as one measure of performance.  The higher the Sharpe ratio, the higher the return to the portfolio’s variance.  A high return coupled with a low Sharpe ratio could imply that the returns were achieved with too much risk–a potential indication of volatile returns in the future.  (Of course, past performance is no guarantee of future performance and correlations between the securities can quickly change.)

Efficient Frontier - Short Selling with No MaxEfficient Frontier - No Shorting and 75 Max