How does ADR pricing parity work and what creates arbitrage opportunities?

Question

AcadiFi · Accepted Answer

An American Depositary Receipt (ADR) represents a claim on shares of a foreign company, held by a depositary bank. The ADR price should theoretically equal the foreign share price multiplied by the exchange rate and adjusted for the ADR ratio.

**Parity Formula:**

> ADR Price = (Foreign Share Price x ADR Ratio) x Exchange Rate (FC per USD)

Or equivalently:
> ADR Price = Foreign Share Price x Ratio / (USD per FC)

```mermaid
graph TD
    A["Foreign Share
Price = ¥2,400"] -->|"x ADR Ratio (1:2)"| B["Equivalent
¥4,800"]
    B -->|"÷ ¥150/USD"| C["Parity ADR
Price = $32.00"]
    D["Actual ADR
Trading at $33.50"] -->|"Premium!"| E{"Arbitrage?"}
    E -->|"Sell ADR"| F["Short ADR
at $33.50"]
    E -->|"Buy Underlying"| G["Buy Foreign
Shares at ¥2,400"]
    F --> H["Convert &
Deliver"]
    G --> H
    H --> I["Profit = $1.50
per ADR"]
    style C fill:#c9a84c,color:#000
    style I fill:#10b981,color:#000
```

**Worked Example:**
Nakagawa Electronics (fictional) trades in Tokyo at ¥2,400 per share. The ADR ratio is 1 ADR = 2 ordinary shares. The current exchange rate is ¥150/USD.

- Parity ADR price = (¥2,400 x 2) / 150 = **$32.00**
- If the ADR trades at $33.50, it is at a **$1.50 premium**

An arbitrageur would:
1. Buy 2 ordinary shares in Tokyo for ¥4,800 total
2. Deposit them with the depositary bank to create 1 ADR
3. Sell the ADR in New York for $33.50
4. Net profit: $33.50 - $32.00 = **$1.50** (before transaction costs)

**Why Parity Can Break:**
- Time zone gaps (Tokyo is closed when NY is open)
- Capital controls restricting cross-border flows
- High transaction costs or withholding taxes
- Liquidity differences between markets
- Depositary bank fees for creation/cancellation

**Exam Tip:** Know the parity formula cold and be ready to identify whether a premium or discount exists. The CFA exam often gives you three variables and asks you to compute the fourth.

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How does ADR pricing parity work and what creates arbitrage opportunities?

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