Interest rate parity is the equalization of the rate of return to financial assets across countries. The uncovered and covered interest rate parity conditions link foreign and domes- tic asset prices and identify potential returns from investment. More precisely, the uncovered interest rate parity (UIRP) condition equates the difference between interest rates to the do- mastic currency's expected rate of depreciation.（Hajnalka Illes. 2009）
First and foremost, this report I choose UK and US to analyse. In addition, I suggest UK as the home country and US as foreign country. My birthday is July 25th. Thus, I select the data from July 25th 2011 to April 25th 2012 with nine months.
A. It is obvious that the interest rates and percentage change in nine months are demonstrated in the following chat.
The red line is US interest rate. The blue line is UK interest rate. And the green line is difference. The different interest rate line is always remain a stable form 25/07/2011 to 25/04/2012. To give it more detail, the number of green line decreased drastically form 25/10/2011 to 25/12/2011 during two months. Moreover, in 19/12/2012, there are bottom out at 0.37324%, and reach in a peak at 0.45571% in 15/02/2012. Sum up, the green line has gradually fall down. It means the different rate between UK and US is decreasing. Then, the gap is getting small. (Rh-Rf is decreasing). The expected is decreasing, based on the (Wang, P.J (2009) P50).
Thus, home country is expected to appreciate. There will have a lower arbitrage profit margin and decrease arbitrage opportunities.
B.
The diagram indicates an overall view of percentage change between UK and US. As shown in the graph, there is a moderate fall as the whole line. What's more, it reaches a peak at 0.060542 in 19/08/2011, and bottom out at -0.042169 in 17/01/2012. The percentage change has a rapid increase form 0.00880 to 0.060542 and a sharp decrease form 0.060542 to -0.019149 between11/08/2011 and 22/09/2011.
We use the percentage change to measure the relation between actual changes rate and expected rate, and then, how to judge and choice whether the UIRP hold and whether have an arbitrage.
For percentage change, a rule of thumb does not exist. That is because the standard deviation of percentage change depends on the baseline scores, and it is very hazardous to state a rule. We also proved this by doing a simulation with a simple transformation. The simulation result showed how the standard deviation of percentage change depends on the baseline scores. (Kun Han, L. 2009)
Question 2
According to the graph, it shows the comparison of spot rate and expected rate. They are both indicating a stable pattern between 25/07/2011 to 25/10/2011. And the expected rate line is higher than the spot rate line.
The expected exchange rate for the three months of the Uncovered Interest Rate Parity is that:
The three months interest rate of UK in July 25th is 0.70781%. For instance, if I invest £100 in the bank, when the three months later, I will get £100.70781.（100+100*0.85975%）.
Moreover, the interest rate of US in three months is 0.2521%.
The spot rate in three months is £0.61413744/$
Thus, through the UIRP, I can get the Expected that:
E0 (S1)= (1+rh)/(1+rf)*S0 =(1+0.70781%)/(1+0.2521%)*£0.61413744/$
=£0.616929/$
The spot exchange rate on October 25th in three months is £0.62613487/$
Because the expected spot rate of that point is £0.616929/$, and is less than £0.62613487/$, thus, the exchange rate is higher than I would have expected spot rate. The expected depreciation of the home currency is smaller than the interest differential, so invest in the home currency.
Question 3
A
There is a forward premium. Equal to the difference between the two interest rates over the period.
CIRP is sometimes approximated as:
This graph provides an overview of interest different UK and US and forward premium.
The percentage per annum (p.a.) discount (-) or premium (+) is a forward quote in relation to the spot rate is computed by the following formula (Rodriguez, R. M. ): Forward premium (Discount) =(Forward rate - Spot rate)/ Spot rate.
Forward premium:
(F-S0)/S0=(0.61482/ -0.61413744/)/0.61413744
=0.001111
Interest rate differentials:
(rh-rf)/(1+rf)=(0.72594%-0.29006%)/(1+0.29006%)
=0.004346
Because the left and right sides of IRP are not equal, CIRP is not holding.
B.
Because CIRP is not holding, there is an arbitrage possibility. If I borrow £100 and invest in dollar, and the spot rate is £0.614137/$, then, I will get $162.83. (100/0.614137)
This currency will be saved in the bank at 0.29% in US for three months. The investment return in three months is about $163.3. (162.83*(1+0.0029). The forward rate in three months is £0.61482/$. Then, I will get the £100.4. The Trading Profit is £0.4.
If I save the £100 in the UK bank in three months, and I will get return £100*(1+0.725%)=£100,725.
Arbitrage Profit = £100,725 - £100.4 = £0.325. Thus, if you invest £100 in the other country, you will lost £0.325 after 3 months.
Question 4
A. Through
I can get the E (SI)=(Rh-Rf)*S0+S0
After calculating, the average of the difference between expected exchange rate and spot rate is -£0.000248$. In addition, it is near zero but it not equal zero. Thus, I suggest the Uncovered Interest Rate Parity not hold over this period. The standard deviation is very small that indicates that most of expected exchange rate can be accounted for forward exchange rate. (Juselius, K. (1995).
B. Through the calculating above, I can draw the result of average is -£0.000248$. Turn to UIRP; the expected rate is not fixed, the forward rate is replaced by the value of the spot rate S1 that is expected to prevail one period in the future. If the forward rate always agreed with current expectations of the future spot rate (S1), the UIRP can be hold. (McCallum, B. T. (1996). In this case, the average expected rate E is not equal to the F (the different is -£0.000248$). Thus, I think the UIRP is not hold.
Form other perspective, there are many reason result in the URIP is not hold.
First and foremost, Political situation. If the global situation is strained, it will lead to instability in the foreign exchange market, some of the currencies of the non-normal inflow or outflow will occur. Finally, the result is that the sharp fluctuations in exchange rates. The stability of the political situation related to the stability of the currency in the usual sense, a country's political situation is more stable, the currency of the country is more stable. The impact of political factors on UIRP illustrated I can provide some examples recently. QE3 reduces the tail risk of an outright economic contraction, but is unlikely to lead to a sustained recovery in an economy that is still enduring a painful deleveraging process. In the short run, QE3 will lead investors to take on risk, and will stimulate modest asset reflation. But the equity-price rise is likely to fizzle out over time if economic growth disappoints, as is likely, and drags down expectations about corporate revenues and profitability. (www.guardian.co.uk/ 2012)
Secondly, International balance of payments. The international balance of payments situation will lead to fluctuations in the exchange rate of its currency. The balance of payments is a summary of all of the residents of a country's foreign economic and financial relations. A country's international balance of payments reflects the country's economic status in the international arena, but also affect the running of the country's macro and micro economic. The impact of the international balance of payments situation is the relationship between supply and demand on the foreign exchange impact of the exchange rate.
Thirdly, when a country's dominant interest rates relative to another country's interest rates rise or fall, in pursuit of a higher return on capital, the low interest rate currency will be sold, while the high interest rates of the currency will be bought. Due to the increase in demand for relatively high interest rate currencies, the currency will appreciate against other currencies.
At last, the market operator speculation is also an important factor to affect the exchange rate. Most transactions essence speculation, such speculation will lead to a different currency flows, and thus have an impact on the exchange rate. When people analyze the factors affecting the exchange rate changes to come to some sort of currency exchange rates will rise, and people will buy these currencies. Conversely, when people expected a currency would fall, will compete to sell, so that the exchange rate decline.
C. Judging from what I have calculated above, UIRP is not holding, there is arbitrage possibility.
First and foremost, I need to calculate the average of interest of six months.
The average of home interest rate is 0.8498% at six months. And the average of foreign interest rate is 0.43065%. Furthermore, through the UIRP, I can get (E (S1)-S0)/ S0= (Rh-Rf)/(1+Rf). If (S1-S0)/S0- (Rh-Rf)/ (1+Rf)=0. It will hold. If (S1-S0)/S0- (Rh-Rf)/(1+Rf) >0, it should invest in home currency. If (S1-S0)/S0- (Rh-Rf) / (1+Rf) <0, it should invest in foreign currency. Thus, I can get (0.62613487-0.61413744)/0.61413744-(0.008498-0.0043065)/(1+0.0043053)=
0.0078239 > 0. Thus, it betters to invest in home currency.
I suggest the customer should invest in the home country. Therefore, the arbitrage is not possible in foreign exchange markets. Uncovered interest rate parity (UIRP) predicts that high yield currencies should be expected to depreciate. (Bekaert, G. Wei, M & Xing Y. H. (2007).
