Parity

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Parity

Key takeaways

  • Parity denotes equality or equivalence in price or value between two assets.
  • It appears in multiple contexts: convertible bonds, options, commodities, and currencies.
  • Parity concepts help identify conversion opportunities, fair option pricing, and potential arbitrage.

What parity means in finance

Parity describes a price level at which two assets or securities represent equal economic value. Depending on context, it can indicate:
* The break-even price to convert a convertible bond into common stock.
* An option trading exactly at its intrinsic value.
* Two currencies exchanging one-for-one.
* A benchmark for comparing commodity returns to farmers’ costs.

Convertible-bond parity

Conversion parity price is the share price at which converting a bond into stock is economically equivalent to holding the bond.

Formula:
Conversion parity price = Market value of convertible security / Conversion ratio

Example:
A convertible bond is trading at $1,200 and converts into 20 shares. Parity = $1,200 / 20 = $60 per share. If the stock trades above $60, conversion can be profitable.

Parity in options

  1. Intrinsic parity
  2. An option is at parity when its market price equals its intrinsic value (for a call: max(0, stock price − strike)).

  3. Example: A call with strike $50 on a stock trading at $60 has $10 intrinsic value; if the option costs $10, it is at parity.

  4. Put-call parity

  5. Put-call parity expresses the relationship between European call and put prices with the same strike and expiration.
  6. Formula: C + PV(X) = P + S
    • C = call price
    • P = put price
    • S = current stock price
    • PV(X) = present value of the strike price X
  7. Deviations from this relationship signal potential arbitrage.

Parity in currencies and forex

Currency parity occurs when two currencies exchange at a one-to-one rate. Parity concepts in FX include:

  • Interest Rate Parity (IRP)
  • IRP links spot and forward exchange rates to interest rate differentials between countries.
  • Formula: F0 = S0 × (1 + ic) / (1 + ib)
    • F0 = forward rate
    • S0 = spot rate
    • ic = interest rate in country c
    • ib = interest rate in country b

  • The idea: hedged returns across currencies should be equal; IRP helps identify arbitrage and hedge costs.

  • Covered vs. uncovered interest rate parity

  • Covered IRP: no-arbitrage holds when forward contracts are used to hedge FX risk.
  • Uncovered IRP: theoretical parity between interest rates and expected exchange rate changes without using forwards.

Purchasing Power Parity (PPP)

PPP compares the purchasing power of currencies by asking whether a basket of goods costs the same in different countries after adjusting for exchange rates. It’s a long-run benchmark for currency valuation rather than a short-term trading tool.

Parity for commodities and agriculture

In agricultural contexts, parity price can mean the purchasing power of a commodity relative to farmers’ production costs (wages, interest, equipment). Historically, parity measures have been used in policy to assess fair farm prices and justify support actions.

Risk parity

Risk parity is an asset-allocation approach that weights portfolio allocations by risk contribution (e.g., equities, credit, interest rates, commodities) rather than by capital. The goal is to balance sources of portfolio risk rather than dollar allocations across asset classes.

Percent of parity

Percent of parity measures how close two prices or rates are to parity, with parity defined as 100%. For example, if one price is at 90% of parity, it is 10 percentage points below parity.

Why parity matters

Parity concepts reveal when assets are fairly priced relative to each other and highlight deviations that may create conversion opportunities or arbitrage. Understanding different types of parity (conversion, option, interest rate, purchasing power, and risk) helps investors make informed decisions across markets.