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Analysis of nubits custodial system

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Analysis of nubits custodial system

  1. 1. Section 1: The Interest Rate Parity Condition RUSD = Et["t+1] "t (1 + RNB) (1) Equation 1 shows the basic expression for the uncovered interest parity con- dition. Economists use this equation to explain the relationship between interest rates and current exchange rates. The uncovered interest parity condition is an arbitrage condition for investment in risk-free assets. The basic form of the equation focues on entirely on investment as a source of demand for currency and also ignores risk. We will consider risk and alternative sources of demand later in the document. Here, we just focus on an investor choosing between two risk-free investment assets. To understand the Equation 1, consider an investor who is deciding whether to invest 1 USD in a USD-denominated bank deposit or invest 1 USD in nubits. The investor plans to spend USD one year from now, so regardless of which option he chooses, he will need USD in the future. The investor is assumed to choose whichever option yields the highest expected return. If the investor decides to choose USD, then he will receive 1+RUSD USD one year from now. If the investor picks nubits, he will exchange his 1 USD for 1 "t Nubits, where "t is the current USD/Nubits exchange rate measured in terms of USD per Nubit. He will then hold his 1 "t Nubits for one year, yielding 1 "t (1 + RNB). He is not certain of what the exchange rate one year from now will be, but expects that on average this exchange rate will be Et["t+1]. This expression, Et["t+1], denotes the exhange rate investors making decisions at time t expect to obtain one year from now at time t+1. Based on this expected exchange rate, an investor choosing nubits will expect to obtain Et["t+1] "t (1 + RNB) USD when he converts his 1 "t (1 + RNB) nubits back into USD next year. The investor chooses whichever option yields the highest return. Therefore, if 1 + RUSD > Et["t+1] "t (1 + RNB), then USD yield a higher expected return than nubits and the investor should choose the USD deposit. If 1 + RUSD < Et["t+1] "t (1 + RNB), then Nubits yield a higher expected return and the investor choose Nubits. As long as investors are free to choose between the two assets, market forces will tend to equalize returns between the new assets, so that 1 + RUSD = Et["t+1] "t (1 + RNB). To see why, suppose that all investors prefer USD to Nubits. If this is the case, then demand for USD will exceed supply of USD at the current exchange rate "t. Demand for USD comes from people seeking to sell nubits. Supply of USD comes from people seeking to buy nubits. To match people seeking to sell nubits with people seeking to buy nubits, the current exchange rate "t will have to fall, i.e. Nubits will have to depreciate. If we examine Equation 1, we can see that a fall in "t increases the expected return on investments in Nubits. Through this mechanism, the current exchange rate adjusts to a level where If 1 + RUSD = Et["t+1] "t (1 + RNB). At this equilibirum exchange rate, both investment strategies yield the same expected return and investors are indierent between the two assets. To highlight some key points, it is useful to rewrite Equation 1 as shown 1
  2. 2. in Equation 2. Here, I have just used algebra to rewrite Et[t+1] t (1 + RNB) as RNB + Et[t+1]

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