Comprehensive Guide to Parity Price in Investing

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Parity price is the price at which two related assets, or two ways of holding the same exposure, are worth exactly the same. The most common use is in convertible bonds: the parity price is the share price at which converting the bond into stock gives the holder the same value as the bond’s current market price. Above that share price, conversion is worth more than the bond. Below it, the bond is worth more than the shares it converts into.

The same idea of equivalence appears in options, currencies, international price comparisons and U.S. farm policy. Each context has its own formula, so check which “parity” a document or quote means.

What parity means in finance

In general usage, parity means equality. A price is “at parity” when it equals a benchmark, “above parity” when it exceeds it and “below parity” when it falls short. The benchmark depends on the context: the value of shares received on conversion, an option’s intrinsic value, a one-to-one exchange rate, or a historical purchasing-power standard.

Investors use parity to check whether one asset is priced in line with another it is mechanically tied to. A gap between them may be a premium buyers pay willingly, such as the downside protection in a convertible bond. It may also reflect costs or constraints, or be a mispricing that arbitrage traders try to close.

Parity price formula for convertible bonds

A convertible bond pays interest like a regular bond but lets the holder exchange it for a fixed number of common shares. That fixed number is the conversion ratio. The parity price formula is:

Conversion parity price = market price of the convertible ÷ conversion ratio

The result is a share price. If the stock trades at that price, the shares you would receive on conversion are worth exactly what the bond costs in the market today.

A closely related figure is conversion value:

Conversion value = conversion ratio × current share price

Some bond desks also quote parity as a percentage: conversion value ÷ bond price × 100. At 100%, the stock and the bond are at parity.

Worked example (hypothetical)

Suppose a convertible bond with a $1,000 face value trades at $1,100 and converts into 25 shares.

• Parity price: $1,100 ÷ 25 = $44 per share
• If the stock trades at $40, conversion value is 25 × $40 = $1,000. That is below the $1,100 bond price, so converting now would turn $1,100 of market value into $1,000 of stock.
• If the stock rises to $48, conversion value is 25 × $48 = $1,200. That is above the bond’s $1,100 price, so the shares are worth more than the bond is trading for.

In practice, a bond’s market price tends to move with the stock as conversion value rises, so the parity price is not fixed. It changes every time the bond’s price changes.

Parity price vs. conversion price

These two terms are easy to confuse. The conversion price is set in the bond’s terms: face value ÷ conversion ratio. In the example, $1,000 ÷ 25 = $40. It does not change with the market, except for contractual adjustments such as those made after stock splits. The parity price uses the bond’s current market price instead of face value, so it moves.

Conversion premium and “above parity”

When a convertible trades for more than its conversion value, the difference is the conversion premium:

Conversion premium = (bond price − conversion value) ÷ conversion value

With the stock at $40, the premium is ($1,100 − $1,000) ÷ $1,000 = 10%. Buyers pay this premium because the bond keeps paying interest and has a claim on repayment at maturity, which plain shares do not. When the bond trades close to parity, it behaves mostly like the stock. When it trades far above parity, it behaves more like a straight bond, and measures such as yield to maturity become more relevant to its value.

Parity in options

Trading at intrinsic value

An option is said to trade at parity when its premium equals its intrinsic value, with no time value left. For a call, intrinsic value is the share price minus the strike price (if positive). For a put, it is the strike minus the share price.

Hypothetical example: a call with a $50 strike on a stock trading at $58 has $8 of intrinsic value per share. If the option’s premium is also $8, it is at parity. Since one standard U.S. equity option contract usually covers 100 shares, that is $800 per contract. Deep in-the-money options near expiration often trade close to parity because little time value remains.

Put-call parity

Put-call parity is a different relationship. It links the price of a European call and a European put with the same underlying asset, strike price and expiration:

C + PV(K) = P + S

• C = call price
• PV(K) = present value of the strike price, discounted at the risk-free rate to expiration
• P = put price
• S = current price of the underlying

The logic is that a call plus a risk-free bond paying the strike at expiration produces the same payoff as owning the stock plus a put. Identical payoffs should cost the same.

Hypothetical example, assuming no dividends, a 5% annual risk-free rate and one year to expiration: stock at $100, strike $100, call priced at $10.45. PV(K) = $100 ÷ 1.05 = $95.24. The implied put price is $10.45 + $95.24 − $100 = $5.69. If the put traded meaningfully away from that figure, a trader could in principle buy the cheap side and sell the expensive side. Dividends, early exercise on American-style options, borrowing costs and transaction costs all change the result.

Currency parity and interest rate parity

In foreign exchange, two currencies are at parity when one unit of each buys exactly one unit of the other, an exchange rate of 1.00. The euro fell to parity with the U.S. dollar on July 12, 2022, the first time EUR/USD had touched 1.00 in about 20 years.

Interest rate parity (IRP) is the relationship between interest rates and exchange rates. Its premise is that, once currency risk is hedged, investing in either currency should earn the same return. The forward rate absorbs the interest rate difference:

F₀ = S₀ × (1 + i_c) ÷ (1 + i_b)

Here S₀ is the spot rate and F₀ the forward rate, both quoted as units of currency c per one unit of currency b, and i_c and i_b are the interest rates for the period in each country.

Hypothetical example: EUR/USD spot at 1.1000 (dollars per euro), a one-year dollar rate of 5% and a one-year euro rate of 3%. The one-year forward rate is 1.1000 × 1.05 ÷ 1.03 = 1.1214. The higher-yielding currency, the dollar, trades at a forward discount, which offsets its interest rate advantage. Forex traders compare quoted forward rates against this result to look for arbitrage.

Covered vs. uncovered interest rate parity

Covered interest rate parity holds when a forward contract locks in the exchange rate, so the no-arbitrage condition can actually be enforced with a hedge. Uncovered interest rate parity drops the forward contract. It is a theory that the expected future spot rate will offset the interest rate gap, so it involves exchange rate risk and is a prediction rather than an arbitrage condition.

Purchasing power parity

Purchasing power parity (PPP) compares what money buys in different countries. It prices the same basket of goods in two currencies and asks what exchange rate would make the baskets cost the same:

Implied PPP exchange rate = cost of the basket in country A’s currency ÷ cost of the basket in country B’s currency

Hypothetical example: if a basket costs 120 units of currency X and $100 in the United States, the PPP rate is 1.20 X per dollar. If the market rate is 1.50, the dollar buys more in country X than PPP implies. PPP is used to compare living standards and economic output across countries and to judge whether a currency looks over- or undervalued over long periods.

Parity price in agriculture and percent of parity

In U.S. farm policy, parity price measures the purchasing power of a farm commodity relative to the costs farmers pay, such as wages, interest and equipment. The Agricultural Adjustment Act of 1938 built parity into federal price support, and the modern parity formula relies on a 10-year average of prices farmers received. When market prices fell below a set share of parity, the government could support prices, including through direct purchases.

That share is expressed as percent of parity:

Percent of parity = market price ÷ parity price × 100

Parity equals 100%. A commodity selling at $4.50 against a $6.00 parity price is at 75% of parity, 25 percentage points below it. In grain contracts, a reference to “price and parity” generally points to a price measured against this kind of benchmark, but check the contract’s own definitions.

Risk parity is a different concept

Risk parity is a portfolio construction approach, not a price. Instead of splitting capital among stocks, bonds and cash, it sizes positions so that each asset class, often grouped as equities, credit, interest rates and commodities, contributes a similar share of the portfolio’s risk. Because bonds are typically less volatile than stocks, this can mean holding more of them, sometimes with leverage.

Limitations of parity price

• Parity ignores what the premium buys. A convertible above parity still carries interest payments, a repayment claim and call or conversion terms. An option above parity carries time value. Treating any gap from parity as mispricing misreads both.
• Theoretical parities rest on assumptions. Put-call parity assumes European exercise and known dividends. Interest rate parity assumes free capital movement and no transaction costs. PPP assumes goods are comparable and tradable. Real markets deviate for these reasons, and the gaps can persist.
• Arbitrage is not free. Spreads, financing costs, taxes and settlement constraints can make a visible deviation from parity unprofitable to trade.

FAQs

The Bottom Line

Convertible bond investors, options traders and forex traders all use parity to test whether linked prices line up. A gap from parity often reflects something buyers pay for on purpose, such as interest income, repayment claims or time value. Spreads, financing costs and taxes can also keep an apparent mispricing from being profitable to trade, so confirm which parity a quote or contract means before acting on it.