iBusiness, 2013, 5, 69-73
http://dx.doi.org/10.4236/ib.2013.53B015 Published Online September 2013 (http://www.scirp.org/journal/ib)
Theoretical Analysis of Financial Portfolio Model
Xingang Wang
Graduate School of Northeast Forestry University.
Email: 920028102@qq.com
Received June, 2013
This article introduces portfolio selection model proposed by Markowitz in 1952, as well as research of model pro-
moted continually by subsequent researchers, and then introduces a more classic pricing model CAPM in stock market,
and discusses difficulties in the study of modern portfolio theory, and forecasts problems of benefits and risks.
Keywords: Portfolio; CAPM; Benefits and Risks
1. Portfolio Selection Model
Portfolio (portfolio) refers to that different investor assets
are grouped together by a certain percentage as an in-
vestment, and stocks, bonds, discharge capacity, collecti-
bles, and other objects can be part of portfolio as an in-
vestment. Portfolio Theory discusses the interrelation
between each asset and other assets of risk and return,
and how investors choose their optimal portfolio reason-
able and other issues.
1) Standard portfolio model
Before H. Markowitz founded the modern theory of
portfolio, Western financial asset investment theory has
experienced more than a century. After World War II,
Western nations suffered rapid economic recovery and
investment activities of financial assets also would be
booming. In the context of this reality, Markowitz
founded portfolio selection theory. Markowitz used ma-
trix algebra, vector spaces, probability and statistics and
other mathematical methods, to do qualitative and quan-
titative analysis of portfolio selection theory in portfolio
Portfolio is an effective way to diversify investment
risks. In 1952 Markowitz published a classic paper Port-
folio Selection, and laid the basis for Portfolio theory,
and thus won the Nobel Prize in economics. Purpose of
portfolio selection model proposed by Markowitz is to
diversify investment risks essentially under the premise
of maximizing without loss of yield. He pointed out that
the risk of the portfolio not only depends on features of
individual securities, [1]but also on correlation between
securities in the securities portfolio. Generally speaking,
the lower the correlation between securities is; the lower
the portfolio's risk is.
In Markowitz’s theory, the Evaluation indexes of Risk
Securitization are thus two, named investment average
yield µ and yield variance σ², μ are the Evaluation in-
dexes of the securities profitable size, and σ ² are securi-
ties risk indicators. Investors can use the following mod-
els to determine the optimal portfolio.
Optimal portfolio can be determined by the following
Model A
Min =x²Ώx
Where X is the variance of securities investment rate
of return, n securities investment ratio vector is X, the
covariance matrix X is n kind of stock returns, X is n kind
of bond yields mean vector, X elements for 1
n-dimensional vector, for the portfolio expected rate of
Model A fails to consider the negative investment
proportional coefficient, due to the negative investment
ratio means selling the relevant securities, and short sell-
ing in some occasions, especially in difficult to realize
our country, so it is necessary to consider the case of no
short sale.
Model B
Min a²=X²ΏX
Model A and model B are allowing short-selling or not
under the conditions of the Makovecz mean ---- variance
model. Their meaning is: In the given securities invest-
ment is expected to yield under X conditions, the securi-
ties portfolio investment risk. Based on the X positive
definite, [2]and its corresponding organization invest-
ment risk optimal model of A solution.
Copyright © 2013 SciRes. IB
Theoretical Analysis of Financial Portfolio Model
At present there is no analytical model of B, but the
domestic and foreign experts have proposed some algo-
rithm, tree algorithm to improve the solution model of B
optimal solutions are given. The optimal model A and
model B solutions usually can be used as an effective
portfolio. But because the expected variance models es-
pecially the computational complexity of model B, so far
in solving large-scale investment securities organizations
are still restricted. Some scholars in order to solve this
problem using a similar linear programming technique or
index model to reduce the parameters to be estimated.
Also some scholars use the income difference, deviation
as a measure of risk, in order to simplify the calculation.
Below is a brief introduction of several other models
1) Max Standard Analysis
Due to the law and policies, there are some propor-
tions or limitation in total amount for securities groups in
single or all securities investments. If such limitation
differs to every security, then the following constraint
sets are listed:
ΣXi =1
Xt 0,i =1,...,n
Xt Ui, i=1,...,n
All these constraint sets above are the same as that of
standard portfolio selection mode except the max in-
vestment number Ui (it is assumed as a constant) of each
securities. The max standard analysis is an exception of
portfolio selection mode.
2) Tobin-Sharp-Lintner Model
Tobin-Sharp-Lintner Mode allows to considering the
other flow direction of capitals. However, there is a
premise that is the flowing out amount of money can not
overpass its own amount but the flowing in money has
no limitation. Therefore, portfolio selection is restricted
by the following items:
ΣXi =1+Xn+1
Xi 0,i=11,...n
Xn+1 -1
or it can be written as
ΣXi -Xn+1=1
Here it should be noticed that the limitation of Xn +1 is
not 0 but -1. In the analysis of Tobin (1958), Sharp (1964)
and Lintner (1965), the variable Xn+1 represents bor-
rowing if it is a positive number and loan if it’s a nega-
tive number. As for the variance Vn+1=σn+1, if n+1 is 0,
then i=1, ... , n, σn+1 equals 0 as well. Usually, the rate
that a investor get form the loan and borrowing refers to
the risk-free rate. It can be expressed as γ0. Since Xn+1
means the borrowing money, μn+1 = -γ0.
3) Model for Bear Position That Need Attachment
If the variable has no non-negative limitation, i.e, only
under the condition of ΣXi =1, the following feasible
solutions may appear:
X1 = -1000
X2 = +1001
Xi = 0 i = 3, ..., n
The answers above mean the 1000 unit bear of securi-
ties 1 and the 1001 unit bull of securities 2. In fact, it is
impracticable for individual, investment institution or
brokerage. According to the law, mortgage is a must.
Thus, the constrained items can be showed in the fol-
lowing ways:
aΣXi S A + ΣXi
i=1 i=1
XiL 0, i =1, ... , K+G
XiS 0, i =1, ... , K+G
A here means assets; XiL means the bull position of
securities i; XiS means bear position of securities i. The
money that total number multiplies a which means the
require of mortgage should not surpass the money that
right capital surpluses the bear value which can’t be used
as mortgage, i.e the Securities K.
2. Capital Assets Pricing Model
Capital Assets Pricing Model, short for CAPM, is found
and raised single and respectively by William F. Sharpe,
an American economist who won the Nobel Economics
Prize in 1990, John Linter and Jack Treynor. This model
is at the core of capital market theories and it’s a signifi-
cant achievement of modern financial theories and secu-
rities theories. This model attaches great importance to
guiding the securities investment.
1) Assumptions of CAPM
CAPM is developed from the portfolio selection and
the assumptions about which are more rigorous than
capital group theories. The basic assumptions are listed
as follows:
a) All investors are risk aversion. They weight the
gains or risks or assets with the expected value or vari-
ance or standard deviation of the asset returns.
b) Investors determine the investment based on the
single gains and risks and the investment horizon are the
c) There’s no obstacle in securities market, which
means the transacting fees are zero. The transacting
amount of assets is divisible. Investors can buy any asset
Copyright © 2013 SciRes. IB
Theoretical Analysis of Financial Portfolio Model 71
in market price according to his economic ability.
d) The judgment of investors to the insurance of asset
gains is the same.
e) All investors could borrow or lend unlimited funds
be issued at the risk free rate and borrowing and lending
rates are the same.
f) Tax will not influence securities transactions and
asset selection and there not any kinds of market imper-
g) All investors can only buy or sell assets at the mar-
ket price (price taker).
Under these assumptions, the first three and the last
one are relatively realistic. First, the vast majority of in-
vestors are risk averse, and they mostly estimate invest-
ment income and risk in accordance with the expected
benefits and possible volatility. Second, though the sin-
gle-period revenue assumptions seeming simple, as the
future of income can be considered from the asset prices
of the end period, and the asset price difference between
ending and beginning of the period will be reflected as
current benefits and risks. Therefore, the second assump-
tion is not difficult to accept.
Third, in the developed securities market, the transac-
tion costs, which are relatively low, will not have much
impact on the asset transaction, and most investors are
price takers. Assumptions d), e), f) are different from the
actual situation. For example, consistency expectation is
impossible, and actually quite complex tax system is very
complex, which will certainly be an impact on securities
transactions and selection of investors. There must be
difference in interest rates when borrowing and lending
money, it is impossible to borrow and lend money unlim-
itedly. But it is necessary for the capital asset pricing
model to propose these assumptions, and in turn, the
capital asset pricing model is useful for securities in-
vestment. The impact of deviation between assumptions
can be further discussed.
2) Capital and Asset Pricing Model
The applications of Markowitz’s decentralization
thought in the asset allocation management require a lot
of computing. Sharp think we can use a simplified
method to achieve the same effect. The method he pro-
posed requires the investor to know relationship between
each stock's annual earnings and annual earnings of the
market, which can be used to represent by share price
Investment risk can be classified into two categories,
systematic risk and unsystematic risk. If you use ratio of
covariance COVjm of an asset (assuming the asset j) and
the market portfolio and the market portfolio variance σ ²
M, COVJM / σ ² M = βj as its systematic risk measure of
the strength , the relationship between an asset J's reve-
nue expectations and the whole system air can be repre-
sented as follows:
E(Rj)= Expected return of assets J
Rf= Benefits of risk-free assets
E(RM)= Expected return of market portfolio
βj= coefficient β of asset j
The above formula is capital asset pricing model
(CAPM), which reflects relationship between risks and
return of each asset.
3) The Features of Capital Asset Pricing Model
CAPM has following two significant properties
under the balanced situation the relationship be-
tween the returns from assets and the risk have every-
thing to do with the SML(Security Market Line).High
risk high returns, vice verse. The relationship between
E(R) and β is the straight line up from left to right. As
The β in the Asset Portfolio is the component of β’s
weight-sum in the asset of this group. For instance, the
investors invest the capital x with ratio a in βx, invest the
capital y with ratio b in βy, so the β in Asset Portfolio
ax+by can be shown as:
This important property shows that CAPM is true for
any Asset Portfolio.
4) Determination of β
We utilize the CAPM’s relation between its earning
and the risk in the process of the portfolio investment in
order to guide the option of the securities, and to estimate
the relevant security β is the key of the application of the
The estimate of the β used to adopt the Linear Regres-
sion and some historical data. Generally, the adopted
Linear Regression Model is:
aj refers to the intercept term from the regression
βj refers to the estimated value of β, the slope in the
regression equation
Rmt refers to the portfolio of the market
Rjt refers to the return of the asset j
Ejt refers to the random error
Rmt and Rjt are the historical data, aj and βj can be
gotten from the regression estimation.
Copyright © 2013 SciRes. IB
Theoretical Analysis of Financial Portfolio Model
3. The Issues about the Gain and Forecast in
Security Portfolio Theory
Among the various kinds of theories about the option of
Security Portfolio the further gain and variance are the
basis of the decision. And it’s a difficult point of the pre-
sent study that how to forecast the security portfolio. As
the security portfolio is a random variable so it’s will not
just a simple repetition. The historical data is insufficient
for some investment projects or assets, especially
emerging industries which because of the changes of the
economic development, policies and etc. So the forecast
by the historical data like ‘driving by the rear-vision
mirror’, [3] so the effect is unsatisfactory phenomenon.
There is no investor can forecast the further gain of the
securities precisely, from this point, there are two Bayes-
ian methods which suitable to the analysis of the securi-
ties of the financial market: fundamental analysis and
technical analysis
1) Fundamental analysis
Fundamental analysis, is the analysis and study of the
securities, especially the stock, and put priority in the
intrinsic value of the securities. By analysis the macro-
investmental environment, especially the basic case of
economic environment, the publisher’s industry, to seek
the value of the securities and decide whether it’s worthy
to be invested.
The change of the securities’ price can be caused by
several reasons. In political, the war the political turmoil
the leadership change and so on, will affect the investor’s
confidence more or less and then affect the stock market;
in economic aspect ,the economic growth the inflation
the change of the interest rate the exchange rate all of
them will have an effect on the stock market.
National policies such as control the money supply,
adjustment of tax, rate of tax, to support, lean or restrict
to an industry and etc, all will affect the stock price. So
keep a close eye on the change of the macro-politics and
economy is very important for the analysis and study.
Industry analysis refers to analyzing the issuer and the
listing Corporation out of what kind of industry and the
company is in the status of the industry. The company
position in the industry is also very important, in differ-
ent position in the same industry, its ability to grow dif-
ferent. The company's high status, high visibility, easy to
obtain the stable and huge profits, but its growth ability
may be weak. The position of the lower company, visi-
bility is not high; the lack of competitiveness, but future
growth capacity may be strong. Growth firms are a better
choice for investors.
Analysis of the company itself is the most important
part of the basic analysis. [4]To include many aspects
analysis company, such as the products of the company,
in what the product cycle, market share, new product
development ability. The key to the analysis of the com-
pany’s marketing efficiency, production efficiency and
management efficiency. Through the analysis of financial
indicators, such as the balance sheet, income statement,
marketing situation analysis of the company’s, the com-
pany also analysis of stability, activity ability, profit abil-
ity, growth ability through the company's other indica-
In short, the basic analysis method is refers to the use
of statistical data, using a variety of economic indicators,
the proportion, method of dynamic analysis, from the
macro political, economic, to the industry analysis, until
the business profit status and Prospect of micro analysis,
evaluation of enterprises issued by the securities, and as
far as possible to predict its future change, as investors
investment basis.
2) Technical analysis
Technical analysis is based on the statistical data of the
future past stock market movements. [5]Technical analy-
sis is purely focused on the analysis of price and the
quantity of securities, without considering the company's
financial position and profitability. According to the
price and trading volume change, to predict the stock
price up or down, to determine the behavior of invest-
ment. This method considers all affect securities, espe-
cially various kinds of factors of stock, will be reflected
in the price level and stock trading volume. If the phe-
nomenon of certain activities, the market price changes,
including the cycle has appeared in the past, is very
likely to appear again in the future. History will repeat
Technical analysis method mainly through statistical
quantity price and trading of securities. This analysis
method is developed to today, can be said to be rich and
colorful, perfection. Such as Dow Theory, the moving
average line, K line graph, chart, and bar chart.
Fundamental analysis and technical analysis have
strengths; they analyze the stock market from a different
perspective, reflecting the change of the stock market to
a certain extent. Difference between fundamental analy-
sis and technical analysis: the former is mainly to look
forward, pay attention to the future earnings and risk; the
latter mainly look back, to the market already happening
to predict future basis. In practical analysis, should be to
combine the two organic.
Through the analysis of the previous price data, [6]the
future trend can be predicted. However, the basic analy-
sis for the importance of stock prediction can not be ig-
nored. Therefore, the Bayesian method is proposed in
this paper, which embodies the idea: according to the
latest news, including the expert experience and subjec-
tive judgment, revised historical data model.
Through the analysis of the previous price data, we
can predict the future trend. However, the importance of
basic analysis for the stock prediction can not be ignored.
Copyright © 2013 SciRes. IB
Theoretical Analysis of Financial Portfolio Model
Copyright © 2013 SciRes. IB
Therefore, the Bayesian method is proposed in this paper,
which embodies the idea: according to the latest news,
including the expert experience and subjective judgment,
revised historical data model.
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[3] G. Lee, Financial Economics, Chengdu. Sichuan Univer-
sity press, 1999.
[4] Y. Lu, Financial Market Investment Decision Optimiza-
tion in Probability Criterion, the Heilongjiang Province
Natural Science Fund Project (G0521), 2008.
[5] Y. F. Meng, “Securities Investment,” Xiamen. Xiamen
University press, 2006
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