Research on Asset Allocation Based on Quantitative Investment

Yichen Liu

Department of Natural Science, University of Manchester, Manchester, M13 9PL, U.K.

Keywords: Asset Allocation, Markowitz Model, Expected Excess Return, Sharpe Ratio, Limitations.

Abstract: This paper discusses the application of quantitative investment models in asset allocation. The main model

studied is the Markowitz model. The Markowitz model calculates the excess return, covariance and standard

deviation to obtain the Sharpe ratio. Maximizing the Sharpe ratio under a certain risk level can have the

optimal asset allocation weighted ratio. The purpose is to analyze how quantitative models can optimize

investment portfolios and asset allocation by balancing the risk and return. By studying cases of asset

allocation of different companies in the technology market, the application and effectiveness of the Markowitz

model in different conditions are shown and factors that may affect research results and judgments are found.

The results show that quantitative investment methods can improve portfolio performance more than

traditional methods. Finally, the paper discusses the advantages and limitations of the Markowitz model,

provides valuable insights to investors and proposes directions for future research in this field.

1 INTRODUCTION

With the advancement of data technology and the

enhancement of computational power, quantitative

investment had become an indispensable focal point

in the financial sector. This method employs

mathematical modeling and statistical algorithms to

analyze market data, in order to effectively customize

the asset allocation strategy for companies. This

research discusses the application of the Markowitz

model in optimizing asset allocation strategies. It

conducts detailed analysis and comparisons of the

model's effectiveness across various companies in the

same field. Furthermore, this study identifies the

potential strengths and limitations of the model,

providing critical insights into its practical

implications.

Alberg and Lipton found that listed companies

need to analyze income, debt and other financial

conditions through retrospective analysis, simulation

and quantitative methods (Alberg and Lipton, 2018).

What is more, quantitative investment has gradually

replaced traditional investment methods. Li and Xu

indicated that researchers increasingly try to apply

machine learning and deep learning to quantitative

investment (Li and Xu, 2023). Sharma and Kaushik

pointed out that it is very significant to predict the

https://orcid.org/0009-0008-8039-2679

market value of a stock. Computers can be used as

advanced and convenient tools to help researchers

create investment models (Sharma and Kaushik,

2017). Ibbotson believed that in addition to the

overall market trends that will affect changes in the

time series returns for funds, asset allocation is very

important in determining performance. The

importance of asset allocation also reflects the

necessity of quantitative investment (Ibbotson, 2010).

Fabozzi and Markowitz pointed out that the three

most important parts of an effective investment

portfolio are expected returns, variance of asset return

and correlation. Therefore, whether a quantitative

investment portfolio is usable can be judged by

observing whether the selected investment portfolio

model contains these three data (Fabozzi and

Markowitz, 2011). However, Farinelli et al. believed

that the Sharpe ratio has weaknesses in quantitative

investment construction. It is not as stable as the

asymmetric parameter ratio (Farinelli et al., 2008).

In this study, the Markowitz model will be used as

the research target. Parkinson believed that the

Markowitz model provides strategies for investors

who want to obtain high returns with low risk.

Investors should identify an optimal allocation point

to allocate asset portfolios (Parkinson,2024). In

addition, Maiti discussed the importance of

126

Liu, Y.

Research on Asset Allocation Based on Quantitative Investment.

DOI: 10.5220/0013001200004601

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 1st International Conference on Innovations in Applied Mathematics, Physics and Astronomy (IAMPA 2024), pages 126-130

ISBN: 978-989-758-722-1

systematic and unsystematic risk for risk and return.

Maiti introduced the two important parameters of

variance and covariance in detail and also plotted the

optimization of Markowitz portfolio using R

programming (Maiti, 2021). However, Markowitz's

weaknesses have gradually been pointed out by many

researchers. Lolic proposed an improvement method,

which is to abandon some expected optimality to

reduce the concentration of weights. Such an

improvement better achieves risk-adjusted returns

based on out-of-sample risks (Lolic, 2024). Ravipati

also discussed further developments of the

Markowitz model and the details that require

attention, as the model becomes unstable when its

mean and variance are replaced (Ravipati, 2012).

Therefore, the Markowitz model is a very

important and mature quantitative investment tool in

modern society.

2 METHODOLOGY

2.1 Data Source

In this research paper, the application of Markowitz

model in the same field but different companies are

mainly studied. The research subjects are Apple Inc.,

Alphabet Inc, Microsoft Corporation and

Amazon.com Inc. Some of the data are discovered

through the Yahoo Finance website. These data are

the asset values of each company. Find the asset

classification for each company. For example,

Apple's assets include current assets and non-current

assets. The data used in this article is current assets.

To illustrate, Apple's current assets include cash,

receivables, inventory and other current assets, so

there are four optimal asset allocation categories

studied. The risk-free rate that needs to be used in the

calculation is found in Wharton Research Data

Services. Find the return rate of zero-coupon bond

U.S. Treasury bonds in the Fama-French Portfolios

and Factors function. This is the basis for calculating

annual risk-free rate.

2.2 Variables Description

In order to analyze the Markowitz model, it is

necessary to find out its research variables and

indicators. The main indicators studied in this

research paper are expected excess return,

covariance, and Sharpe ratio. And the optimal asset

allocation weight is determined based on changes in

these data. A high expected excess return indicates a

high rate of return for the company. Covariance

matrix is used to find the adjusted covariance matrix

to calculate the variance of the combination, the

standard deviation, which is the volatility and Sharpe

ratio. The larger the Sharpe ratio, the higher the return

of the portfolio under the given volatility.

The Table 1 below is some of the data that the

model needs to use when studying four different

companies, including expected excess returns,

standard deviations, and the risk-free return rate.

Table 1: Variables needed in Markowitz model.

Variables Apple Google Microsoft Amazon

Expected

excess

return

0.051 0.264 0.140 0.277

Standard

deviation

0 0.107 0 0.050

Risk-free

rate

0 0 0 0

2.3 Model Introduction

The Markowitz model theory advocates that investors

achieve portfolio optimization under given risks

through reasonable asset allocation. It is based on the

following assumptions. Firstly, investors are rational

and they pursue maximizing expected returns.

Secondly, investors are willing to take certain risks to

obtain higher returns. Lastly, investors achieve risk

diversification by constructing portfolios that

consider the correlations between assets.

Analyzing the Markowitz model requires several

steps. First, the expected excess return is calculated

based on the collected data. To calculate the return

rate in each year, return rate:

𝑟















(1)

which is the difference between the current year's

returns and the previous year's returns divided by the

previous year's returns. After that, excess return is:

𝑅



= 𝑟



−𝑟



(2)

The expected excess return is the average excess

return of this category in different years. The second

step is to calculate the covariance matrix of the

company's asset allocation through the data analysis

function of excel. Find its adjusted covariance matrix

by multiplying covariance by degree freedom.

The third step is to calculate the variance and

standard deviation of the combination based on the

adjusted covariance matrix that has been calculated.

The standard deviation represents the volatility of the

asset. The larger the standard deviation, the greater

Research on Asset Allocation Based on Quantitative Investment

127

the volatility and the greater the risk. The final step is

to calculate the Sharpe ratio:

Sharpe ratio =













(3)

Find the proportional weight of different asset classes

by maximizing the Sharpe ratio. This way can help

investors ultimately choose the optimal portfolio and

asset allocation.

3 RESULTS AND DISCUSSION

3.1 Model Evaluation

The Table 2 is found on Yahoo Finance and shows

the value of Apple's assets from September 30, 2020

to September 30, 2023. So Apple's annual return on

assets, excess returns and expected excess return can

be calculated. The calculation results are shown in the

Table 3.

Table 2: Return on assets in each year.

30/09/2

020

30/09/2

021

30/09/2

022

30/09/2

023

Cash 90,943,

000

62,639,

000

48,304,

000

61,555,

000

Receiva

bles

37,445,

000

51,506,

000

60,932,

000

60,985,

000

Inventor

4,061,0

6,580,0

4,946,0

6,331,0

Other 11,264,

000

14,111,

000

21,223,

000

14,695,

000

Table 3: Apple’s expected excess return.

2021 2022 2023 ex

ecte

Cash -0.311 -0.229 0.274 -0.089

Receivables 0.376 0.183 0.001 0.186

Inventory 0.620 -0.248 0.280 0.217

Othe

0.253 0.504 -0.308 0.150

The Table 4 below shows the covariances of Apple's

current assets in the past three years, which are

calculated based on excess returns. The covariance

can be used to find the adjusted covariance matrix in

order to calculate the standard deviation, Sharpe ratio

and weighted ratio.

Through the same operation process, the results of

the Markowitz model in reallocating the asset ratios

of the other three companies can also be calculated

and be shown in the Table 5.

Table 4: Covariance of Apple’s assets

Cash Receiv

ables

Inventory Other

current

assets

Cash 0.067 -0.036 0 -0.080

Receivab

les

-0.036 0.023 0.022 0.034

Inventory 0 0.022 0.128 -0.051

Other

current

assets

-0.080 0.034 -0.051 0.115

Table 5: Results of Markowitz model.

Apple Alphabet Microsoft Amazon

Cash 0.460 0 0.223 0.042

Receiva

bles

0 0.365 0.281 0.958

Inventor

0.155 0 0.069 0

Hedging None None 0.003 None

Other

current

assets

0.386 0.635 0.423 None

Sharpe

ratio

1,840,

460

2.465 2055.886 5.523

The asset allocation of Google's parent company is

very clear. It invests 0.365 in receivables and 0.635 in

other current assets. This asset allocation also makes

Google's Sharpe ratio very good, which is a feasible

asset allocation ratio. Amazon's asset allocation is

0.042 for cash and 0.958 for receivables. Microsoft

and Apple have the same problem. Their Sharpe

ratios are too high to be realistic.

3.2 Discussion

It can be found that the Sharpe ratios of Apple and

Microsoft are too large. Such a large Sharpe ratio is

impossible. The possible reason for this phenomenon

is that both companies paid dividends not long ago.

The distribution of dividends will have an indirect

impact on the Sharpe ratio. Firstly, the distribution of

dividends will affect the rate of return on assets. If an

investor reinvests the dividends in the company's

stock, the expected rate of return on the assets will

increase due to the dividend income. Secondly, due to

stock price adjustments and market feedback, there

will be fluctuations in the short term. However, this

fluctuation is short-lived and has little impact on the

long-term standard deviation. The risk-free rate

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calculation is based on the US Treasury bond. The

dividend paid by a company will not have any impact

on it. If paying dividends significantly increases the

expected return but the standard deviation does not

change much, the Sharpe ratio will rise.

Apple's most recent dividend was on May 10,

2024, when it paid 0.25 dividends. Microsoft's last

dividend was on May 15, 2024, with a dividend of

0.75. The other two companies with relatively normal

Sharpe ratios have no history of paying dividends.

Therefore, this is one of the reasons why Apple and

Microsoft get particularly large Sharpe ratios by using

the Markowitz model for asset allocation.

3.3 Critical Thinking

The operation of the Markowitz model is not difficult,

so its application is very wide. At the same time, it

effectively diversifies risks by building a portfolio of

multiple assets, thereby reducing the volatility

brought by a single asset. This model also helps

investors optimize their investment portfolios and

quickly determine the weight of asset allocation in an

intuitive and easy-to-understand way.

Markowitz has a wide range of applications and is

highly applicable. However, this model still has

limitations. This model relies on historical data, but

historical data cannot fully represent future market

performance and predict future returns and risks.

Markets do not repeat. In addition, the model follows

a normal distribution. However, assets may show

non-normal distributions in the actual market.

Thirdly, the model uses covariance matrix

calculation, but the estimation of the covariance

matrix is very difficult and cannot guarantee

accuracy. Therefore, the estimation of the covariance

matrix will also bring errors. Finally, the model is all

based on rationality and data-based decisions.

However, in real life, investors do not always remain

rational. They may be affected by external factors

such as emotions and preferences and so on.

This study only focuses on data from the past

three years. A higher number of samples reduces the

error of the model. In addition, This research only

studies Markowitz's quantitative investment model.

In fact, there are many types of quantitative

investment models, such as the Black Littleman

model, which combines investors' subjective views

with historical data to better determine the optimal

asset allocation. They also have different usage

methods. Moreover, this research only studies the

application of the Markowitz model for companies in

the technology field. This is not comprehensive. It is

essential to study the effects of using the model on

many different types of companies. Like the Financial

sector with JPMorgan Chase, BlackRock and Morgan

Stanley and the Food Industry with Coca-Cola, Nestle

and PepsiCo.

4 CONCLUSION

In short, quantitative investment models are very

helpful in the current market. These models provide

absolutely rational and systematic methods and

decisions to help investors improve the performance

of their portfolios. However, despite the advantages

of quantitative investment models, they also face

many challenges and limitations. Models need to

constantly adapt to market changes. At the same time,

there are certain differences between the model and

the actual market, and the calculation method of the

model is also based on historical data, which may

cause errors.

In conclusion, the application of quantitative

investment models in asset allocation and portfolio

construction is indispensable. It has become a

powerful tool for modern investment portfolios.

Models help investors achieve more optimized

portfolios by utilizing data, accurate calculation

methods and advanced analytical methods. However,

in the face of market complexity and volatility,

continuous innovation and development are

necessary. Future developments in this field should

lead to more precise and effective strategies.

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Ibbotson, R. G., 2010. The Importance of Asset Allocation.

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