Data for this paper was collected using the Yahoo Finance API deployed using the R programming language to retrieve historical stock prices. The data consists of daily closing prices for eight stocks on the OSE index: Mowi ASA (MOWI.OL), Equinor ASA (EQNR.OL), Gjensidige Forsikring ASA (GJF.OL), DNB ASA (DNB.OL), SalMar ASA (SALM.OL), Yara International ASA (YAR.OL), Orkla ASA (ORK.OL), Telenor ASA (TEL.OL). The data gathered spans from January 1, 2018, to May 1, 2024. The eight stocks were selected since they have the largest trading volume from OSE ( Figure 1 ):

All the selected stocks were positively correlated, as shown in Figure 2 . Salmar ASA and Mowi ASA, both companies within aquaculture, show the highest correlation.

Each agent was deployed with a predetermined trading strategy. Each agent began with an initial 10,000 Norwegian kroner (NOK) asset to invest in the stock market. The agents were restricted to 10 trades per trading day and allowed daily trade. Each agent based their strategies on 5 days of historical data. The strategy of each agent was deterministic, meaning that they had to follow their initial strategy during the whole trading time. The agents did not interact with each other when trading in the market. Each agent acted in the market by selling, holding or buying stocks according to their strategy. Each model’s performance was reported daily, covering the period from January 2, 2018, to May 1, 2024. It was assumed that the trading activities of the agents did not affect the stock prices. This is justified by the small trading volumes each agent handled using the simulations.

The effect of trading cost on the reported returns was investigated using a sensitivity analysis of prices ranging from 0.001 to 0.501 and 1.001. In addition, the effect on returns based on the agents’ access to historical data ranging from 10, 25, 50, 100, and 200 days was analyzed.

The first agent used the strategy Buy and Hold. This strategy was passive, meaning that the agent only made one trade during the assessed time. The agent bought all stocks in equal parts and kept all stocks to the end of the simulation.

The second agent used the strategy Trend Following. In this strategy, the agent was buying or selling stocks based on discerning trends in stock price movements to decide whether to buy or sell. The difference between consecutive prices was used to assess the direction of the trend, meaning deciding on buying, selling or holding the different stocks Equation (1).

$\Delta P_t=P_t-P_{t-1}$ (1)

where:

$\Delta P_t$is the price difference at time t;

$P_t$is the stock price at time t;

$P_{t-1}$is the stock price at time $t-1$.

Trading signals:

$\text{If}\Delta P_t>0,\text{then Buy}$

$\text{If}\Delta P_t<0,\text{then Sell}$

$\text{If}\Delta P_t=0,\text{then Hold}$

The third agent was trading based on Mean Reversion, which is based on the premise that stock prices will eventually revert to their average. The strategy generated signals to buy when prices were below the historical average and signals to sell when they were above it, as seen in Equation (2).

$S_t-S_{t-1}=\alpha \left({\mu }_s-S_{t-1}\right)\Delta t+{\sigma }_s\epsilon \sqrt{\Delta t}$ (2)

where:

S_t the price at time t;

$S_{t-1}$ price at the previous time –1;

α degree of mean reversion, also known as the mean reversion rate or gravity, μs long-term mean of S;

${\sigma }_s$ volatility of S;

ε: random drawing from a standardised normal distribution at time t, (t): n~(0, 1).

Trading signals:

$\text{If}{S}_t=S_{t-1},\text{then Hold}$

$\text{If}{S}_t>S_{t-1},\text{then Sell}$

$\text{If}{S}_t<S_{t-1},\text{then Buy}$

The fourth agent was trading based on Momentum, which is the assumption of continuation of current price trends. It involved calculating a moving average and adjusting the portfolio based on whether current prices were above or below this average, which in turn led the agents to decide to sell, buy or hold stocks Equation (3).

$M{A}_t=\frac{C_t-C_{t-1}\cdots C_{t-n}}{n}$ (3)

where:

MA_t is the moving average at time t;

C is the closing price of a given stock;

Cn is the closing price over time n.

Trading signal:

$\text{If}Cn>M{A}_t,\text{then Buy}$

$\text{If}Cn<M{A}_t,\text{then Sell}$

$\text{If}Cn=M{A}_t,\text{then Hold}$

The performance of the different trading strategies was recorded daily, showing the value of the agents’ portfolio ( Figure 3 ). The yearly accumulative value of the portfolio and Sharpe Ratio were calculated. The Sharpe Ratio measures the performance of an investment relative to its risk, calculated by subtracting the risk-free return rate from the investment’s return and dividing it by the standard deviation of its returns. The risk-free return was set to 3.9%, which is the risk-free rent possible to get in 2024 in Norway. The standard deviation was calculated in addition to the average return. Standard deviation quantifies the variability of the data around the mean. A higher standard deviation (SD) suggests higher risk, as returns vary more from the average compared to a lower SD.

All the calculations were done using the statistical program R ( R Core Team, 2021 ) within RStudio ( RStudio Team, 2020 ). With the packages “quantmod”, “zoo” and “corrplot” ( Ryan et al., 2024 ; Taiyun Wei et al., 2022 ; Zeileis et al., 2023 ).

Increasing trading costs impacted the profitability of all strategies, as evidenced in Table 2 . With higher costs, all strategies converge towards zero or negative returns and corresponding decreases in their Sharpe Ratios. This shows the influence of transaction costs on trading strategies. If the methods will be deployed in the market, an investigation of free alternatives should be considered.

The present evaluation overlooks the effect of the agent’s action on the market: as each agent’s trading volume increases, the agents’ actions will affect the market movement. As all the agents are sensitive to trading costs, higher assets should be implemented to improve the accumulative performance. This will lower the relative effect of the trading costs. With the introduction of an extended amount of historical data, the mean return of the trading strategies is generally increased for all the strategies ( Table 3 ). This can be explained by the agents holding the stocks longer without changing the portfolio, therefore lowering the trading costs, and altering the performance. While the mean return after each trading tended to increase, based on the access to more historical data, the Sharpe Ratio remained relatively constant. This shows that even with access to more data, the trading agents deliver high variability (volatility).