International Financial Management Group Assignment
1. Purchasing Power Parity and Uncovered Interest Rate Parity
For this question, we will analyse the validity of purchasing power parity and uncovered interest rate parity between Australia and the USA. We need data from both countries on inflation (as measured by changes in consumer price in- dices), relative interest rates and the exchange rate. These data can be obtained from the RBA webpage and the FRED Economic Data webpage maintained by the Federal Reserve Bank of St Louis. The following analysis must be conducted over the pe- riod March 1991 until December 2016. However, to compute all the variables we care about, we must gather data covering March 1990 until December 2016 (we will calculate year on year changes for inflation). Make sure that the data you download spans these ranges for all series where available.
Data Downloading - RBA
- From the RBA website, download the data contained in the link "Consumer Price Inflation - G1". We care about the columns A and C - the date and the year on year change in the CPI index measured at the quarterly frequency.
- From the RBA website, download the data contained in the link "Interest Rates and Yields - Money Market - Monthly - F1.1". We care about columns A and B - the date and the cash rate target. Note that the cash rate data is only available from August 1990, this will be fine as we do not need to calculate changes in this cash rate, we just need to know the level.
- From the exchange rates page on the RBA website, download the data con- tained in the link "Exchange Rates - Monthly - July 1969 to December 2009" and "Exchange Rates - Monthly - January 2010 to latest complete month of current year" and collate these into a single excel worksheet. We care about column A and C, the date and the monthly exchange rate expressed as S(USD/AUD).
Data Downloading - FRED
- From the FRED website, search for the term "CPIAUCSL" and follow the link to the item: "Consumer Price Index for All Urban Consumers: All Item". Download these data into an excel file. We care about both columns A and B - the date and the level of the consumer price index at the monthly level.
- From the FRED website, search for the term "FEDFUNDS" and follow the link to the item: "Effective Federal Funds Rate". Download these data into an excel file. We care about both columns A and B - the date and the effective Federal Funds Rate at the monthly level (measured in %).
We now need to create a single spreadsheet with quarterly observations spanning 30 March 1991 to 31 Dec 2016. You may need to use excel's "vlookup" function to do this. For each date, we need to find the corresponding entry for the year on year % change in the Australian CPI index (column C from the RBA inflation data), the RBA target cash rate (column B from the RBA interest rates data), the year on year % change in the US CPI index (we must calculate this year-on-year change using the index values in column B of the FRED CPI data), the Effective Federal Funds Rate from column B of the FRED Fed Funds data and the quarterly discrete return in S(USD/AUD) (we must calculate this % return from column C of the RBA monthly exchange rate data).
To check that you have correctly inputted the data, the first five rows and the last two rows of data should appear as per Table1.
Table 1: Final Dataset Example
|
Date
|
CPI (Aus)
|
CPI ?% YoY (Aus)
|
RBA Cash Rate
|
CPI (US)
|
CPI ?% YoY (US)
|
FFR Effective
|
S(USD/AUD)
|
S(USD/AUD)
?%
|
|
31-Mar-1991
|
58.90
|
4.80
|
12.00
|
134.80
|
4.82
|
6.12
|
0.7752
|
0.25
|
|
30-Jun-1991
|
59.00
|
3.30
|
10.50
|
136.00
|
4.70
|
5.90
|
0.7681
|
-0.92
|
|
30-Sep-1991
|
59.30
|
3.10
|
9.55
|
137.00
|
3.40
|
5.45
|
0.7995
|
4.09
|
|
31-Dec-1991
|
59.90
|
1.50
|
8.50
|
138.20
|
2.98
|
4.43
|
0.7598
|
-4.97
|
|
31-Mar-1992
|
59.90
|
1.70
|
7.50
|
139.10
|
3.19
|
3.98
|
0.7684
|
1.13
|
|
30-Jun-1992
|
59.70
|
1.20
|
6.50
|
140.10
|
3.01
|
3.76
|
0.7488
|
-2.55
|
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
...
|
|
30-Sep-2016
|
109.40
|
1.30
|
1.50
|
241.01
|
1.49
|
0.40
|
0.7630
|
2.75
|
|
31-Dec-2016
|
110.00
|
1.50
|
1.50
|
242.82
|
2.09
|
0.54
|
0.7236
|
-5.16
|
(a) Now that we have our data, we will analyse how well both purchasing power parity and uncovered interest rate parity (or, equivalently, the forward expectations hypothesis) do at explaining changes in exchange rates. In your excel worksheet, create two new columns containing the variables i-ii below and report the following summary statistics for these variables and the quarterly return in the FX spot rate: the mean, the median, the standard deviation, the skewness, the kurtosis, the range and the minimum and maximum. Comment on the mean and median values of the inflation differential and the interest rate differential (i and ii). Which country had higher real rates on average? Comment on the skewness of the exchange rate and its implications for investors performing a short USD / long AUD carry trade.
i. The inflation difference between the US and Australia: πUS - πAus
ii. The difference in central bank interest rates between the US and Australia: iUS - iAus
(b) Plot the spot rate, the inflation differential and the interest rate differential data series over time.
(c) Calculate and report the correlation matrix for the spot rate return, the inflation differential and the interest rate differential. Assuming that current inflation rates are good proxies for expected inflation rates, what correlations would we expect to see if purchasing power parity holds? What correlations would we expect to see if uncovered interest rate parity held? Do the correlations support these predictions?
(d) We will now run two linear regressions to more formally test whether inflation differentials and interest rate differentials explain movements in the Australian dollar vs. the US dollar.
i. Firstly, run a regression where the dependent variable is the quarterly S(USD/AUD) return and the independent variable is the inflation differential πUS - πAus:
st = απ + βπ (πUS - πAus)t + ut (1)
where st is the return in the exchange rate and u is an error term. Report the regression output and comment on the results. Purchasing power parity suggests that βπ = 1 (assuming inflation rates in both countries are relatively low). Perform this hypothesis test and interpret the result with respect to the PPP prediction.
ii. Secondly, run a regression where the dependent variable is again the quarterly S(USD/AUD) return but now where the independent variable is the interest rate differential iUS - iAus:
st = αi + βi(iUS - iAus)t + εt. (2)
Report the regression output and comment on the results. Uncovered interest rate parity suggests that βi = 1 (assuming interest rates in both countries are relatively low). Perform this hypothesis test and interpret the result with respect to the UIRP prediction.
2. Hedging Alternatives
Lunar Capital Partners (LCP) is an Australian Private Equity firm. They invest in assets in both Australia and New Zealand. The fund predominantly borrows in Australian dollars and its distributions are denominated in Australian dollars. LCP are considering purchasing a New Zealand auto-repair chain, AutoNZ, for a total consideration of NZD50m. If the deal took place, it would require LCP to pay this amount in one month from today. The General Partners of LCP are concerned about the currency risk of this potential deal. They have asked you to discuss possible hedging alternatives with them. Specifically, they wish to consider the following alternatives:
- Leaving the currency un-hedged
- Entering into an FX forward contract
- Using the money market to construct a hedge
- Purchasing an option with strike price equal to 0.9250.
The mid-price of the spot rate, S(AUD/NZD), today is 0.9180. They wish to consider three scenarios: where the spot rate appreciates 8% to 0.9914, where the spot rate depreciates 4% to 0.8813 and where the spot rate remains unchanged from today's level. Table2contains market prices available to LCP.
|
Table 2: Market Prices
|
|
FX:
|
Bid
|
Ask
|
|
Money Market:
|
Borrowing
|
Lending
|
|
S(AUD/NZD)
|
0.9175
|
0.9185
|
|
Australia (BBSW)
|
1.675%
|
1.575%
|
|
F1m(AUD/NZD)
|
0.9174
|
0.9184
|
|
New Zealand (Bank Bill Yield)
|
1.840%
|
1.740%
|
|
FX Option:
|
|
NZD Call / AUD Put
|
Premium (AUD)1
|
NZD Put / AUD Call
|
Premium (AUD)1
|
|
1 month K = 0.9250
|
0.0076
|
1 month K = 0.9250
|
0.0144
|
1FX option premia are quoted in AUD required to purchase the stated option in a value of 1 NZD. For example, at a premium price of 0.0250 it would cost AUD 25,000 to purchase an NZD Call / AUD Put on NZD 1,000,000.
(a) Suppose they leave the currency exposure unhedged. Calculate the AUD required to purchase AutoNZ under the three scenarios, assuming that the bid- ask spread in 1 month's time is still 0.0010. If they leave the currency un- hedged, and the deal goes ahead, how much additional AUD must LCP pay under the worst of these three scenarios (from LCP's point of view) relative to the unchanged spot rate?
(b) Suppose they enter into a forward contract to hedge the entire NZD amount. Specify the details of the contract (long or short) and the price at which the contract will be struck. If the deal goes ahead, LCP will be completely insulated from movements in the spot rate. However, if the deal does not go ahead, LCP must still honor the forward contract. Calculate the profit and loss on the forward contract under the three spot price scenarios listed above.
(c) Being sophisticated investors, LCP are aware of the covered interest rate parity arbitrage condition between relative FX spot and forward rates, and relative interest rates in Australia and New Zealand. Calculate the two-way (i.e. to buy NZD / sell AUD and to sell NZD / buy AUD) price of constructing an FX forward position via the money market and spot FX market. Do the prices in Table2admit an arbitrage opportunity? Are LCP better off transacting in the FX forward market or the spot market and money market to construct a forward position?
(d) Now consider the case where LCP purchase an option to hedge their possible FX exposure (assume again that they enter into an option contract that hedges the entire NZD amount). Which of the options in Table2should they purchase? How much premium does it cost in AUD?
(e) Carefully plot the total deal cost for LCP after they purchase this option assuming that the deal completes. In other words, for a range of spot prices, plot the cost in AUD for purchasing the NZD50m after purchasing the option in part (d) and exercising it optimally. Be sure to include details about where the payoff profile kinks, the costs at the kink point and where the cost profile intersects the y-axis as well as any other interesting points you wish to include.
(f) Carefully plot the portfolio payoff profile for LCP after they purchase this option assuming that the deal does not complete (i.e. plot the net AUD amount that the option is worth at expiry given that they exercise the option optimally and then clear the resultant position in the prevailing spot market).
Total 500 word answering last 3 questions in part 2.
Attachment:- Assignment File.rar