## What Is Parity Price?

Parity price refers to a price level that sets two assets or securities equal in value to one another. It is a concept that is used in several markets, including fixed income, equities, commodities, and convertible bonds. For convertible bonds, the parity price concept is used to determine when it is financially beneficial to convert a bond into shares of common stock.

If two assets are trading at parity, it can be inferred they are at the same price or value.

### Key Takeaways

- Parity price describes a price level in two or more assets that represent equal or equivalent value.
- Depending on the type of asset that it is used to price, parity prices can be used in a variety of different contexts.
- Parity is the price at which it becomes profitable for investors to convert their convertible bonds into shares of common stock.
- Parity can also be used to compare the value of two currencies.

## Understanding Parity Price

Investors often have to make decisions about the relative value of two different investments. Parity is a term used to describe when two things are equivalent to one another. Thus, it can be used to refer to two securities having equal value, such as a convertible bond and the value of a stock (if the bondholder chooses to convert a convertible bond into common stock).

In addition to using parity price for a convertible security, investors can use it to make investment decisions about commodities and currencies. Parity price can help determine the value of stock options because parity is defined as the price at which an option is trading at its intrinsic value. In addition, the concept of parity is also used to compare the value of two currencies.

## Purchasing Power Parity (PPP)

Purchasing power parity (PPP) is a method of comparing the purchasing power between countries. PPP compares the cost of a basket of goods in one country with the cost of the same goods in another country. However, purchasing power parity adjusts for the exchange rates between the two countries. In other words, purchasing power parity adjusts two similar products should be the same price in both countries after figuring for exchange rates.

## Factoring in Commodities

For agricultural commodities, the parity price is the purchasing power of a particular commodity relative to a farmer's expenses, such as wages, loan interest, and equipment.

The Agricultural Adjustment Act of 1938 defines parity price as the average price received by farmers for agricultural commodities during the previous 10 years; if the parity price for a commodity is below the current market price, the government may provide price support through direct purchases.

## Parity in the Forex Markets

Parity is also found in foreign exchange (forex) markets, the exchange rate relationship between two currencies is exactly one-to-one.

Companies based in the United States that have operations in foreign countries must convert U.S. dollars into other currencies. If a U.S. firm does business in France, for example, the company can convert U.S. dollars into euros and send those euros to fund its French business operations. If the exchange rate is $1 to €1, the currencies are at parity.

On July 12, 2022, the euro reached parity with the U.S. dollar for the first time in 20 years (EUR/USD was 1.00), as the euro fell to its lowest level against the U.S. dollar since 2002.

### Interest Rate Parity

Interest rate parity (IRP) is the fundamental equation that governs the relationship between interest rates and currency exchange rates. The basic premise of interest rate parity is that hedged returns from investing in different currencies should be the same, regardless of their interest rates. That means if we consider two countries, and interest rates go up in one of them, then the exchange rate of their currencies will also have to adjust in a commensurate manner. Forex traders use the concept of interest rate parity to identify arbitrage and other trading opportunities.

The formula for IRP is:

$\begin{aligned} &F_0 = S_0 \times \left ( \frac{ 1 + i_c }{ 1 + i_b } \right ) \\ &\textbf{where:}\\ &F_0 = \text{Forward Rate} \\ &S_0 = \text{Spot Rate} \\ &i_c = \text{Interest rate in country }c \\ &i_b = \text{Interest rate in country }b \\ \end{aligned}$

## Parity Price: How Convertible Bonds Work

The conversion parity price on a convertible security refers to the break-even price on a convertible security

A convertible bond offers bond investors the opportunity to convert said bond into a fixed number of shares of common stock at a specific price per share. Investors purchase convertible bonds because the owner can earn interest on a fixed-income investment (and they have the option of converting into the company’s equity). Parity price is the market price of the convertible security divided by the conversion ratio (the number of common stock shares received upon conversion).

Conversion Parity Price = Value of Convertible Security / Conversion Ratio

### Example

Assume, for example, that a $1,000 IBM convertible bond has a market price of $1,200, and the bond is convertible into 20 shares of IBM common stock. The parity price is:

$1,200 / 20 shares = $60 per share

If the market price of IBM common stock is above $60 per share, the investor can profit by converting it into common stock.

## Parity in Options Trading

When an investor purchases a stock option, the owner has the right to buy a fixed number of stock shares at a stated price (and the right to buy the shares expires on a fixed date). One $50 Microsoft call option, for example, means that the owner can buy 100 shares of Microsoft common stock at $50 per share before the option expires. If the market price of Microsoft is $60 per share, the intrinsic value of the option is ($60 - $50), or $10 per share. If the price of the stock option is also $10, the option trade is at parity.

Parity is also used in options in the context of put-call parity. This describes the relationship that exists between put and call options that have the same underlying asset, expiration date, and strike prices, whereby the price of a call option implies a certain fair price for the corresponding put option with the same strike price and expiration and vice versa.

You can determine the put-call party by using the formula: *C + PV(x) = P + S*

Where:

- C is the call price
- PV(x) is the present value of the strike price, x
- P is the put price
- S is the current market price of the underlying security

## What Is Risk Parity?

Risk parity is an asset management process that evaluates risk based on asset classes rather than the allocation of capital. Tradition asset allocation strategy divides assets between stocks, bonds, and cash. The goal is to provide diversification and reduce risk by using these types of investments. Risk parity, on the other hand, allocates dollars based on four components: equities, credit, interest rates, and commodities.

## What Is Covered vs. Uncovered Interest Rate Parity?

Covered interest rate parity exists when a no-arbitrage condition can be achieved through the use of forward contracts as a hedge against foreign exchange risk. Uncovered interest rate parity is the theoretical equivalence between nations' interest rates and exchange rates without considering forwards.

## What Is Percent of Parity?

Percent of parity is a way of describing how much difference there is between two prices or rates and achieving parity. Here, parity is equal to 100%, so if the percent of parity between X and Y is 90%, it is 10 percentage points away from parity.

## The Bottom Line

Parity means equality. The word comes from the Latin *paritas*, which means equal, and is sometimes shortened to "par." In finance, parity price can refer to several things depending on the context, however, in all cases it refers to some sort of equality or equivalence. For instance, parity in forex markets means that two currencies exchange for exactly 1:1. In options theory, put-call parity describes the equivalence between calls and puts of the same strike. For convertible bonds, the parity price is the equivalent amount paid for a share of common stock if the option on a convertible security is exercised. In general, parity is an important concept because it also allows us to understand deviations and differences from some expected parity condition, providing arbitrage and trading opportunities.