Parity Price

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Parity Price — Definition and Uses

Parity price describes a price level at which two assets or securities are equal in value. The concept appears across markets—convertible bonds, options, commodities, currencies, and interest-rate relationships—and helps investors identify equivalence points, conversion opportunities, or arbitrage.

Key Concepts

  • Parity = equality or equivalence in value between two instruments.
  • How parity is applied depends on context: conversion decisions for convertible bonds, intrinsic value for options, exchange-rate comparisons for currencies, purchasing power for goods, and risk allocation across asset classes.

Convertible Bonds: Conversion Parity

Conversion parity (or parity price) for a convertible bond is the implied price per share if the bond is converted into equity.

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

Example:
A $1,200 market price for a convertible bond that converts into 20 shares implies a parity price of $1,200 / 20 = $60 per share. If the stock trades above $60, conversion is potentially profitable.

Options: Intrinsic Parity and Put–Call Parity

  • Intrinsic parity: An option is at parity when its market price equals its intrinsic value. E.g., a call with a $50 strike on a $60 stock has $10 intrinsic value; if the option costs $10, it is at parity.

  • Put–call parity: A theoretical relationship linking European puts and calls with the same strike and expiry.
    Formula:
    C + PV(X) = P + S
    Where C = call price, P = put price, S = current stock price, PV(X) = present value of strike price X.
    This relationship helps identify mispricing and arbitrage opportunities.

Currencies and Purchasing Power Parity (PPP)

  • Forex parity: Two currencies are at parity when they exchange one-for-one (1:1).
  • Purchasing Power Parity (PPP): Compares the cost of a basket of goods across countries after adjusting for exchange rates—the idea being identical goods should cost the same in both countries once prices are converted into a common currency.

Interest Rate Parity (IRP)

Interest rate parity links spot and forward exchange rates to interest rates in two countries. It expresses the no-arbitrage condition for covered currency investments.

Formula:
F0 = S0 × ((1 + ic) / (1 + ib))
Where F0 = forward rate, S0 = spot rate, ic = interest rate in country c, ib = interest rate in country b.

  • Covered IRP: The no-arbitrage condition when forward contracts are used to hedge exchange-rate risk.
  • Uncovered IRP: A theoretical relation between expected spot rates and interest rates without hedging (subject to risk premia and expectations).

Commodities and Agricultural Parity

For agricultural commodities, parity can mean the purchasing power of a commodity relative to farmers’ production costs (wages, loan interest, equipment). Policymaking definitions have historically linked parity prices to average past prices to assess price support needs.

Risk Parity

Risk parity is an asset-allocation approach that weights portfolio allocations by risk contribution (equities, credit, rates, commodities) rather than by dollar capital. The goal is balanced risk exposure across asset classes.

Percent of Parity

Percent of parity measures how close two prices or rates are to equality. Parity equals 100%; if one is at 90% of parity, it is 10 percentage points away from full parity.

Takeaways

  • Parity denotes equality between values and is a cross-market concept useful for valuation, conversion decisions, and identifying arbitrage.
  • Key formulas:
  • Convertible parity = value of convertible / conversion ratio
  • Put–call parity: C + PV(X) = P + S
  • Interest rate parity: F0 = S0 × ((1 + ic) / (1 + ib))
  • Understanding parity conditions helps investors spot conversion opportunities, detect mispricing, and assess currency and commodity relationships.