On the Experimental Investigation of

Investment Strategies in the Real and Virtual

Financial MarketsJonas Mockus, Igor Katin, Joana Katina

Šiauliai, 2013 m.

IntroductionThe optimal financial investment (Portfolio) problem was investigated by leading financial organizations and scientists. Nobel prices were awarded for the Modern Portfolio Theory (MPT) and further developments. The aim of these works was to define the optimal diversification of the assets depending on the acceptable risk level.In contrast, the objective of this work is to provide a flexible, easily adaptable model of virtual financial markets designed for the needs of individual users in the context of utility theory and to present this model on the web. The aim is to optimize investment strategies. This aim is the new element of the proposed model and simulation system since optimization is performed in the space of investment strategies; both daily and long-term.

The PORTFOLIO model of a

virtual financial market• Predictions:

o AR(p) ( Used for experiment: AR(1), AR(3), AR(6), AR(9) )o AR-ABS(p) ( Used for experiment: AR-ABS(1), AR-ABS(3), AR-ABS(6), AR-

ABS(9) )

• Buying-selling strategies:o Short terms

• Strategy No. 1, risk-aware stockholders: buying the best - selling the losers by three profitability levels

• Strategy No. 2, risk-aware stockholders: buying the best - selling all the losers

• Strategy No. 3, risk-neutral stockholders: buying the best - selling all the rest.

• Strategy No. 4, risk-averse stockholders: selling and buying in proportion to profitability.

The PORTFOLIO model of a

virtual financial marketo Buying-selling strategies:

• Long term strategies:o Maximizing Sharpe Ratio - Modern Portfolio Theory (MPT)o Defining risk by survival probabilities and individual utility

functiono Applying short term strategies in the long term investment

Buying and sellingWe consider a virtual market of major players and stocks. The following notation is used:• is the price of stock at time , predicted by the player ,• is the actual price at time ,• is the actual profit accumulated at time by the player buying-selling stock ,• is the dividend of stock at time ,• is the yield at time ,• is the interest rate at time ,• is the haircut,• is the relative stock price change at time as predicted by the player :

Expected profitability (relative profit) of an investment at time depends on the predicted change of stock prices , dividends , the bank rate , and haircut :

Buying and sellingThe aim is profit, thus a customer will buy some amount of stocks , if profitability is greater comparing with the relative transaction cost ; , and will sell stocks, if the relative loss (negative profitability ) is greater as compared with the transaction cost , or will do nothing, if .

The product is the initial investment to buy shares using an investors’ own capital at the initial price . The initial funds to invest are and the initial credit limit is ., is the credit available for a customer at time . The investors’ own funds in cash available for investing at time t are defined by the recurrent expression:

where . Here the product defines the money involved in buying-selling stocks.Stocks are obtained using both investors own money and the funds borrowed at moment t. The borrowed sum of the stockholder i accumulated at time t is

Bank profitIf a stockholder i gets insolvent at time , the bank losses are

The total bank losses accumulated at time are

The bank income:

The bank profit:

Predictions• AR(p) model

………………………………………….

Predictions

Predictions• AR-ABS(p) model

AR-ABS(p) model using variables u, v, ε with equalities

Here

Predictions• AR-ABS(p) model using variables u, v equalities

Multi-Stock Operations, Portfolio

Problem

Strategy No. 1, risk-aware stockholders: buying the best - selling the losers by three profitability levels

Strategy No. 1, risk-aware stockholders: buying the best - selling the losers by three profitability levels

Strategy No. 2, risk-aware stockholders: buying the best - selling

all the losers

Strategy No. 3, risk-neutral stockholders: buying the best - selling

all the rest

Strategy No. 4, risk-averse stockholders: selling and buying in

proportion to profitability

Defining risk by survival probabilities and individual utility function

Defining risk by survival probabilities and individual utility function

Maximizing Sharpe Ratio - Modern Portfolio Theory (MPT)

Software of the PORTFOLIO model

The PORTFOLIO model is a part of the general on-line system for graduate studies and scientific collaboration.The most recent PORTFOLIO versions are on the web-sites:• http://www.getweb.lt/igor/• http://www.getweb.lt/joana/the later site is meant for the prediction models.

Average profits of eight prediction models

by the first strategy using virtual data

Average profits of eight prediction models

by the first strategy using historical data

The Best Investment Strategy

The most profitable portfolio defined using

the first strategy and AR(6) prediction

model

Conclusions• 1. The growing power of internet presents new problems and opens new possibilities

for distant scientific collaboration and graduate studies. Therefore some nontraditional ways for presentation of scientific results should be defined.

• 2. The optimization models show the possibilities of some non-traditional ways of graduate studies and scientific collaboration by creating and using a specific environment for E-education

• 3. After experiment with real data results shows that profit doesn’t relate on prediction accuracy. Profit does not depend on prediction error.

Thank you for your attention!