*The Business Professor*, updated April 11, 2019, last accessed October 20, 2020, https://thebusinessprofessor.com/lesson/parity-definition/.

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**Parity Definition**

In general, parity denotes a state of equality between two or more entities. The definition of parity has several implications. In the context of the securities market, parity denotes the equal valuation of two discrete securities. It can also refer to a situation where several brokers making identical bids for the same security are placed in equal footing. Parity also has implications in foreign-exchange markets; in situations where two discrete currencies attain an exchange rate relationship of exactly and exchange rate relationship of exactly one 1:1, they can be said to be at parity with each other. Two metals are said to be at parity when their cash prices are exactly equal.

### A Little More on What is **Parity**

In economics, the term parity can be used to describe either of the following

- An equality in the prices of discrete securities.
- An equal bid offered by various brokers bidding on the same security.
- An equal rate of exchange between two currencies traded in a foreign exchange (forex) market.
- Equality in the cash prices of two metals.
- Equality in purchasing power.
- Equal pay for equal work.

The concept of parity plays a vital role in the investment sphere. It especially aids investors in making investment decisions based on the values of two different market instruments. For example, an investor owning a bond may consider either of two options:

- Holding on to the bond in order to earn interest at a stipulated rate
- Converting the bond into a fixed quantity of common stock shares

In the above situation, assuming that the present market value of the bond is $1000, and each share of the common stock is worth $10 in the market, then the value of the bond will be exactly equal to the value of 100 shares of the common stock, thus signifying that the bond is at parity with the stock.

Parity also plays a significant role in call options – arrangements that allow buyers to purchase underlying assets (such as stocks, bonds or commodities) at stipulated ‘strike prices’ within assigned time frames. An investor buying such an asset aims to gain from a positive intrinsic value of the option (i.e. when the market price of the stock exceeds its strike price). When the market price of the call option equals its intrinsic value, it is said to be trading at parity.

Currencies issued by two different countries can also be at parity at certain points in time. For example, the Canadian dollar was at parity with the U.S. dollar at least twice during trading sessions; once on November 25, 1976 and again on September 20, 2007.

Similarly, metals traded in cash markets can be at parity with one another. For example, in late 2018, palladium prices were at parity with gold prices. Likewise, in early 2019, the prices of palladium futures were at near parity with gold futures.

**Risk Parity**

Risk parity is an asset allocation strategy based on weighing risks associated with certain asset classes (e.g. equities and commodities) in lieu of evaluating allocation of capital. Risk parity is employed to diversify investments while maintaining focus on underlying risks and expected returns. Risk parity funds typically invest in market instruments such as stocks, bonds, currencies, and commodities by stipulating optimal risk target levels.

### References for Parity

- https://www.investopedia.com/terms/p/parity.asp
- https://en.wikipedia.org/wiki/Parity
- https://www.dictionary.com/browse/parity
- http://www.businessdictionary.com/definition/parity.html
- https://www.kitco.com/commentaries/2019-01-08/Palladium-and-Gold-Futures-Inch-Closer-to-Parity.html

**Academic Research on ‘Parity’**

The purchasing power **parity **puzzle, **Rogoff, K. (1996). ***Journal of Economic literature***, ***34***(2), 647-668. **The authors utilize a compositional multinomial logit model to study the effect of the introduction of the euro on currency invoicing, by using sample data of Norwegian imports from OECD countries for the period 1996-2006. They conclude that the introduction of the euro has resulted in Eurozone countries that have trade relations with Norway drastically increasing their share of home currency invoicing. Furthermore, Norwegian imports have been increasingly using the euro as a vehicle currency in lieu of the U.S. dollar.

The purchasing-power **parity **doctrine: a reappraisal, **Balassa, B. (1964). ***Journal of political Economy***, ***72***(6), 584-596. **The author adopts a novel approach to perusing the concept of purchasing-power parity. He introduces two different interpretations of this concept that he calls the *absolute* and the *relative* interpretations. Absolute interpretation: This interpretation states that the delineation of purchasing-power parities as a ratio of consumer goods prices for any two countries favors the approximation of the equilibrium exchange rates. Relative interpretation: This interpretation states that changes in relative prices indicate requisite exchange rate adjustments.

Low-density **parity **check codes over GF (q), **Davey, M. C., & MacKay, D. (1998). . ***IEEE Communications Letters***, ***2***(6), 165-167. **This paper scrutinizes the performance of binary low density parity check (LDPC) codes and concludes that when decoded by employing a probabilistic decoding algorithm, LDPC codes demonstrate performances nearing the Shannon limit. The authors employ the analogous codes over GF(q) for q>2, with binary symmetric channels and binary Gaussian channels. The results display significant improvements over the performance of the binary codes, including a rate 1/4 code with bit error probability <10/sup -5/ at E/sub b//N/sub 0/=0.2 dB.

The myth of **parity**, **Neuborne, B. (1976). ***Harv. L. Rev.***, ***90***, 1105. **The author strongly contends that federal and state trial courts are not equally competent in enforcing federal constitutional rights. He cites the presence of numerous institutional dissimilarities between federal and state trial courts to conclude that constitutional litigators have always favored trials in federal courts to have their constitutional claims arbitrated.

The capacity of low-density **parity**-check codes under message-passing decoding, **Richardson, T. J., & Urbanke, R. L. (2001). ***IEEE Transactions on information theory***, ***47***(2), 599-618. **The authors outline a procedure for measuring the capacity of low-density parity-check (LDPC) codes under message-passing decoding. The procedure involves decoding binary-input memoryless channels with discrete or continuous output alphabets. Any rate of transmission that is below the LDPC capacity will result in a randomly small target probability of error. Conversely, any rate of transmission above the LDPC capacity will cause the probability of error to bound away from zero by a strictly positive constant.

The overvaluation of purchasing power **parity**, **O’Connell, P. G. (1998). ***Journal of international economics***, ***44***(1), 1-19. **The author states that recent studies of purchasing power parity have shown that mean-reversion exists in real exchange rates. Nevertheless, these studies have ignored cross-sectional dependence in the data, on occasions inflating the significance level of tests with a nominal size of 5 percent to an incredible 50 percent. The paper goes further to state that when controlled for cross-sectional dependence, panels did not display evidence against the random walk null.

The purchasing power **parity **debate, **Taylor, A. M., & Taylor, M. P. (2004). ***Journal of economic perspectives***, ***18***(4), 135-158. **The paper traces the origins of the concept of purchasing power parity (PPP) and studies its utilities in both the short and the long terms. Towards the beginning of the 21st century, PPP estimates showed significant improvements owing to the usage of larger sets of data as well as nonlinear economic methods.

**Parity**–time synthetic photonic lattices, **Regensburger, A., Bersch, C., Miri, M. A., Onishchukov, G., Christodoulides, D. N., & Peschel, U. (2012). ***Nature***, ***488***(7410), 167. **The design of new artificial optical structures has, thus far, been exploiting their refractive index properties. However, newer methodologies incorporating ‘parity–time symmetry’ have suggested the simultaneous usage of both gain and loss in order to achieve newer levels of optical behavior. This study observes the travel of light in large-scale temporal lattices that are parity–time symmetric. Additionally, the authors assert that operating periodic structures near their exceptional points will will make them function as unidirectional invisible media.

Purchasing power **parity **in the long run, **Abuaf, N., & Jorion, P. (1990). ***The Journal of Finance***, ***45***(1), 157-174. **The authors scrutinize the long-term effects of purchasing power parity (PPP). The paper seeks to disprove the theory that the real exchange rate follows a random walk. The authors apply powerful techniques of estimation to a multilateral framework and conclude that while deviations from purchasing power parity are sizeable in the short term, they still require a period of roughly three years to be reduced in half.

Purchasing power **parity **tests in cointegrated panels, **Pedroni, P. (2001). ***Review of Economics and Statistics***, ***83***(4), 727-731. **Pedroni scrutinizes the strong version of purchasing power parity for a panel of post Bretton Woods data and compares outcomes by employing fully modified and dynamic OLS approaches. Based on these outcomes, Pedroni is able to disprove the hypothesis and introduce a new between-dimension dynamic OLS estimator. He concludes that the between-dimension FMOLS and DOLS approximations of the long term deviation from PPP are larger than the corresponding within-dimension approximations.

The interest rate **parity **theorem: A reinterpretation, **Aliber, R. Z. (1973).***Journal of Political Economy***, ***81***(6), 1451-1459. **Aliber samples 163 central banks and evaluates their indices of central bank autonomy (CBA). He also evaluates comparable indices for a subgroup of 68 banks within the sample. Aliber concludes that economic and political CBA indices have shown significant improvements within the span of a couple of decades. However, he contends that it is only through further improvements that central banks in emerging economies can hope to attain satisfactory political autonomy.