Learn about execution algorithms (TWAP, VWAP, POV)

6.5.8 · Stock-Market › HFT & Advanced Concepts

WHY — inki zaroorat kyun hai?

Teeno classic scheduling algorithms is baat mein alag hain ki schedule kya drive karta hai:

Algo	Schedule driven by	Ek-line idea
TWAP	clock	har equal time mein equal amount trade karo
VWAP	volume profile	expected market volume ke proportion mein trade karo
POV	live realized volume	jo abhi trade ho raha hai uska ek fixed percentage trade karo

Figure — Learn about execution algorithms (TWAP, VWAP, POV)

1. TWAP — Time-Weighted Average Price

HOW — first principles se slice size derive karo. Total quantity $Q$ , slices ki number $N$ . Hum chahte hain har slice equal ho, use $q$ bolte hain.

$\sum_{i = 1}^{N} q = Q ⟹ N q = Q ⟹ q = \frac{Q}{N}$

Yeh step kyun? Equal slices ka matlab hai ki $q$ ke $N$ copies ka sum poore parent order $Q$ ke barabar hona chahiye; solve karne par $q = Q / N$ milta hai.

Benchmark price jiske against tumhe measure kiya jaata hai woh har slice par sample kiye gaye prices ka simple average hota hai:

$TWAP = \frac{1}{N} \sum_{i = 1}^{N} P_{i}$

Yeh step kyun? Kyunki humne price $P_{i}$ wale time par equal quantities trade ki, isliye average price paid unweighted average of prices ke barabar hota hai — isliye "Time-Weighted."

2. VWAP — Volume-Weighted Average Price

HOW — schedule derive karo. Maano $u_{i} = \frac{V _{i}}{\sum _{j} V _{j}}$ slice $i$ mein din ke expected volume ka fraction hai (volume profile, historical data se estimate kiya gaya). VWAP ko perfectly track karne ke liye, yeh quantity trade karo:

$q_{i} = Q \cdot u_{i}$

Yeh step kyun? Agar har slice mein tum apne order ka utna hi fraction trade karo jitna market apne total volume ka trade karti hai, toh tumhara participation constant rahega, aur tumhara volume-weighted average price market ke VWAP ke barabar hoga.

Proof ki yeh VWAP match karta hai. Tumhara average price hai $\overset{ˉ}{P} = \frac{\sum _{i} P _{i} q _{i}}{\sum _{i} q _{i}} = \frac{\sum _{i} P _{i} ( Q u _{i} )}{\sum _{i} Q u _{i}} = \frac{\sum _{i} P _{i} u _{i}}{\sum _{i} u _{i}} .$ Kyunki $u_{i} \propto V_{i}$ , yeh $\frac{\sum P _{i} V _{i}}{\sum V _{i}} = VWAP$ ke barabar hota hai. ✔ Yeh step kyun? Constant $Q$ cancel ho jaata hai, aur wohi volume-weighted average reh jaata hai jo VWAP define karta hai.

3. POV — Percentage of Volume (a.k.a. Participation)

HOW — the tradeoff. Tumhari order finish hone ki total time realized market volume par depend karti hai. Agar window ke dauran total market volume $V_{mkt}$ hai, tum complete karte ho $Q_{filled} = ρ V_{mkt} .$ Yeh step kyun? $q_{i} = ρ V_{i}$ ko sum karne par $ρ \sum V_{i} = ρ V_{mkt}$ milta hai.

Toh $Q$ poora fill karne ke liye tumhe market volume ka $V_{mkt} \geq Q / ρ$ chahiye hoga. Completion time tumhare control mein NAHI hai — yahi adaptivity ki cost hai.

Common Mistakes (Steel-manned)

Flashcards

Execution algorithms kaunsa problem solve karte hain?

Yeh ek bade parent order ko child orders mein slice karte hain taaki market impact (bahut fast trading) aur timing risk (bahut slow trading) ko balance kiya ja sake.

TWAP slice size formula aur kyun

q_{i} = Q / N

; har equal time-slice mein equal quantity kyunki

N

equal slices ka sum

Q

hona chahiye.

VWAP benchmark formula

VWAP = \frac{\sum _{i} P _{i} V _{i}}{\sum _{i} V _{i}}

— traded volume se weighted average price.

VWAP schedule (child size)

q_{i} = Q \cdot u_{i}

jahan

u_{i} = V_{i} / \sum_{j} V_{j}

slice

i

mein expected volume ka fraction hai.

POV child order rule

q_{i} = ρ V_{i}

— abhi actually trade ho rahe volume ka fixed percentage

ρ

trade karo.

POV ko Q fill karne mein kitna time lagta hai?

Jab tak cumulative market volume

Q / ρ

tak nahi pahunchta; completion time GUARANTEED nahi hai.

TWAP aur VWAP kab same schedule dete hain?

Jab market volume time ke across uniform ho (

V_{i}

constant), taaki volume weights time weights ke barabar ho jayein.

VWAP ka POV se comparison mein key drawback

VWAP ek forecast volume profile par rely karta hai; POV realized live volume ke saath adapt karta hai.

POV ka TWAP/VWAP se comparison mein key drawback

POV quiet days mein order complete nahi kar sakta; yeh completion certainty ko low impact ke liye sacrifice karta hai.

Market impact kya hota hai?

Tumhari apni trading se hone wali adverse price movement (buying se price upar jaata hai, selling se neeche).

Recall Feynman: 12-saal ke bachche ko explain karo

Socho tum school ki canteen se 100 chocolate bars khareedna chahte ho, lekin agar sab ek saath khareedoge toh shopkeeper notice karega ki tum sach mein chahte ho aur price badha dega. Toh tum thode thode karte khareedoge.

TWAP = har 10 minute mein same number of bars khareedna, chahe kuch bhi ho.
VWAP = recess ke time zyada bars khareedna jab sab khareed rahe hain (taaki koi notice na kare) aur class ke time kam jab canteen khaali hoti hai.
POV = hamesha "counter par har 10 bacho mein se ek" rehna — jab line lambi ho zyada khareedna, jab choti ho kam. Catch yeh hai: agar aaj koi nahi khareedta, tum kabhi finish nahi karte!

Connections

Market Impact & Slippage — woh cost jo yeh algos minimize karte hain.
Implementation Shortfall — ek alternative benchmark jo impact aur delay dono ko penalize karta hai.
Order Book Dynamics — child orders bid/ask depth ke saath interact karte hain.
Volume Profile & U-Shape — intraday volume curve jis par VWAP rely karta hai.
HFT Market Making — counterparty jo aksar in child orders ko fill karti hai.
Almgren-Chriss Optimal Execution — math framework jo TWAP/VWAP ko generalize karta hai.