Designing A Basket Of Goods For Purchasing Power Parity Analysis - Australia And Canada

Designing a basket of goods in two countries for the purpose of demonstrating your understanding of purchasing power parity.

You are required to design a basket of goods in two countries for the purpose of demonstrate your understanding of purchasing power parity.  The two countries will be Australia and Canada. The basket of goods should contain ten different consumer goods. The ten different consumer goods are to be from two groups out of the 11 groups used by the Australian Bureau of Statistics (ABS). (See Inflation and its Measurement, 2017 for further details on the 11 groups).  The products that you select can be any type of consumer goods but you are required to provide a reason of why you chose the specific products.

• Exchange rate prediction

You have setup a prediction model last year. Your target is to make a prediction of the exchange rate between Australia and Canada. The prediction is to be for the expected exchange rate at the end of 2018. The prediction should be made assuming the current date is the January 1^st of 2018. This means that the prediction is for a full year ahead exchange rate change. You can use any information available to you when you attempt the assignment but the exchange rates in this part do not represent the actual rates from the market.

The regression model you are to use has the following coefficients.

Change in exchange rates (CAD/AUD) = 0.0001 + 0.5723*GDP growth rate differential (CAD-AUD) + 0.4521*expected inflation rate differential (CAD – AUD)

In the regression model, the GDP growth rates and the expected inflation rates for the two countries must be used to generate the independent variables. The bid and ask rates for CAD/AUD are expected to change at the same rate as indicated by the model. (i.e. the change in the exchange rates predicted for CAD/AUD are equal for the bid, ask and mid rates.)

At the start of 2018 (1/ Jan/ 2018), the spot rate of CAD/AUD was 1.0344 (bid) – 1.0352 (ask). You also checked the current FX quotes for the CAD/USD and USD/AUD currency pairs. The quotes were as below.

	CAD/USD			USD/AUD
1/Jan/2018	Bid	Ask		Bid	Ask
Spot	1.2890	1.2892		0.8025	0.8030
1 Months Forward	-10	-8		1	1
2 Months Forward	-17	-16		2	2
3 Months Forward	-24	-21		2	5
6 Months Forward	-43	-42		8	10
1year Forward	-78	-75		21	22

Required: Questions to answer

Note: To provide the supporting data for your report you will be required to calculate the following in Microsoft Excel. (Your Microsoft Excel spreadsheet needs to be prepared in a way that a colleague could open your spreadsheet and justify your calculations.) That is, use Excel formulas in your calculations so that the final answers can be justified and reconciled by reference to the formula in the cell.

• Design a basket of goods
• Interview two people and survey what type of expenditures they had in their household for the past three months to “maintain a standard of living”

1. From the survey results select ten products you wish to include in your basket of goods. What are the products you picked and why?
2. What is the price for each product in Australia and where did you obtain the price?
3. What is the price for each product in Canada and where did you obtain the price?
4. Evaluate the concept of ‘Law of One Price’ by observing the actual spot rate and comparing it with the implied PPP exchange rate. Discuss possible practical issues that could have impacted the implied PPP exchange rate.

• Exchange rate prediction

1. Explain how you collected the data for the prediction model and what issues you considered in selecting the data.
2. Provide a prediction for the expected CAD/AUD spot exchange rate at 31/Dec/2018.
3. Does an arbitrage opportunity exist if you use your predicted CAD/AUD rate and the FX quotes table for CAD/USD and USD/AUD? If so, what would be the profit?

Assume that you can freely borrow and invest in AUD, CAD, or USD using the central bank interest rates (cash rate for AU, target for the overnight rate for CA, the lower bound of the target range of the federal funds rate for US)

1. Discuss ways you can test the performance of your model and ways to improve the performance of your model.

<Reference Data>

     Historical spot exchange rates for AUD/CAD can be found in the following link: 

A list of products used to calculate the Consumer Price Index (CPI) is in the following link: 

     Australian Bureau of Statistics (CPI explanation) Statistics Canada 

     OECD database (economic projections)

Designing a basket of goods in two countries for the purpose of demonstrating your understanding of purchasing power parity.

With the ramified changes in economic condition and increasing investment options, each and every investor could use the international investment options to create value on the investment.  In this report, design basket of goods has been prepared. After that interview with the two people and survey of the kind of expenditure made by them in last three months will be discussed. After that products have been selected for the international finance analysis. After that, purchasing power parity of the client in different countries will be assessed. In the end, computation of the arbitrage profit will be done by following proper formula and computation method.

DESIGN A BASKET OF GOODS

A. INTERVIEW OF TWO PEOPLE AND THE SURVEY OF THE KIND OF EXPENDITURE DONE BY THEM IN PAST THREE MONTHS

On the basis of survey done in Australia of two households, the following expenditures were found expended by the people. This included expenditure incurred for bread and butter, milk, cheese, fruits, vegetables, tea, coffee, honey, wine, oil, ice creams, cakes, breakfast cereals, beef and veal, garments and footwears, chicken breasts, rice, housing rent, water, electricity, carpets, furniture, glassware, childcare, healthcare, maintenance and repairing of vehicles, fuel charges, communication, postal charges, newspaper, travel and holiday, education, insurance, eggs, soft drinks, electrical equipment, magazines, stationary, pets, sports participation (Li, Lin, & Hsiao, 2015).

B. PRODUCTS SELECTED FOR ANALYSIS AND REASONS FOR SAME

There are several products have been listed below to formulate and design a basket of goods, the following ten products are being selected:

1. Bread
2. Milk
3. rice
4. Coffee
5. Eggs
6. water
7. Wine
8. Beef and veal
9. Chicken breasts
10. apples

The above products are being selected for the current study due to a few reasons. All these products are highly used in day to day life and that way are able to properly reflect the scenario prevailing in both Canada and Australia. Another reason is the easy availability of data required for study for these products as they are commonly used necessities (Huang, & Yang, 2015).

c. PRICE OF EACH PRODUCT IN AUSTRALIA AND THE PLATFORM FOR PICKING PRICE

The below given table will reflect the products and its price value in the AUD currency value.

PRODUCT	PRICE IN AUD
Bread (500 grams)	2.51
milk (1 litre)	1.41
Cheese (1 kg)	8.99
Rice (1 kg)	2.65
Egg (1 dozen)	4.29
Water (1.5 litre bottle)	1.79
Wine	15
Beef and veal (1 kg)	15.40
Chicken breasts (1 kg)	10.17
Apples (1 kg)	4.06

The price of the above products has been taken from the average prices reflected for Australia on the basis of a survey. The table given reflects the average prices of around 40 household items.

D. PRICE OF EACH PRODUCT IN CANADA AND PLATFORM FOR PICKING THEM

PRODUCT	PRICE IN CAD
Bread (500 grams)	2.77
milk (1 litre)	2.18
Cheese (1 kg)	11.68
Rice (1 kg)	3.82
Egg (1 dozen)	3.27
Water (1.5 litre bottle)	2.22
Wine	15
Beef and veal (1 kg)	13.71
Chicken breasts (1 kg)	12.7
Apples (1 kg)	3.85

The price of the above products has been taken from the average prices reflected for Canada on the basis of a survey. The site presents the average prices of around 40 household items (Huang, & Yang, 2015).

Using a prediction model to analyze expected exchange rates based on GDP growth and expected inflation rates.

E. CONCEPT OF ‘LAW OF ONE PRICE’

This law states that the price of any currency in international market remains same. It means that the price of a commodity is equal in every country if the effect of exchange rates is taken into consideration. This law stands as another name for concept of purchasing power parity. This concept stands for eliminating arbitrage profits. This is so because if a commodity is cheaper in one market and costlier in another market, then the consumer can buy the commodity in one market and sell in another to make profits. This law states that the price of common basket of goods should be same all over the world (McKinnon, & Ohno, 2016).

Purchasing power parity of Exchange rate

It is evaluated that Purchasing power parity is the theory which reflect the exchange rates between currencies are in equilibrium when their purchasing power is same in both countries.

FORMULA FOR COMPUTING IMPLIED PURCHASING POWER PARITY EXCHANGE RATE:

The formula used for computing the implied exchange rate is the Price Ratio.

i.e.           PRICE OF A COMMON BASKET COMMODITY IN CANADA

            PRICE OF A COMMON BASKET COMMODITY IN AUSTRALIA

This ratio gives the exchange rate CAD/AUD.

E.G. if we consider the price of bread in both the countries, the following exchange rate is obtained (McKinnon, & Ohno, 2016).

=            PRICE OF BREAD IN CANADA

            PRICE OF BREAD IN AUSTRALIA

=          2.77

            2.51

= 1.1036 CAD/AUD

After evaluating the data given in this assignment, it could be inferred that this figure is almost equal to the given spot rate of CAD/AUD 1.0344. It means that if the purchasing power parity concept holds good, then the exchange rate should have been equal to CAD/AUD 1.1036, in order to eliminate arbitrage profits.

But the figure cannot stand completely equal to the given exchange rate due to certain practical implications being:

• Restrictions on imports and exports being quotas, tariffs and certain other laws, makes the sale of goods in different international markets difficult impacting the natural price.
• In addition to the inflation effects considered in the law of one price concept, the transportation costs add to the price impacting the implied exchange rate.
• The price of every commodity naturally varies internationally, because some locations are actual producers and others stand as importers.

EXCHANGE RATE PREDICTION

A. COLLECTION OF DATA USED FOR PREDICTION

The model to be used for computing the change in the exchange rate is already provided and mentioned below (McKinnon, & Ohno, 2016).

 Change in exchange rates (CAD/AUD) = 0.0001 + 0.5723*GDP growth rate differential

(CAD-AUD) + 0.4521*expected inflation rate differential (CAD – AUD)

This formula uses the following data:

1. GDP growth rate of Canada
2. GDP growth rate of Australia
3. Expected inflation rate of Canada
4. Expected inflation rate of Australia
5. Growth rate differential (CAD-AUD)
6. Inflation rate differential (CAD-AUD)

The data used for analysis was collected from the Australian Bureau of Statistics website and the statistics Canada website. The following results are obtained (Jolliffe, & Prydz, 2015).

1. GDP growth rate of Canada :           7%
2. GDP growth rate of Australia :           6 %
3. Expected inflation rate of Canada :           2%
4. Expected inflation rate of Australia :           9%
5. Growth rate differential (CAD-AUD) :           -.9% i.e. -.009
6. Inflation rate differential (CAD-AUD) :           .3% i.e. -.003

Calculating implied purchasing power parity exchange rate using the price ratio formula.

THE ISSUES IN CONSIDERING SELECTED DATA

Being a layman and not an economist or trend analyser, it’s difficult to rely on the selections made as the story behind the figures is unknown. It’s kind of taking a leap of faith to reach a conclusion, by using the data mentioned in form of statistical information. Another issue lies in ignorance of factors that affect these figures when international markets are being considered (Huang, & Yang, 2015).

B. PREDICTION OF EXPECTED CAD/AUD SPOT EXCHANGE RATE AT 31 DECEMBER 2018

The data required for the same is gathered as shown above. The calculations made are done in separate excel sheets and are shown here in brief for reference (Bahmani-Oskooee, Chang, & Wu, 2015).

First of all, the difference that exchange rate will face shall be computed using this formula:

Change in exchange rates (CAD/AUD) = 0.0001 + 0.5723*GDP growth rate differential

(CAD-AUD) + 0.4521*expected inflation rate differential (CAD – AUD)                                               

                                                           = -.0037            (calculation shown in excel file)

SPOT RATE TODAY: 1.0344 - 1.0352 CAD/AUD (BID-ASK RATE)

EXPECTED SPOT RATE:  1.0307 - 1.0389 CAD/AUD

This is so because the bid and ask rates are assumed to have changed with the same exchange rate difference.

The changes in the exchange rate may result to profit and loss to the investors which may directly and indirectly impact the arbitrage profit and loss had by the investors from its investment (Pelagatti, & Colombo, 2015).

Change in exchange rates (CAD/AUD) = 0.0001 + 0.5723*GDP growth rate differential

C. EXISTENCE OF ARBITRAGE OPPORTUNITY

Arbitrage opportunity exists in case where there are three currencies. In this we start with one currency and sell it to pass through the other two currencies, in order to land on the currency that we started with. The arbitrage opportunity is used to increase the overall outcomes and profit of the investors. There are several investors who are using the arbitrage opportunities to create value on their investment (Kim, et al. 2015).

This could be understood by using the below given example effectively.

E.G. if the currencies are x, y and z then we are required to start with x to land on x back again. The two paths could be:

                                    y                      z                      x

x

                                    z                      y                      x

In the given analysis, it is assumed that the future forward rates calculated for CAD/USD and USD/AUD shall be same as the expected spot rates on that date, i.e. on 31^st December 2018.

Evaluating selected data for issues and limitations.

The forward rate one year after as computed in excel file is 1.2812 - 1.2817 CAD/USD and 0.8046 - 0.8052 USD/AUD. If investors want to create value on its investment then they needs to use proper forward and future contract and book them by using the different spot rate (Taylor, & Taylor, 2014).

THE ARBITRAGE PROCESS CAN BE CARRIED OUT IN TWO PATHS,

PATH ONE: Starting with CAD 12817, selling it to buy USD @ 1.2817 CAD/USD, selling the USD obtained @ 0.8052 USD/AUD and selling the AUD @ 1.0307 CAD/AUD.

            PROFIT/LOSS: (16 CAD)

PATH TWO: starting with CAD 12817, selling it to buy AUD @ 1.0389 CAD/AUD, selling AUD to buy USD @ .8046 USD/AUD and selling USD to buy CAD @ 1.2812 CAD/USD.

These two paths are used to evaluate the profit and loss of company in all the investment opportunities.

            PROFIT/LOSS: (99 CAD)

As clear from above, there is no arbitrage profit. The reason is the presence of BID-ASK spread, or transaction cost to the arbitrager. If there had been a single transaction rate, chances are there of making arbitrage profit. Due to the presence of bid-ask spread, both the paths have resulted in making loss to the arbitrager, leaving no space for making profit.

It is observed that if investors select for the path one then he will have loss of AUD -16 (Gabaix, & Maggiori, 2015).

COMPUTATION IN PATH ONE
TRANSACTION	RATE	QUANTITY	AMOUNT
SELLING CAD TO BUY USD	1.2817	12817	$                 10,000.00
SELLING USD TO BUY AUD	0.8052	10000	$                 12,419.27
SELLING AUD TO BUY CAD	1.0307	12419	$                 12,800.55
NET PROFIT/LOSS			$                        -16.45

This shows that use of the exchange rate while making investment is utmost required if international investors want to create value on its investment.

However, if path two is selected for the investment then in this case as well investors have to bear loss in its international investment (Rogers, Scotti, & Wright, 2016).

COMPUTATION IN PATH TWO
TRANSACTION	RATE	QUANTITY	AMOUNT
SELLING CAD TO BUY AUD	1.0389	12817	12337
SELLING AUD TO BUY USD	0.8046	12337	9926
SELLING USD TO BUY CAD	1.2812	9926	12718
NET PROFIT/LOSS			-99

Hence, the law of one price or purchase power parity stands significant in this case. This could be inferred that the law of purchasing power parity may be used by investors to determine whether the investment in one particular product may increase the overall outcomes and efficiency of the busienss at large. It will also assist investors to create value on the investment will save it from the possible losses (Cavusgil, et al. 2014).

D. WAYS TO TEST THE PERFORMANCE OF MODEL AND WAYS TO IMPROVE IT

            One most significant way to test the model is to change the amount of CAD initially used. If the arbitrager is still making loss with the changed amount, then the model proves its efficiency. The arbitrage profit and loss arise due to the changes in the spot and bid prices given and contracted rate at the particular stipulate rate. It is observed that if these models are performed effectively and there is made changes in the identified model by shuffling the investment in buying currency from the particular bank then it might help investors to reduce the loss incurred on the investment.  The way to test the performance of model is to analysis the investment choices and options offered by the different banks on international level. if the spot and bid price of the currency is highly variable and showing the differences in the amount charged by the one bank to another then investor could use the swap model to create value on the investment (Mueller, Stathopoulos, and Vedolin, 2017).

            The way the model can be improved, for the favour of arbitrager is to remove the bid-ask spread, or to remove the transaction cost. This way there will be a single exchange rate used for buying and selling of the currencies. In that case, there will be profit surely on one path and loss on another. However when there are both bid and ask rates, chances stand for the loss making in both paths as we have already seen. The single exchange rate for buying and selling currency will save the investors from the possible busienss losses (Cenedese, Sarno, and Tsiakas, 2014).

            It is analyzed that removing the transaction cost and bid and ask spread is not feasible. Each and every foreign transactions and investment requires transactions cost and the same will be paid by the investors. However, investors may increase the overall profitability of their investment if they select only those projects which offer higher return and accompanied with the less transaction costs. Ideally, differences between the bid and ask rate arises due to the high volatility of the market.

Creating arbitrage profit in the market is only possible when the international investment capital market is highly volatile and banks are quoting different bid and ask rate in market ( Blanchard, and Adler, 2015).

Conclusion

            In this report, several facts and international market risk have been analyzed which not only assist in identifying the best possible time off the investment but also increase the value of the investment at large. There are several international risks which have been faced by the investors whenever they make investment in particular currency. In case, if the international finance market is highly volatile and banks are quoting different bid and ask rate in market then this situation could be used by investors to create value on their investment. This could also be used by investors to create arbitrage profit in their investment. It is also stated that price of a commodity is equal in every country if the effect of exchange rates is taken into consideration. Therefore, by using the purchasing power party, investors could determine the value of the one commodity in context with the other countries. Now in the end, it could be inferred that changes in the exchange rate throughout the time might result to profit and loss to the investors which may directly and indirectly impact the arbitrage profit and loss had by the investors from its investment.

References

Bahmani-Oskooee, M., Chang, T. and Wu, T.P., 2015. Purchasing power parity in transition countries: panel stationary test with smooth and sharp breaks. International Journal of Financial Studies, 3(2), pp.153-161.

Bahmani-Oskooee, M., Chang, T. and Wu, T.P., 2015. Purchasing power parity in transition countries: panel stationary test with smooth and sharp breaks. International Journal of Financial Studies, 3(2), pp.153-161.

Bahmani-Oskooee, M., Chang, T., Chen, T.H. and Tzeng, H.W., 2017. Revisiting purchasing power parity in Eastern European countries: quantile unit root tests. Empirical Economics, 52(2), pp.463-483.

Blanchard, O. and Adler, G., 2015. Can Foreign Exchange Intervention Stem Exchange Rate Pressures from Global Capital Flow Shocks? (No. w21427). National Bureau of Economic Research.

Cavusgil, S.T., Knight, G., Riesenberger, J.R., Rammal, H.G. and Rose, E.L., 2014. International business. Pearson Australia.

Cenedese, G., Sarno, L. and Tsiakas, I., 2014. Foreign exchange risk and the predictability of carry trade returns. Journal of Banking & Finance, 42, pp.302-313.

Gabaix, X. and Maggiori, M., 2015. International liquidity and exchange rate dynamics. The Quarterly Journal of Economics, 130(3), pp.1369-1420.

Huang, C.H. and Yang, C.Y., 2015. European exchange rate regimes and purchasing power parity: An empirical study on eleven eurozone countries. International Review of Economics & Finance, 35, pp.100-109.

Jolliffe, D. and Prydz, E.B., 2015. Global poverty goals and prices: how purchasing power parity matters.

Kim, H., Fujiwara, I., Hansen, B.E. and Ogaki, M., 2015. Purchasing power parity and the Taylor rule. Journal of Applied Econometrics, 30(6), pp.874-903.

Li, H., Lin, Z. and Hsiao, C., 2015. Teing purchasing power parity hypothesis: a semiparametric varying coefficient approach. Empirical Economics, 48(1), pp.427-438.

McKinnon, R. I., & Ohno, K. (2016). 7 Purchasing power parity as a monetary. The Future of the International Monetary System: Change, Coordination of Instability?: Change, Coordination of Instability?, 42.

Mueller, P., Stathopoulos, A. and Vedolin, A., 2017. International correlation risk. Journal of Financial Economics, 126(2), pp.270-299.

Pelagatti, M. and Colombo, E., 2015. On the empirical failure of purchasing power parity tests. Journal of Applied Econometrics, 30(6), pp.904-923.

Rogers, J.H., Scotti, C. & Wright, J.H., 2016. Unconventional monetary policy and international risk premia.

Taylor, A.M. and Taylor, M.P., 2014. The purchasing power parity debate. Journal of economic perspectives, 18(4), pp.135-158.