Understand bid-ask spread components — Hinglish notes

6.3.5 · Stock-Market › Market Microstructure

Bid-ask spread HAI kya?

Market maker (MM) dono sides simultaneously quote karta hai. Woh din mein kaafi baar bid pe sasta khareed ke aur ask pe mehnga bech ke spread kamaata hai. Positive spread competition ke baad bhi kyun bachi rehti hai? Kyunki MM ko sach mein kharche uthane padte hain; agar spread zero hota toh woh diwaaliya ho jaata.

Spread kyun exist karta hai? Teeno components

Spread teeno compensations ka sum hai jo MM demand karta hai. Yeh hai Stoll / Glosten–Harris decomposition:

$S = order processing 2 C_{o} + inventory holding 2 C_{i} + adverse selection 2 C_{a}$

Hum har ek ko mid ke around half-spread ke roop mein likhte hain, toh full spread har half ka do guna hota hai.

1. Order-processing cost ( $C_{o}$ )

Fixed, mechanical costs: exchange fees, clearing, technology, MM ki mehnat/profit margin. Yeh kaise behave karta hai: har trade pe roughly constant rehta hai, isliye yeh saste/illiquid stocks ke liye spread zyada wide karta hai (chhoti price pe fixed cost bada lagta hai).

2. Inventory-holding cost ( $C_{i}$ )

Jab tum MM ko bechte ho, toh uske paas ab ek long position aa jaati hai jo woh chahta nahi tha. Use hold karne mein woh price risk uthata hai aur capital phansaa deta hai. Yeh kaise behave karta hai: woh inventory unload karne ke liye apne quotes skew karta hai — agar woh zyada long hai, toh woh buyers ko attract karne ke liye bid aur ask dono neeche kar deta hai. Volatility $σ$ aur holding time ke saath badhta hai.

3. Adverse-selection cost ( $C_{a}$ )

Yeh wala subtle hai. Kuch traders informed hote hain (unhe woh news pata hoti hai jo MM ko nahi). Agar ek informed trader khareedta hai, toh price badhne wali hai — MM us fill pe nuksaan uthata hai. Woh pehle se informed aur noise traders mein fark nahi kar sakta, isliye woh average pe break even karne ke liye spread wide kar deta hai. Yeh kaise behave karta hai: informed trading ki probability aur information asymmetry ke saath badhta hai.

Figure — Understand bid-ask spread components

DERIVATION: pehle principles se adverse-selection spread

Aaiye spread ko yaad karne ki jagah banaayen. Yeh ek stripped Glosten–Milgrom model hai.

Ask derive karna. MM ko $P_{a}$ = $V$ ki expected value given ki buy order aayi set karni hai. KYUN? Kyunki ek rational competitive MM zero expected profit kamaata hai; ask conditional expectation ke barabar hona chahiye, warna competitors undercut kar dete hain ya woh paisa kho deta hai.

$P_{a} = E [V ∣ buy] = v_{H} P (v_{H} ∣ buy) + v_{L} P (v_{L} ∣ buy) .$

$P (buy ∣ v_{H})$ compute karo. Agar value High hai, toh informed traders ( $α$ ) sab khareedte hain; noise ( $1 - α$ ) prob $1/2$ se khareedte hain: $P (buy ∣ v_{H}) = α + (1 - α) \frac{1}{2} = \frac{1 + α}{2} .$ Agar value Low hai, toh informed sab bechte hain, noise ab bhi aadha time khareedte hain: $P (buy ∣ v_{L}) = (1 - α) \frac{1}{2} = \frac{1 - α}{2} .$

Buy ki total prob $= \frac{1}{2} \cdot \frac{1 + α}{2} + \frac{1}{2} \cdot \frac{1 - α}{2} = \frac{1}{2}$ (symmetric, accha sanity check).

Bayes: $P (v_{H} ∣ buy) = \frac{\frac{1}{2} \cdot \frac{1 + α}{2}}{\frac{1}{2}} = \frac{1 + α}{2} .$

Toh $P_{a} = v_{H} \frac{1 + α}{2} + v_{L} \frac{1 - α}{2} = m + \frac{α}{2} (v_{H} - v_{L}) .$

Symmetry se (ek sell order): $P_{b} = m - \frac{α}{2} (v_{H} - v_{L}) .$

Spread: $S = P_{a} - P_{b} = α (v_{H} - v_{L}) .$

Worked examples

Forecast-then-Verify

Common mistakes (Steel-manned)

Flashcards

Bid-ask spread ke teen components kya hain?

Order-processing cost, inventory-holding cost, aur adverse-selection cost.

Quoted bid-ask spread define karo.

S = P_{a} - P_{b}

, ask minus bid.

Mid-price kya hai aur yeh kya represent karta hai?

m = (P_{a} + P_{b}) /2

; market ka prior best estimate of fair value.

Glosten–Milgrom model mein spread kiske barabar hota hai?

S = α (v_{H} - v_{L})

: informed traders ka fraction times value uncertainty.

Competitive market maker ask ko

E [V ∣ buy]

kyun set karta hai?

Zero-profit condition — competition quote ko conditional expected value ke barabar force karta hai; warna woh undercut ho jaata hai ya paisa kho deta hai.

Kaun sa component earnings release se pehle spread widen karta hai?

Adverse selection — informed trading ka chance/impact zyada hota hai.

Spread paane ke liye har half-spread component ko 2 se kyun multiply karte hain?

Har cost mid ke dono sides (bid aur ask) par charge hoti hai, isliye full spread har half-spread ka do guna hota hai.

Effective spread ka formula?

2 \times ∣ P_{trade} - m ∣

; actual round-trip cost, quoted se chhota ho sakta hai agar price improvement mile.

Adverse-selection cost kin do quantities ke saath badhti hai?

Informed trading ki probability

α

aur information asymmetry / value uncertainty

(v_{H} - v_{L})

Buy order aane ke baad expected true value kis direction mein move karti hai?

Upar — ask ki taraf; order khud informative hota hai (price impact).

Recall Feynman: 12 saal ke bache ko samjhao

Socho tum ek lemonade stall chalate ho jahan tum used cups khareedte bhi ho aur fresh lemonade bechte bhi ho. Tum 5 rupaye mein bechte ho, 4 rupaye mein wapas khareed lete ho — woh 1 rupaye ka gap tumhara spread hai. Gap kyun rakho? (1) Cups, sugar, aur tumhara time sab mein paisa lagta hai (order processing). (2) Agar tum ek cup khareed lo jo tumhe chahiye nahi, toh shayad tum usse roke raho aur woh kharaab ho jaaye (inventory). (3) Kabhi kabhi ek baccha saari lemonade khareed leta hai kyunki use pata hota hai ki bahut garmi aane wali hai aur sab chahenge — tum saste mein bech diye aur nuksaan uthaya (adverse selection). Un clever bachon se toot na jaane ke liye tum gap thoda aur wide rakhte ho. Wahi gap bid-ask spread hai!

Connections

Market Microstructure — parent chapter.
Market Makers and Liquidity Provision — kaun spread quote karta hai.
Glosten-Milgrom Model — poora information-based derivation.
Order Flow and Price Impact — trades mid ko kaise move karte hain.
Adverse Selection and Information Asymmetry — sabse gehra spread component.
Effective vs Quoted vs Realized Spread — measurement ke variants.
Volatility and Liquidity — inventory cost driver.