Covered and Uncovered Interest Rate Parity

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Luckyguy

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Reading 14, Q#5 of CFAI, page 592.
I understand that:
  1. Covered Interest rate parity (CIRP) = spot rate* ( 1+ Rc(n/360))/ ( 1+ Rb(n/360))= Forward rate –
  2. Uncovered Interest rate parity (UIRP)= spot rate* ( 1+ Rc(n/360))/ ( 1+ Rb(n/360))= Expected Future Spot .
Now I am breaking down explanation for my understanding:
  1. By arranging the terms of the equation defining interest rate parity- I am fine with this.
  2. And assuming that uncovered interest rate parity is in effect – From this sentence I can understand that uncovered not bound by arbitrage, although scenario says that covered and uncovered are in effect but I am unable to understand context of this sentence in explanation?
  3. The forward exchange rate is equal to the expected future spot exchange rate , Ff/d = Sef/d with the expected percentage change in the spot rate equal to the interest rate differential – I believe it is just elaboration of CIRP formula.
  4. Thus, the forward exchange rate is an unbiased forecast of the future spot exchange rate- I believe conclusion but unable to understand.
 
I’m intrigued by the idea of what your fingers were thinking when they typed “sport rate” instead of “spot rate”.
When we say that a statistic is an unbiased estimator of a parameter, we mean that the expected value of the statistic is the same as the value of the parameter. (For example, the variance of a sample from a population is an unbiased estimator of the variance of the population; the reason we divide the sample variance by n – 1 instead of dividing by n is that dividing by n would give a biased estimate (too small), while dividing by n – 1 gives an unbiased estimate.)
Similarly, a forecast is unbiased if its value is the expected value of the quantity it’s forecasting. Here, the forward rate is an unbiased estimate of the future spot rate. The forward rate applicable to covered interest rate parity is an unbiased estimate of the future spot rate, assuming that interest rate parity holds; it may, or it may not. Covered interest rate parity ensures the future spot rate; uncovered interest rate parity crosses its fingers, closes its eyes, and hopes really, really hard.
 
The differene between expected future spot rate and forward rate explains the difference between Uncovered parity and Covered parity .In covered parity The interest rate differential is at the equilibrium leve to the exhange rate differential . Where as in the uncovered parity the expected future spot rate is opened .
 
Elaborate in what way?
Covered interest rate parity means that the future exchange rate is ensured (i.e., has to be a specific value) because there will be arbitrage opportunities if it should deviate from that value. I wrote an article that may be of some help in this: http://financialexamhelp123.com/covered-interest-rate-parity-irp-pricing....
Uncovered interest rate parity says that we expect that the future exchange rate will be this value because of certain forces (risk-free rates on the currencies in question) that tend to force exchange rates to specified values. However, without securities (i.e., forward contracts) that insist on a particular value, those forces may not operate as hoped, and the actual future exchange rate may deviate from our expectation. This is the basis of carry trade: we imagine that exchange rates aren’t going to move as much as interest rate parity suggests that they should, and try to make money accordingly.
 
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