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Summary of research and developments
Introduction
The
problem of efficient and rational money management has
appeared in Ukraine at the same time when the stock exchange
of the country has been organized. During this period the
process of capital investment started. It is aimed to adjust
normal process of economical development by means of
creation efficient mechanism of transformation of
temporarily surplus funds into loanable funds, conversion of
saving into capital investments.
In developed country
the majour originator of investment process is an
institution of professional traders. Services of mutual
funds, trusts and bond houses play the most important role
in the creation of funds involvement activity.
This services haven't gained that much spread in the
domestic model of stock exchange due to some peculiarities
of stock conjuncture and a poor experience of using economic
mathematical models of money management.
Actuality
of the graduation work theme
Nowadays
there is a great diversity of money management dynamic
methods which are used by stockbrokers for their aims. But
most of them are not reliable enough and vary much
from each other in speed of reaching some definite goals and
complicacy of implementation. In order to gain desirable
results and minimize risks it is necessary to analyze
efficiency of these methods via some certain rates and
factors. The results of comparison will show which one
satisfies traders' purposes best.
The goal of the
investigation
The goal of the
investigation consists of getting reliable datum as for the
comparative analysis of dynamic methods of money management.
In order to do this a few problems should be solved. The
definite series of rates and factors are to be calculate as
those of :
- average rate of return;
- standard deviation of an
investment portfolio;
- Sharpe ratio;
- profit factor.
The datum for calculation
will be obtained by means of model simulation.
Expected practical value of the research
The
future results of the work while used in money management
can provide stockbrokers with some reliable data of ways to
maximize future profits of investment portfolio minimizing
its risks or staying within some restrictions (of maximal
acceptable loss, amount of capital involved, time
restriction etc.) Besides the assumption made may be used
for further researches in order to optimize existing dynamic
algorithms of money management or offering a new one.
Survey of research and
developments
Survey of research and
developments in DonNTU
The
investigation of the theme of the work are conducted by
associate professor Smirnov Alexander, PhD jointly with
Guryanova and Revega. The results of their work are
represented in the articles "About Vince's "Optimal f" [1],
"New in Dynamic Capital Management" and "Multicriteria
Analysis of Dynamic Algorithms of Money Management" [4,5].
The Main propositions of Ralph Vince's
"optimal f" theory
To increase the efficiency of
economic system it is often used to reinvest profit returned
into new investment projects. This lets stockbrokers to gain
additional profit though deals with increasing risks. The
American scientist Ralph Vince suggested the theory of
"optimal f" - the optimal part of capital for increasing
investments.
He introduced such notions
as:
- holding period returns
(HPR)
-
profit or loss of an
investor (P&L)
HPR = 1 + P & L ,
if profit
HPR = 1 - P & L
, if loss
(1)
where:
G
and
- is geometrical and arithmetical average
correspondingly
n - number of transactions
In case the profit is reinvested the geometrical average is
more representative than AHPR. The ratio of initial
and ultimate investor's funds is designate as TWR
(Terminal
Wealth
Relative):
(2)
The geometrical average is
designate as:
(3)
Without any sufficient mathematical
proves by means of reflection R. Vince introduce the notion
of a share of invested funds а
which according to his point of view is "optimal f"
for
max TWR
(4)
where:
- f -
percentage of funds to be reinvested
-
(-P&L) -
profits and loss with opposite sighns
-
P&Lj min -
the biggest loss
-
opt f -
one of the values of
f , when TWR = TWRmax.
Survey of foreign research and
developments
There are a great
diversity of research on the theme abroad. Ralph Vince in
his work "The Mathematics of money Management. Risk Analysis
Techniquesfor Traders" criticizes the Kelly's formula and
introduce his own criteria "optimal f"- percentage for
reinvestment. [3]
The theory suggested by
Vince is criticized in the article of Leo J. Zamansky,
Ph.D., and David C. Stendahl "Secure Fractional Money
Management". The introduce their own criteria named "secure
f". To formulate the problem solved by secure f, they add a
constraint into the calculation of optimal f. The constraint
may reflect the acceptable maximum drawdown (and/or other
characteristics). This is a more conservative strategy that
has the benefit of finding the percent of equity invested in
every trade that would have yielded the highest possible
return subject to the acceptable maximum drawdown. This
formulation of the problem is such that its solution will
maximize TWR and guarantee that the drawdown when running
the system on past data does not exceed the amount defined
by the trader — value D. [6]
Conclusions
For empirical researchers, the conclusion that
capitalization and money management may play a role in
determining the success or failure of speculative traders
cannot be ignored. The underestimation of any strategy
drawbacks can result that the propensity for
account balances to be reduced to zero by undercapitalizing
futures trading positions and possibility of this is
quite high and may contribute to the failure of many
speculators. Finally, many works on the performance of
technical trading models have reported results for a single
futures contract for simplicity/comparability or for other
reasons. The research presented here allows greater
reconciliation between planned results and the trading
performance more likely to be encountered by traders with
respect to risk attitudes observed in behavioral finance
characteristics and the reinvestment of profits in
speculative trading.
References
1. Смирнов А.В., Гурьянова Т.В. Об
«оптимальном f» Ральфа Винса. Научные труды Донецкого
национального технического университета, серия
«Информатика,
кибернетика и вычислительная техника»,
вып. 9 (132), Донецк, ДонНТУ, 2008. - С 216-220
2. Швагер Дж.
Технический анализ. Полный курс. - М.: Альпина Паблишер,
2001. - 768с.
3. Винс Р. Математика
управления капиталом.Методы анализа риска для трейдеров и
портфельных менеджеров: Пер. с англ. – М.: Альпина Паблишер,
2001. – 400 с.
4. Смирнов А.В.,
Гурьянова Т.В. Новое в динамическом управлении капиталом.
Научные труды Донецкого национального технического
университета, серия
«Информатика, кибернетика и
вычислительная техника», 2009 (в
печати).
5. Смирнов А.В.,
Гурьянова Т.В. Многокритериальный
анализ эффективности алгоритмов динамического управления
капиталом. Научные труды Донецкого национального технического
университета, серия
«Информатика, кибернетика и
вычислительная техника», 2009 (в
печати).
6.
Zamansky, Leo J., and David Stendahl [1997]. Dynamic
zones, Technical Analysis of STOCKS & COMMODITIES, Volume
15: July.
7.
Мертенс А.В. Инвестици: Курс лекций по современной
финансовой теории. - К.: Киевское инвестиционное агенство,
1997.- 416 с.
8. Van K. Tharp, Ph.D.
Special Report on Money Management/
Copyright © 1997 by I.I.T.M., Inc.
9.
Брандт З. Анализ данных. Статистические и вычислительные
методы для научных
работников и инженеров: Пер. с англ. – М.: Мир, ООО «Изд.
АСТ», 2003. – 686 с.
10.
Лоу А.М., Кельтон В.Д. Имитационное моделирование. Классика
CS. 3-е изд.: Пер.
с англ. – СПб.: Питер; Киев: Изд. группа BHV, 2004. - 847 с.
