Risk & Money Management

Q1. (4 marks)

• The 1-2% rule states a trader should risk no more than 1-2% of total trading capital on any single trade. (2 marks)
• Purpose: to limit the impact of any single loss, preserve capital, and survive losing streaks so the trader stays in the game long enough for edge to play out. (2 marks)

Q2. (6 marks) (a) Max risk = 2\% \times 50{,}000 = 0.02 \times 50000 = \1{,}000$. *(2 marks)* (b) Stop distance$= 200 - 190 = $10$per share. *(1 mark)* Shares$= \dfrac{\text{Risk}}{\text{Stop distance}} = \dfrac{1000}{10} = 100$ shares. (3 marks: 2 for method, 1 for answer)

Q3. (4 marks) Formula: $\text{Shares} = \dfrac{\text{Account} \times \text{Risk\%}}{\text{Entry} - \text{Stop}}$ (2 marks)

• Numerator = dollar amount willing to lose (account × risk fraction). (1 mark)
• Denominator = stop distance = risk per share. Dividing gives number of shares. (1 mark)

Q4. (6 marks)

• Maximum drawdown = the largest peak-to-trough decline in account equity over a period, usually expressed as a percentage. (2 marks)
• Drawdown limit = a threshold on cumulative equity decline from a peak; if breached, trading is scaled back or stopped for a longer term. (2 marks)
• Daily loss limit = a cap on losses within a single trading day; resets each day. Drawdown is cumulative/multi-period, daily limit is a short-term intra-day control. (2 marks)

Q5. (5 marks) (a) 5\% \times 20{,}000 = 0.05 \times 20000 = \1{,}000$. (2 marks) (b) A circuit breaker is a pre-set rule that halts (stops) all trading for the rest of the day (or a defined period) once the loss limit is hit, preventing emotional revenge trading and further losses. (3 marks)

Q6. (9 marks) (a) $b$ = net odds / reward-to-risk ratio (amount won per unit risked); $p$ = probability of winning; $q = 1-p$ = probability of losing. (3 marks: 1 each) (b) $p = 0.6$, $q = 0.4$, $b = 2$. $f^* = \dfrac{bp - q}{b} = \dfrac{(2)(0.6) - 0.4}{2} = \dfrac{1.2 - 0.4}{2} = \dfrac{0.8}{2} = 0.4$ (40%). (4 marks: 2 method, 2 answer) (c) Fractional Kelly reduces volatility/drawdown risk and guards against errors in estimating $p$ and $b$ (full Kelly is aggressive and estimates are uncertain). (2 marks)

Q7. (5 marks)

• Correlation risk = the risk that multiple positions move together, so a diversified-looking portfolio actually behaves like one big bet. (2 marks)
• Two positively correlated positions (e.g. two bank stocks, or two tech stocks) tend to rise and fall together; a single adverse market move hits both simultaneously, effectively doubling the exposure/loss rather than diversifying it. (3 marks for valid example + explanation)

Q8. (5 marks)

• Total portfolio exposure = the sum of capital (or total risk) committed across all open positions at once. (2 marks)
• Even if each trade risks only 1-2%, many simultaneous trades add up; correlated losses could trigger many stops at once, producing a large combined drawdown. A total exposure cap limits aggregate risk. (3 marks)

Q9. (5 marks)

• Risk of ruin = the probability that a trader loses enough capital to be unable to continue trading (account depleted below a viable level). (3 marks)
• Two factors that increase it: (i) risking too large a fraction per trade; (ii) low win rate / poor reward-to-risk edge; (also acceptable: high correlation, long losing streaks, small account). (2 marks: 1 each)

Q10. (3 marks)

• Principle: increase position size when equity/performance grows and the strategy is working; decrease size after losses or during drawdown. (2 marks)
• Benefit of reducing size after a losing streak: protects remaining capital, limits further damage while confidence/edge is uncertain, and eases psychological pressure. (1 mark)

[
  {"claim":"Q2a: 2% of 50000 = 1000","code":"result = (0.02*50000 == 1000)"},
  {"claim":"Q2b: shares = 1000/(200-190) = 100","code":"result = (1000/(200-190) == 100)"},
  {"claim":"Q5a: 5% of 20000 = 1000","code":"result = (0.05*20000 == 1000)"},
  {"claim":"Q6b: Kelly f* = (2*0.6-0.4)/2 = 0.4","code":"result = (Rational(2*Rational(6,10)-Rational(4,10),2) == Rational(2,5))"}
]