What Markets Are

Question 1

(a) Spread & price discovery (6)

• Definition (1): Bid–ask spread = lowest ask − highest bid = best price a buyer pays minus best price a seller receives.
• Absolute spread (1): $1501.00 - 1499.00 = ₹2.00$.
• Mid-price (1): $\frac{1501+1499}{2} = ₹1500.00$.
• Spread in bps (1): $\frac{2.00}{1500.00} \times 10000 = 13.33$ bps.
• Interpretation (2): A tighter spread means the marginal cost of immediacy is low → high liquidity. It also means the market's best buyers and sellers agree closely on value, so the mid-price reflects consensus information tightly (efficient price discovery). Wide spreads signal uncertainty/thin depth/adverse-selection risk.

(b) VWAP & implementation shortfall (7)

• Order = 550 shares. Ask 1 supplies 300 @ 1501, Ask 2 supplies remaining 250 @ 1502. (2 for correct fill split)
• Cost $= 300(1501) + 250(1502) = 450300 + 375500 = 825800$. (1)
• VWAP $= 825800 / 550 = ₹1501.4545...$ ≈ ₹1501.45. (2)
• Implementation shortfall vs mid (1500): $1501.4545 - 1500 = ₹1.4545$ per share; total $= 1.4545 \times 550 = ₹800$. (1)
• In bps: $\frac{1.4545}{1500}\times10000 = 9.70$ bps. (1)

(c) Kyle's lambda (6)

• Marginal price moved from 1501 (first 300 shares) to 1502 (next 400). The incremental price jump per share as depth is consumed: over the ask side, price rises ₹1 across the 300→700 cumulative boundary.
• Estimate $\lambda$ = Δprice / Δquantity using level spacing: $\lambda = \dfrac{1502-1501}{ \text{shares to move one level}}$. Taking the shares consumed to move from level-1 exhaustion (300) to next tick = 400-share layer: a reasonable estimate $\lambda \approx \dfrac{1}{400} = ₹0.0025$/share. (2) (Accept $\lambda \approx 1/350$ using average depth ≈ ₹0.00286; state method.)
• Predict last (700th) share of a 700-share buy: 700 exactly exhausts both levels (300+400), so the last share fills at ₹1502 (the marginal price). Using linear model $P(700) = 1500 + \lambda(700)$: with $\lambda=0.0025$, $P = 1500 + 1.75 = ₹1501.75$ — note the model underestimates discrete book price (1502). (2)
• Assumption that breaks (2): Linearity assumes continuous, uniform depth. Real books are discrete/lumpy (finite tick sizes, uneven level sizes), and impact is often concave (square-root law) for large orders; also liquidity replenishes over time. Any one valid point earns marks.

(d) walk_book function (5)

def walk_book(order_qty, book):
    # book: ascending list of (price, qty) ask levels
    remaining = order_qty
    cost = 0.0
    for price, qty in book:
        take = min(remaining, qty)
        cost += take * price
        remaining -= take
        if remaining == 0:
            return cost / order_qty      # VWAP
    return None                          # book exhausted, unfilled qty remains

• Correct min() partial fill (2), cost accumulation (1), VWAP return (1), None on exhaustion (1).

Question 2

(a) Market cap & classification (8)

• Definition (1): Market cap = share price × shares outstanding = total equity value at market prices.
• Index relation (1): Cap-weighted index $I \propto \sum_i P_i N_i$ (divisor-adjusted); each stock's weight $= \frac{P_i N_i}{\sum P_j N_j}$.
• Computations (1 each = 3):
  • A: $3000 \times 9\times10^8 = 2.7\times10^{12}$ ₹ = ₹270,000 cr.
  • B: $250 \times 4\times10^8 = 1.0\times10^{11}$ ₹ = ₹10,000 cr.
  • C: $45 \times 1.2\times10^8 = 5.4\times10^9$ ₹ = ₹540 cr.
  • (₹1 crore = ₹$10^7$.)
• Buckets (3): A ≈ ₹270,000 cr → Large cap; B = ₹10,000 cr → Mid cap; C = ₹540 cr → Small cap (just above micro threshold).

(b) Time-zone overlap (7)

• NYSE open 09:30 ET, close 16:00 ET; ET (standard) = UTC−5, IST = UTC+5:30 → IST is 10:30 ahead of ET. (2)
• NYSE open in IST: $09:30 + 10:30 = 20:00$ IST; close: $16:00 + 10:30 = 02:30$ IST (next day). (2)
• NSE open 09:15–15:30 IST. (1)
• Overlap of [20:00, 02:30 IST] and [09:15, 15:30 IST]: no overlap — NSE closes at 15:30, NYSE opens at 20:00 IST. Overlap window = ∅ (zero minutes). (2)

(c) Price ≠ size (5)

• A has price ₹3000, C has price ₹45 → naively "A is 66.7× bigger." (1)
• But size = cap: A = ₹270,000 cr vs C = ₹540 cr → A is 500× larger, not 66.7×. (2)
• Share price depends on how equity is sliced (shares outstanding); a low-priced stock with billions of shares can exceed a high-priced stock with few shares. Only $P\times N$ measures true size. (2)

Question 3

(a) Regime classification (6)

• Series peak = 1200 (index 3). (1)
• Final value = 950. Drawdown $= \frac{1200-950}{1200} = \frac{250}{1200} = 0.2083 = 20.83\%$. (2)
• Since decline from peak > 20%, final point is in a bear market. (2)
• Note the early leg 1000→1200 = +20% was a bull run; regime flipped after the peak. (1)

(b) Exchange vs OTC (6)

• Four dimensions (1 each, up to 4): Counterparty — exchange uses central clearing/CCP (anonymous); OTC = bilateral, direct counterparty risk. Transparency — exchange has public order book/prices; OTC opaque/quote-driven. Standardization — exchange contracts standardized; OTC customized. Price formation — exchange = continuous auction; OTC = dealer quotes/negotiation.
• CLOB argument (2): A central limit order book aggregates all buy/sell interest at one venue, so the best bid/ask reflects the whole market's supply–demand; competition among many participants narrows spreads and produces a single transparent consensus price → superior discovery vs fragmented dealer quotes.

(c) Ticker vs scrip code (4)

• Ticker symbol (1): short alphabetic identifier (e.g., INFY on NSE). Scrip code (1): BSE numeric code (e.g., 500209 for Infosys) — same security, different ID scheme.
• Why unique IDs matter (2): Automated/algo systems need unambiguous machine-readable keys to route orders, avoid name collisions, and reconcile the same security across venues; numeric/symbolic uniqueness prevents mis-trades.

[
  {"claim":"Mid-price is 1500 and spread is 13.333 bps","code":"bid=1499; ask=1501; mid=(bid+ask)/2; spread_bps=(ask-bid)/mid*10000; result = (mid==1500) and (abs(spread_bps-13.3333)<0.01)"},
  {"claim":"VWAP for 550-share buy is 1501.4545","code":"cost=300*1501+250*1502; vwap=Rational(cost,550); result = abs(float(vwap)-1501.4545)<0.001"},
  {"claim":"Implementation shortfall vs mid 1500 is 800 rupees total and 9.697 bps","code":"vwap=Rational(300*1501+250*1502,550); mid=1500; total=(vwap-mid)*550; bps=(vwap-mid)/mid*10000; result = (total==800) and (abs(float(bps)-9.697)<0.01)"},
  {"claim":"Market caps: A=270000cr, B=10000cr, C=540cr","code":"A=3000*900000000/10**7; B=250*400000000/10**7; C=45*120000000/10**7; result = (A==270000) and (B==10000) and (C==540)"},
  {"claim":"Peak drawdown of final point is 20.83% (bear market)","code":"series=[1000,1150,1200,1080,990,950]; peak=max(series); dd=(peak-series[-1])/peak; result = (abs(float(dd)-0.208333)<0.001) and (dd>Rational(20,100))"},
  {"claim":"NSE(9:15-15:30 IST) and NYSE(20:00-02:30 IST) do not overlap","code":"nse=(9*60+15, 15*60+30); nyse=(20*60, 24*60+2*60+30); overlap=max(0, min(nse[1],nyse[1])-max(nse[0],nyse[0])); result = (overlap==0)"}
]