Backtesting Frameworks

Section A

Q1. (3)

• Backtesting = simulating a trading strategy on historical data to estimate how it would have performed (1).
• One sentence, using rules exactly as they would trade live (1).
• Key assumption: the future market behaves statistically similarly to the historical period tested (stationarity of the edge) (1).

Q2. (3)

• Survivorship bias = using only stocks that still exist today, ignoring delisted/bankrupt/merged companies (1).
• This inflates returns because failures are excluded (1).
• Fix: use a point-in-time / survivorship-bias-free dataset that includes delisted securities (1).

Q3. (3)

• Look-ahead bias = using information in the backtest that would not have been available at the decision time (1).
• Example: computing a signal using today's closing price to place a trade at today's open; or using restated/revised fundamentals (2) (1 for valid example, 1 for correct reasoning).

Q4. (3)

• Commissions = fixed/known fees charged by broker/exchange per trade (1.5).
• Slippage = difference between expected execution price and actual fill price due to market movement/liquidity (1.5).

Q5. (3)

• In-sample = data used to build/optimise the strategy (1).
• Out-of-sample = fresh data withheld to validate it (1).
• In-sample-only results overstate performance because parameters were fitted (curve-fit) to that same data (1).

Q6. (3) — 1 mark each:

• pandas — data handling/manipulation of time-series price data.
• backtrader — event-driven backtesting engine for strategy simulation.
• zipline — backtesting/algorithmic-trading library (Quantopian lineage).

Q7. (3)

• Max DD = the largest peak-to-trough percentage decline in equity over the test period (2).
• A smaller value is preferable (less severe loss) (1).

Q8. (3)

• Paper trading = simulated live trading with real-time data but no real money (1.5).
• Recommended because it validates execution/latency/data issues and psychological discipline that a backtest cannot capture, before risking capital (1.5).

Section B

Q9. (5)

• Formula: $\text{CAGR}=\left(\dfrac{V_f}{V_i}\right)^{1/n}-1$ (1)
• $=(16105/10000)^{1/5}-1 = (1.6105)^{0.2}-1$ (2)
• $\approx 1.10 - 1 = 0.10 = \mathbf{10\%}$ (2)

Q10. (5)

• Max DD $=\dfrac{\text{peak}-\text{trough}}{\text{peak}}=\dfrac{24000-18000}{24000}=\dfrac{6000}{24000}=0.25=\mathbf{25\%}$ (3)
• Matters: shows worst loss an investor must psychologically/financially survive; drives position sizing and risk of ruin (2).

Q11. (7)

• (a) Commission =40\times\5=\mathbf{$200}$ (2)
• (b) Slippage per trade =0.10\%\times\10{,}000=$10$; total$=40\times$10=\mathbf{$400}$ (3)
• (c) Total cost =\200+$400=\mathbf{$600}$ (2)

Q12. (4)

• (a) It estimates the distribution of possible outcomes / range of drawdowns and returns, i.e. how much the single backtest result depended on the luck of ordering (2).
• (b) Resampling assumes returns are independent and identically distributed, so it destroys real autocorrelation/volatility clustering and tail-dependence, understating true risk (2).

[
  {"claim":"Q9 CAGR = 10%","code":"Vf=16105; Vi=10000; n=5; cagr=(Rational(Vf,Vi))**(Rational(1,n))-1; result = abs(float(cagr)-0.10) < 0.001"},
  {"claim":"Q10 Max DD = 25%","code":"dd=(24000-18000)/24000; result = abs(dd-0.25) < 1e-9"},
  {"claim":"Q11a commission = 200","code":"result = 40*5 == 200"},
  {"claim":"Q11b slippage = 400","code":"slip=40*(0.001*10000); result = abs(slip-400) < 1e-9"},
  {"claim":"Q11c total cost = 600","code":"total=40*5 + 40*(0.001*10000); result = abs(total-600) < 1e-9"}
]