Define liquidity and why it matters

Core Concept

Key dimensions:

• Speed: How fast can you execute a trade?
• Price stability: Does selling move the price against you?
• Transaction cost: Spreads, fees, slippage.

Why Liquidity Exists: The Matching Problem

Markets need two sides for every trade: a buyer and a seller agreeing on price. Liquidity measures how well the market solves this matching problem.

High liquidity = Many buyers and sellers, narrow bid-ask spread, instant execution.
Low liquidity = Few participants, wide spread, price impact from your order.

Deriving the Bid-Ask Spread (First Principles)

The bid-ask spread is the liquidity cost. Let's derive why it exists:

1. Market makers (dealers) provide liquidity by posting buy (bid) and sell (ask) prices.
2. They face inventory risk: if they buy your stock, the price might drop before they resell.
3. They also face adverse selection: informed traders might know more than them.

The spread is simply the observable gap between the two quotes:

From first principles — why market makers demand it:
A market maker's round-trip is: buy from a seller at $P_{\text{bid}}$, later sell to a buyer at $P_{\text{ask}}$. Their gross gain per round-trip is the whole spread $(P_{\text{ask}} - P_{\text{bid}})$. But they must set this spread wide enough to cover two costs:

• $C_{\text{inventory}}$: while the dealer holds the stock, its price can move against them. This cost grows with volatility.
• $C_{\text{adverse}}$: sometimes the counterparty knows something the dealer doesn't (bad news), so the dealer systematically loses to informed traders.

Competition drives the spread down until the gross gain just covers these costs (zero abnormal profit). This is the intuition captured by classic microstructure models (Roll 1984 for inventory; Glosten–Milgrom 1985 for adverse selection). The precise functional form depends on the model chosen and is beyond a bare formula — the key takeaway is:

Why this step? We're showing why the spread is not arbitrary — it is the market maker's break-even compensation for risk, not a random fee.

A full round-trip (buy then later sell) crosses the spread twice, so it costs the entire spread:

For a $100 stock with a %0.10 spread: buying costs \0.05/share (one-way); a full buy-and-later-sell round-trip costs$0.10/share (0.10%).

Why Liquidity Matters: Three Critical Reasons

1. Transaction Costs Scale with Illiquidity

• Stock B (Microcap): Bid $10.00, Ask \backslash10.50 (5% spread). You buy 100 shares → pay \1,050. One-way cost of immediacy:$25 (half-spread × 100).

Why this step? Illiquid markets tax every trade. For active strategies, this erodes returns. Your $25 one-way cost on Stock B is 50× the cost on Stock A for the same trade size.

Math derivation:
If you complete $N$ full round-trips per year, the total spread cost is (each round-trip pays the whole spread):

More cleanly, using the relative spread $s = \text{Spread}/P$ and dollar position $V$:

With $s = 5\%$, 10 round-trips/year on a $10,000 position:

You'd need 50% annual return just to cover trading costs!

2. Price Impact (Market Depth)

When you place a large order in an illiquid market, you move the price against yourself.

Where:

• $Q$: your order size (shares)
• $\lambda$: Kyle's lambda (price impact coefficient, inversely related to liquidity)

Derivation:
Assume market depth $D$ (total shares available at each price level). If you buy $Q$ shares exceeding $D$, you "walk up the order book," paying progressively higher prices. If the price rises linearly with cumulative quantity, the marginal price after quantity $q$ is $P_0 + \lambda q$. The average price you pay is the integral of the marginal price divided by total quantity:

Why this step? The $\frac{1}{2}$ factor comes from integrating over the linear price impact—you pay the average of the price range you sweep, not the worst price.

Average price:

You lose $0.50/\text{share} × 10,000 = $5,000$5,000** to illiquidity.

3. Emergency Exit Risk

Illiquidity traps you in a position. During market stress (crashes, company scandals), liquidity evaporates:

• Bid-ask spreads widen 10-100×.
• Market depth collapses.
• You may be unable to exit at any reasonable price.

Lesson: Liquidity risk is distinct from price risk. Even "safe" assets become dangerous if you can't sell them.

Common Mistakes

Test: Compare

• Stock X: $1, 50M shares/day,$0.01 spread → Liquid (1% spread relative to price).
• Stock Y: $100, 5K shares/day,$5 spread → Illiquid (5% spread).

Measuring Liquidity

1. Bid-Ask Spread (Relative):

   $$\text{Relative Spread} = \frac{P_{\text{ask}} - P_{\text{bid}}}{P_{\text{mid}}} \times 100\%$$

2. Turnover Ratio:

   $$\text{Turnover} = \frac{\text{Trading Volume}}{\text{Shares Outstanding}}$$

   High turnover → liquid (many shares change hands).

3. Amihud Illiquidity Ratio:

   $$\text{ILLIQ} = \frac{|R_t|}{V_t}$$

   Where $R_t$ = daily return, $V_t$ = dollar volume. Measures price impact per dollar traded.

Why this step? Amihud captures the price sensitivity to trading—how much does $1M of buying move the price?

Feynman Explanation

Stock markets work the same way: some stocks (Apple, Microsoft) have millions of people trading every second—super liquid. Others (tiny companies) have maybe 10 trades a day—illiquid. If you need to sell fast (emergency, you need cash), illiquid stocks are scary: you might have to accept half the "real" price just to find a buyer.

Liquidity = How fast can you turn your thing into cash without losing money?

Mnemonic

Active Recall Questions

#flashcards/stock-market

Connections

• 1.1.01-What-is-a-market: Markets enable trade; liquidity measures how well they enable it.
• 1.1.05-Bid-and-ask-prices: Bid-ask spread is the observable manifestation of liquidity cost.
• 1.2.03-Market-makers-and-specialists: Market makers provide liquidity by posting continuous quotes.
• 2.3.02-Transaction-costs-and-slippage: Illiquidity directly drives transaction costs.
• 3.1.04-Market-depth-and-order-book: Depth determines price impact (Kyle's lambda).
• 4.2.01-Liquidity-risk-in-crisis: Liquidity evaporation amplifies market crashes.

Created: 2026-06-30 | Review: Use Amihud ratio to screen for liquid stocks before trading.

Concept Map

Hinglish (regional understanding)