# Mathematics In Trading: Stock, Forex Mathematical Formula

- Pips – Value Of Pips
- Leverage And Margin
- Position Sizing
- Expectancy Of Your Trading System
- Likelihood of Losing and Winning Streaks
- Account Loss And Recovery Rate
- Profitability Check
- Correlation And Risk
- Growth Of Capital

## Pips

Value Of One Pip = (0.0001 / Current Exchange Rate) * Trade Size

######
*Tip: Whenever the USD is the second (quote) currency, the pip value is $10. *

## Lot | ## Units | ## Pip value* |

Standard Lot | 100.000 | $10 |

Mini Lot | 10.000 | $1 |

Micro Lot | 1.000 | $0.1 |

######
**if your base currency is USD.*

## Leverage

Required Account Size = Trade Size In $ / Leverage

$100.000 / 100 = $1.000

## Margin

Leverage = 1 / Margin

50:1 = 1/2% = 1/0.02

## Leverage | ## Margin | ## Notional Position Size (1 Lot) | ## Margin Required (Trading Account) |

1:1 | 100% | $100.000 | $100.000 |

10:1 | 10% | $100.000 | $10.000 |

50:1 | 2% | $100.000 | $2.000 |

100:1 | 1% | $100.000 | $1.000 |

200:1 | 0.5% | $100.000 | $500 |

## Position Sizing

- Your account size [$50.000]
- The % you want to risk per trade [1.8%]
- The stock price [$45]
- Stop Loss Price [$40]

#### Step 1 – Your $Amount Of Risk

Risk = [(Your Account Size) * (%-Risk Per Trade)]

$50.000 * 1.8% = $900

#### Step 2 – Stop Loss

Stop Loss In % = 1 – (Stop Price/Current Price)

1 – (40/45) = 11%

#### Step 3 – Position Size

Position Size = Your $-Risk / %-Stop Loss

$900 / 11% = $8.180

#### Step 4 – Number Of Shares To Buy

Number Of Shares = Position Size / Current Stock Price

$8.180 / $45 = 180

## Expectancy Of Your System

- Winrate [60%] and loss rate [40%]
- Account size [$50.000]
- Risk per trade [1% or $500]
- Risk:Reward ratio [2:1]

Expectancy = Winrate*(Account Size * %-Risk * Risk:Reward) – Loss Rate*(Account Size * %-Risk)Expectancy = 60% * ($50.000 * 1% *2) – 40% *($50.000 * 1%) = $400

Expected Profit Of A Winning Trade = Winrate * (Account Size * %-Risk * Risk:Reward)60% * ($50.000 * 1% * 2) = $600

Expected Loss Of A Losing Trade = Loss Rate* (Account Size * %Risk)40% * ($50.000 * 1%) = $200

## Likelihood Of Losing And Winning Streaks

#### Likelihood Of Winning Streaks

2 Winners In A Row = Winrate * Winrate

60% * 60% = 0.6 * 0.6 = 0.36 = 36%

3 Winners In A Row = Winrate * Winrate * Winrate

60% * 60% * 60% = 21.6%

4 Winners In A Row = Winrate * Winrate * Winrate * Winrate60% * 60% * 60% * 60% = 13%

## Account Loss And Recovery Rate

## Account Size | ## $Value Of 2% Risk | ## %Loss Of The Starting Account |

$ 10.000 | $ 200 | |

$ 9.800 | $ 196 | 2.00% |

$ 9.604 | $ 192 | 3.96% |

$ 9.412 | $ 188 | 5.88% |

$ 9.224 | $ 184 | 7.76% |

$ 9.039 | $ 181 | 9.60% |

$ 8.858 | $ 177 | 11.41% |

The %Loss Of 2 Consecutive Losing Trades, Risking 2%:1-[(1-0.02)*(1-0.02)] = 0.0396 = 3.96%

The %Loss Of 3 Consecutive Losing Trades, Risking 2%:1-[(1-0.02)*(1-0.02)*(1-0.02) ]= 5.88%

## %Risk Per Single Trade | |||||||

1% | 2% | 4% | 5% | 6% | 7% | ||

## Consecutive Losing Trades | 2 | 1.99% | 3.96% | 7.84% | 9.75% | 11.64% | 13.51% |

3 | 2.97% | 5.88% | 11.53% | 14.26% | 16.94% | 19.56% | |

4 | 3.94% | 7.76% | 15.07% | 18.55% | 21.93% | 25.19% | |

5 | 4.90% | 9.61% | 18.46% | 22.62% | 26.61% | 30.43% | |

6 | 5.85% | 11.42% | 21.72% | 26.49% | 31.01% | 35.30% | |

7 | 6.79% | 13.19% | 24.86% | 30.17% | 35.15% | 39.83% | |

8 | 7.73% | 14.92% | 27.86% | 33.66% | 39.04% | 44.04% | |

9 | 8.65% | 16.63% | 30.75% | 36.98% | 42.70% | 47.96% | |

10 | 9.56% | 18.29% | 33.52% | 40.13% | 46.14% | 51.60% |

- it is very likely (and it will happen to every trader) to have 6, 7 or even 10 consecutive losing trades
- if you risk a high %amount per single trade, your losses can be significant
- significant losses take a long time to recover from

## Profitability Check

Risk:Reward Ratio = Take Profit Distance / Stop Loss Distance65 / 40 = 1.625

Required Winrate = 1/ (1+ Risk:Reward Ratio)

1 /(1+ 1.625) = 0.38 = 38%

## Correlation And Risk

A correlation of -1 means that the two instruments are perfectly negatively correlated. If one asset rises, the other one falls at the same rate. The graph shows two instruments with a correlation of -1 – one graph is the mirror image of the other one.

A correlation of +1 means that two instruments move together identically with the same strength and also in the same direction.

The chart shows two stock prices with a correlation of +1 (+100%). Both instruments rise and fall together with the same strength. Although a correlation of +1 is very rare, you will often have correlations that are close to +1, signaling two very similar instruments.

## Post a Comment