Understand spread and execution cost impact — Stock-Market notes

WHAT is the spread?

WHY does a spread exist? Because a market maker stands ready to buy from sellers and sell to buyers instantly. For providing this instant liquidity, they buy low (bid) and sell high (ask), pocketing the spread as their fee for taking risk.

HOW the spread becomes a real cost

Derivation of round-trip spread cost from first principles.

You buy $Q$ shares. You cannot buy at the mid — you pay the ask: $\text{Cost to enter} = Q \cdot \text{Ask}$ Later you sell at the bid: $\text{Received on exit} = Q \cdot \text{Bid}$ The loss purely from crossing the spread (assuming price unchanged) is: $\text{Loss} = Q\cdot\text{Ask} - Q\cdot\text{Bid} = Q\,(\text{Ask}-\text{Bid}) = Q\cdot S$

Why this step? Because entering and exiting each force you to the worse side of the quote — one full spread lost per round trip.

If we usually measure our reference from the mid (what we thought the "fair" price was), then a single side (just buying) already costs half the spread: $\text{Half-spread cost} = Q\cdot\frac{S}{2}$

WHY this destroys frequent traders

Suppose relative round-trip cost is $c$ per trade and you make $N$ trades. If each trade's cost compounds against you: $\text{Capital after } N \text{ trades} = V_0\,(1-c)^N$

Why $(1-c)^N$ ? Each round trip shaves fraction $c$ off before any profit. Over many trades these fractions compound, just like negative interest.

Worked example The overtrading trap

A ₹100,000 account, relative round-trip cost $c = 0.3\%$ (small spread + brokerage), 200 trades/year: $V = 100000\,(1-0.003)^{200} = 100000\cdot e^{200\ln(0.997)}$ $\ln(0.997)\approx -0.003005,\quad 200\times(-0.003005)=-0.601$ $V \approx 100000\cdot e^{-0.601}\approx 100000\times 0.548 = \mathbf{₹54{,}800}$ Why the shock? You lost ~45% of capital to costs alone, before considering whether your trades were right. This is why 80/20 says: cutting trade frequency is the single highest-leverage improvement for most retail traders.

Figure — Understand spread and execution cost impact

Worked examples

Common mistakes

Active recall

Recall Test yourself (hide answers)

What two prices make up a quote, and which do you buy at?
Write the relative spread formula and say why we divide by the mid.
Why do you lose the full spread on a round trip even if price is flat?
Why does $(1-c)^N$ punish frequent trading so harshly?
When is a market order worth paying the spread?

Recall Explain to a 12-year-old (Feynman)

Imagine a shop that buys your used game for ₹90 but sells the same game for ₹100. If you buy it and change your mind and sell it back one minute later, you're already down ₹10 — the shop keeps that gap for being ready to trade any second. That ₹10 gap is the spread. If you keep buying and selling all day, those little gaps add up and eat your pocket money, even if the game's real value never changed. So trade less, and trade things where the gap is tiny.

Flashcards

What is the bid price?

The highest price a buyer is currently willing to pay.

What is the ask (offer) price?

The lowest price a seller is currently willing to accept.

Define the spread.

Ask − Bid; the gap between the best sell and best buy prices.

Formula for relative spread?

(Ask − Bid) / Mid × 100%, with Mid = (Bid+Ask)/2.

Why divide the spread by the mid price?

To compare cost across stocks of different price levels; only the % figure is comparable.

At which price do you BUY with a market order?

The ask (the higher price).

At which price do you SELL with a market order?

The bid (the lower price).

Round-trip spread loss for Q shares?

Q × (Ask − Bid) = Q × S, even if price doesn't move.

Why do you lose a full spread per round trip?

You enter at the worse side (ask) and exit at the worse side (bid), crossing the gap twice.

Capital after N trades with round-trip cost c?

V₀ × (1 − c)^N — costs compound multiplicatively.

Who profits from the spread and why?

Market makers, as payment for providing instant liquidity and bearing inventory risk.

What is slippage?

The extra cost when a large order fills across worse price levels than the top-of-book quote.

Market order vs limit order trade-off?

Market pays the spread for certainty/speed; limit may earn the spread but risks not filling (or adverse selection).

Why does a small absolute spread still matter?

On a low-priced stock it's a large % per trade and compounds over many trades.

Connections

Bid-Ask Spread and Market Makers
Order Types — Market vs Limit vs Stop
Liquidity and Volume
Slippage and Market Impact
Brokerage Fees and Transaction Costs
Overtrading and Behavioural Mistakes
Position Sizing and Risk Management

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho bhai, jab bhi tum stock ka price screen pe dekhte ho, wo ek single number nahi hota — actually do prices hote hain. Bid wo price hai jispe koi tumse kharidne ko taiyaar hai (yaani tum ise sell karoge), aur Ask wo price hai jispe koi tumhe bechne ko taiyaar hai (yaani tum ise buy karoge). Ask hamesha Bid se thoda upar hota hai, aur beech ka gap = spread. Ye spread market maker ki fees hai jo instant liquidity dene ke badle apni jeb mein daal leta hai.

Ab important baat: jab tum buy karte ho to Ask pe (upar wala price) lena padta hai, aur jab sell karte ho to Bid pe (neeche wala) bechna padta hai. Matlab ek round trip mein tum poora spread loss karte ho — chahe stock ka price ek paisa bhi na hile! Isliye ₹0.05 ka spread ₹10 wale stock pe 0.5% ka jhatka hai, but ₹2000 wale stock pe wo 0.0025% — negligible. Isiliye hamesha relative spread (percentage mein) dekho, absolute rupaya nahi.

Sabse bada khel yahan hai: agar har trade ka cost $c$ hai aur tum $N$ trades karte ho, to capital $(1-c)^N$ ke hisaab se ghatta hai — ye compound hota hai negative interest ki tarah. ₹1 lakh, 0.3% cost, 200 trades saal mein = sirf ~₹54,800 bachte hain, sirf cost se! Isliye 80/20 rule kehta hai: kam trade karo, aur liquid (high-volume, tight-spread) stocks mein trade karo. Market order fast hai par spread pay karta hai; limit order spread bachata hai par fill hone ki guarantee nahi. Apni P&L hamesha apne actual fill price se exit bid tak naapo — ticker ka "last price" jhoot bolta hai.

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