House money: after a +3R day, risking 2% instead of 1% for five trades, by the numbers

[Fairman]

House money: after a +3R day, risking 2% instead of 1% for five trades, by the numbers

You are up 3% on the day, three winning trades at 1% risk each. The thought arrives: it is house money, so risk 2% on the next five, since you cannot really lose what you just won.

Take an illustrative setup: each trade wins 1.4R half the time and loses 1R the rest. Five trades.

At 1% risk the possible results in R are 1.4k - (5 - k), where k is the number of winners. Giving back the whole +3% needs five losses in a row, which is 1 in 32, or 3.1%.

At 2% risk the day's gain is gone once the five trades are at -1.5R or worse. That happens with 0 wins (1 in 32) or 1 win (5 in 32, a result of -2.6R). Total 6 in 32, or 18.75%.

The expected result also differs: +1.0R means +1% at the smaller size and +2% at the bigger one.

So doubling the risk doubles the expected gain from +1% to +2% and multiplies the chance of handing back the day's profit by six, from 3.1% to 18.75%. The money from earlier trades is the same money as any other.

[FXS HongKong Scalper]

The numbers show that house money thinking does not change the math, it only doubles exposure. A simple rule I use: risk stays the same regardless of the day's result, and if anything, size goes down after a big winning day, since overconfidence tends to show up then.

[Fairman]

The accounting problem is that profit already in the account no longer belongs to the mental account called the day. A broker's equity figure does not know which trades were the early ones. If you are up 3% on a $10,000 account, you have $10,300, and a 2% risk is $206, which comes out of the same equity as any other trade. Lowering the day's starting point in your head, so that you are playing with the winnings, changes the feeling and nothing else. The chance of a loss that day, the effect on a weekly limit, and the effect on a prop firm's daily limit are all computed from the real balance.

[Fairman]

There is a case for stopping after a good day, which is not the same as house money. It comes from a different place: quality. A rule such as stop at +3R reflects that after the plan's best trades the remaining setups may be worse, or that your attention fades. Whether it helps is testable. Take the journal, find days that reached +3R by the fifth trade, and compare the average R of trades after that point to the average before. If the later trades average 0.02R against 0.2R earlier, stopping costs you little. If they average the same 0.2R, stopping gives up that expectancy.

[Fairman]

Another check is the shape of the five trade distribution. At 1% risk, the 5 trade result in R is spread between -5R and +7R, and the mean is +1R. At 2% the same shape stretches to -10% and +14%. The standard deviation of the result is 1.2R x sqrt(5) = 2.7R, which is 2.7% at 1% risk and 5.4% at 2%. A day that is already +3% could finish anywhere from -7% to +17% at the larger size, against -2% to +10% at 1%. The higher variance is not a bonus. It is a cost that has to be justified by something other than the feeling that the profit is spare.

[Fairman]

A rule for the days that go well can be written before they happen. For example: size does not change within the day, whatever the P&L. Or the opposite, size falls by half after +2R, which cuts the variance when most of the day's work is done. Both are consistent. What is not consistent is changing size by mood at the moment of a win. Writing the rule down the evening before is the part that matters, as at 3% up the justification for the bigger size will feel convincing, while the numbers above stay the same.