Trading Quantitatively

Trading in the stock markets was simulated by letting participants
(also called traders in the following) allocate fictitious money in a
series of offered stock-investing opportunities. Every trading
opportunity had to be taken. Intention was not to imitate the
markets per se, but to represent a trader using a systematic
approach, that is, trading system. It was of no importance to the
participants to be able to pick a stock, possess knowledge about a
specific company, decide time frame of the trades or even have an
opinion of the direction of the markets. Neither was there any
need to decide when to buy or to sell the offered stock. Only one
factor, how much of available capital to be put at risk in each and
every trade, was available for manipulation by the participants.
Allowed position size ranged from minimum 0.5% of available
capital to maximum 100%. Trading on margin was not allowed. All
trading opportunities were on the buy side, no short selling
available. Colored marbles randomly drawn out of a bag
determined the outcome, that is, size of loss or gain of each trade.
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The administrator of the simulation sessions pulled a marble out
and every marble drawn was replaced into the bag, maintaining the
probability of gains and losses.
The simulated trading sessions were administered on two levels.
Participants started level 1 with an initial capital of 10,000 fictitious
Swedish kronor (fSEK). Probability and size of gains/losses on
level 1, that is, the first marble-bag, were according to Table 3,
representing a trading system with both probabilities of wins and
expected value being in the trader’s favor. Level 2, according to
Table 4, represents a trading system where the expected value
again, but not the probability, was in the trader’s favor, thus
reflecting the charasterictics of a trend-following trading system.
The participants were informed of the probability and size of
gains/losses before starting the simulation.
Each level of simulation ended after fifty consecutive trades. If the
trader, at some point during simulation, lost all of his/her capital
before executing fifty trades, the simulation stopped and the trader
was not allowed to continue trading, neither on the present level
nor the next. The simulation also stopped if the trader’s
accumulated gains reached a total capital of 500% or more of
starting capital, for example, 10,000 fSEK growing to 50,000 fSEK.
Table 3. Probability of winning and losing trades in level 1
Level 1
Winning trades Losing trades
Percentage Amount Percentage Amount
55% 1:1 35% -1:1
5% 10:1 5% -5:1
60% 40%
To be able to participate at level 2, traders were required to
increase total capital to 150% of starting capital, or more. If
accumulated gains reached a total of 500% of starting capital, or
more, traders were automatically qualified to participate at level 2.
The amount at the end of level 1 made up the starting equity on
level 2. The more money the traders made at the first level, the
more money they had to invest at the next.
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Table 4. Probability of winning and losing trades in level 2
Level 2
Winning trades Losing trades
Percentage Amount Percentage Amount
10% 1:1 56% -1:1
6% 2:1 10% -2:1
4% 3:1 4% -3:1
3% 5:1
3% 10:1
2% 20:1
2% 30:1
30% 70%
A profit of 1:1 implies that the trader wins an amount equal to the
amount risked. For example: A trader starts with 10,000 fSEK, and
he/she puts 1,500 fSEK at risk in the first stock offered. If it is a win
of 1:1, then he/she has gained 1,500 fSEK and his/her new balance
is 11,500 fSEK. Had the trade been a loosing trade of –5:1, the
trader would have only 2,500 fSEK left to trade with [10,000 – (5 x
1,500)] when offered the second stock.
Every participant received 100 SEK cash (approximately USD 10)
as payment before starting the simulated trading session. The
money was theirs to keep, given one restriction: If the trader at
some point of the simulation lost all of his/her fictitious capital,
he/she had to pay the money back, immediately. On the other side
if the trader was able to increase the starting capital at level 2 into
500% of starting capital or more (e.g., 15,000 fSEK increased to
75,000 fSEK or more), his/her payment was raised to 200 SEK cash
(approximately USD 20).
In short, the benefit of increasing the trading capital was at the first
level, to get to level 2, at the second level, to get a higher
remuneration. The disadvantage of losing all the fictitious money
was to pay the fee back.
All of the simulations took place in a small study/classroom and
lasted 60 – 90 minutes. Number of traders participating at the
same time ranged from one to six. The participants filled wins and
losses, amount at risk and equity balance into a form themselves
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after a brief instruction. The person administrating the simulations
was facing the participants, so he could see them and their forms.
Participants were not allowed to talk to each other or look at each
other’s form.

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