What to Trade
Level 4 (Application) | Time: 60 minutes | Total Marks: 50
Instructions: Show all working. Formulae must be stated before substitution. Round monetary values to 2 decimals unless stated.
Q1. Liquidity & Slippage Decision (10 marks)
A trader wants to buy 8,000 shares of two candidate stocks. The Level-2 order books at the best 3 ask levels are:
| Stock A | Price (₹) | Qty | Stock B | Price (₹) | Qty |
|---|---|---|---|---|---|
| Ask 1 | 250.00 | 3,000 | Ask 1 | 251.00 | 1,000 |
| Ask 2 | 250.50 | 3,000 | Ask 2 | 253.00 | 1,500 |
| Ask 3 | 251.00 | 4,000 | Ask 3 | 256.00 | 3,000 |
The best bid is ₹249.50 for A and ₹249.00 for B.
(a) Compute the volume-weighted average fill price (VWAP) to buy 8,000 shares of each. If the book cannot fill 8,000, fill what it can and note the shortfall. (4) (b) Compute the slippage per share for each (fill VWAP minus the best ask), and the total extra cost versus buying all at best ask. (3) (c) State which stock is more liquid for this order size and give a one-line risk consequence of trading the illiquid one. (3)
Q2. Index vs Basket Correlation (12 marks)
Bank Nifty is (simplified) a 2-stock index with weights: HDFCB 60%, ICICIB 40%. Daily returns over 4 days:
| Day | HDFCB | ICICIB |
|---|---|---|
| 1 | +1.0% | +2.0% |
| 2 | −0.5% | +0.5% |
| 3 | +1.5% | +1.0% |
| 4 | 0.0% | −1.5% |
(a) Compute the daily index return for each day using the weights. (3) (b) Compute the correlation coefficient between HDFCB and ICICIB daily returns. (6) (c) A trader claims: "Because these two are the index, they must be perfectly correlated." Using your result, evaluate this claim in 2 sentences. (3)
Q3. F&O Instrument Selection (10 marks)
A trader is mildly bullish on Nifty (spot 24,000) over the next 2 weeks but wants defined risk. Available:
- Futures (lot 50), margin ₹1,20,000
- 24,000 Call, premium ₹180 (lot 50)
- 24,200 Call, premium ₹90 (lot 50)
(a) For the long 24,000 Call alone, compute maximum loss and the breakeven spot at expiry. (3) (b) The trader instead buys the 24,000 Call and sells the 24,200 Call (a bull call spread). Compute net premium paid, max profit, max loss, and breakeven. (5) (c) Give one reason (from a "what to trade" standpoint) why the spread is preferable here to a naked long future. (2)
Q4. Watchlist Screening & Relative Strength (10 marks)
A screener returns 4 stocks. Relative Strength (RS) here = stock's % gain ÷ sector index % gain over the same period.
| Stock | 20-day % gain | Sector | Sector 20-day % gain | Avg daily value traded (₹ cr) |
|---|---|---|---|---|
| P | +12 | Auto | +8 | 320 |
| Q | +6 | IT | +10 | 90 |
| R | +18 | Auto | +8 | 15 |
| S | +9 | IT | +10 | 210 |
(a) Compute the RS ratio for each stock. (4) (b) The trader's watchlist rules: include only stocks with RS > 1.0 AND avg daily value ≥ ₹100 cr. List the qualifying stocks. (3) (c) Stock R has the highest raw gain but fails. Explain in 2 sentences why the value-traded filter matters more than raw return for a swing trader. (3)
Q5. Currency & Commodity Position Sizing (8 marks)
A trader has ₹5,00,000 capital and risks 2% per trade.
(a) They short USDINR futures (1 lot = $1,000, i.e., contract value moves ₹1,000 per 1.00 move in the rate) with a stop of 0.35 rupees. How many lots keep risk within budget? (3) (b) Alternatively they buy Gold futures (1 lot = 100 g; ₹ moves per lot = 100 × price change per gram) with a stop of ₹40 per gram. How many lots stay within the same risk budget? (3) (c) State one reason correlation between instruments should be checked before holding both positions together. (2)
Answer keyMark scheme & solutions
Q1 (10)
(a) VWAP = (Σ price×qty) / total qty. Reason: fills walk up the book.
Stock A (fills 8,000 fully): 3,000@250 + 3,000@250.50 + 2,000@251 = 750,000 + 751,500 + 502,000 = 2,003,500 / 8,000 = ₹250.4375 ✅ (2)
Stock B: available = 1,000+1,500+3,000 = 5,500 only → shortfall 2,500 shares. Cost = 1,000@251 + 1,500@253 + 3,000@256 = 251,000 + 379,500 + 768,000 = 1,398,500 / 5,500 = ₹254.2727 ✅ (2)
(b) Slippage = VWAP − best ask.
- A: 250.4375 − 250.00 = ₹0.4375/share; extra cost = 0.4375×8,000 = ₹3,500 (1.5)
- B (on 5,500 filled): 254.2727 − 251.00 = ₹3.2727/share; extra = 3.2727×5,500 = ₹18,000 ✅ (1.5)
(c) Stock A is more liquid — fills full size at low slippage. (2) Risk of illiquid B: cannot exit full position quickly; wide slippage worsens on exit, and impact cost can wipe the trade edge. (1)
Q2 (12)
(a) Index return = 0.6·H + 0.4·I. Reason: weighted contribution.
- D1: 0.6(1.0)+0.4(2.0) = 0.6+0.8 = 1.4%
- D2: 0.6(−0.5)+0.4(0.5) = −0.3+0.2 = −0.1%
- D3: 0.6(1.5)+0.4(1.0) = 0.9+0.4 = 1.3%
- D4: 0.6(0)+0.4(−1.5) = −0.6% ✅ (3)
(b) Means: H̄ = (1.0−0.5+1.5+0)/4 = 0.5; Ī = (2.0+0.5+1.0−1.5)/4 = 0.5. Deviations H: 0.5, −1.0, 1.0, −0.5; I: 1.5, 0, 0.5, −2.0. Cov numerator Σ(dH·dI) = 0.75 + 0 + 0.5 + 1.0 = 2.25. ΣdH² = 0.25+1+1+0.25 = 2.5; ΣdI² = 2.25+0+0.25+4 = 6.5. r = 2.25 / √(2.5·6.5) = 2.25/√16.25 = 2.25/4.0311 = 0.558 ✅ (6)
(c) Claim is false. A moderate positive correlation (~0.56) means they move together often but not identically; ICICIB's Day-4 fall vs HDFCB flat shows divergence, so index membership does not force perfect correlation. (3)
Q3 (10)
(a) Long call max loss = premium paid = 180×50 = ₹9,000. Reason: option buyer's loss is capped at premium. Breakeven = strike + premium = 24,000 + 180 = 24,180 ✅ (3)
(b) Bull call spread:
- Net premium = 180 − 90 = ₹90/share = ₹4,500/lot (paid) (1)
- Max loss = net premium = ₹4,500 (1)
- Max profit = (spread width − net premium)×50 = (200 − 90)×50 = 110×50 = ₹5,500 (2)
- Breakeven = lower strike + net premium = 24,000 + 90 = 24,090 ✅ (1)
(c) The spread has defined, smaller risk (₹4,500 vs unlimited/large futures loss and ₹1.2 L margin), matching the trader's "defined risk, mildly bullish" view; cheaper capital outlay. (2)
Q4 (10)
(a) RS = stock% ÷ sector%.
- P: 12/8 = 1.50
- Q: 6/10 = 0.60
- R: 18/8 = 2.25
- S: 9/10 = 0.90 ✅ (4)
(b) RS>1.0: P (1.50), R (2.25). Value ≥100: P(320✓), R(15✗). → Only P qualifies. ✅ (3)
(c) R's ₹15 cr turnover means poor liquidity — large slippage on entry/exit and hard to size up, so realized returns fall short of the paper 18%. A swing trader must exit reliably; illiquidity can trap the position regardless of a strong RS. (3)
Q5 (8)
Risk budget = 2% × 5,00,000 = ₹10,000.
(a) Risk per lot = stop × ₹ per point = 0.35 × 1,000 = ₹350. Lots = 10,000 / 350 = 28.57 → 28 lots (round down) ✅ (3)
(b) Risk per lot = 40 × 100 = ₹4,000. Lots = 10,000 / 4,000 = 2.5 → 2 lots ✅ (3)
(c) If USDINR and gold are correlated (both react to USD/inflation), holding both may not diversify risk — combined moves can double the effective loss, breaching the intended 2% budget. (2)
[
{"claim":"Stock A VWAP for 8000 shares = 250.4375","code":"num=3000*250+3000*250.50+2000*251; result=(Rational(num,8000)==Rational(2003500,8000)) and abs(num/8000-250.4375)<1e-9"},
{"claim":"Stock B fills only 5500 with VWAP ~254.2727","code":"cost=1000*251+1500*253+3000*256; result=(1000+1500+3000==5500) and abs(cost/5500-254.27272727)<1e-4"},
{"claim":"Correlation HDFCB/ICICIB = 0.558","code":"cov=Rational(9,4); r=cov/sqrt(Rational(5,2)*Rational(13,2)); result=abs(float(r)-0.5547)<1e-2"},
{"claim":"Bull call spread max profit 5500, max loss 4500, BE 24090","code":"net=180-90; maxp=(200-net)*50; maxl=net*50; be=24000+net; result=(net==90) and (maxp==5500) and (maxl==4500) and (be==24090)"},
{"claim":"USDINR 28 lots, Gold 2 lots within 10000 risk","code":"budget=0.02*500000; usd=int(budget//(0.35*1000)); gold=int(budget//(40*100)); result=(budget==10000) and (usd==28) and (gold==2)"}
]