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**CHAPTER 4.** **PROBLEM STATEMENT AND HYPOTHESES**

**Introduction**

The preceding chapters have reviewed and discussed the theoretical and empirical issues on carry trade investment and more importantly, the profitability of carry trade in the short-term. Evident from the discussions is that speculative investors only put their bet on currency carry trade investment on the basis of an interest rate differential between two trading currencies. There is no consideration of the risk associated with the movement of the exchange rate. This creates a problem in that volatilities of the exchange rate have a great impact on the profitability of the currency carry trade investment. It is by chance that the speculative investors are able to make a profit.

The objective of this chapter is to unpack the research problem considering the profitability of currency carry trade investment in the short-term and in the long-term, with a view of developing testable hypotheses that will guide the empirical work.

The rest of this chapter is structured as follows: subsection 4.2 discusses the problem statement; subsection 4.3 discusses research questions; subsection 4.4 discusses the hypotheses, and finally, subsection 4.5 summarises the research objectives.

**Problem Statement**

This research determines whether the impact of currency carry trade activity for the South African Rand (as the target currency) is influenced by the exchange rate volatility regime and if so, how businesses and companies should do their planning.

The literature review on the subject of currency carry trade activity provided mixed results on the factors that drive or cause the violation of the UIP hypothesis. Some of the studies attribute the short-term failure of the UIP to the exchange rate volatility. (Among authors who tried to address the issue of exchange rate volatility for carry trade activity see Sy & Tabarraei, 2009; Christiansen et al., 2009; James et al., 2009; Ranaldo & Soderlind, 2009; Ichiue & Koyama, 2010).

As pointed out by Clarida et al. (2009), carry trade returns are higher in the low exchange rate volatility regime and negative in the high exchange rate volatility regime. However, their study did not provide guidance on the exchange rate volatility pattern with regards to the conditions or indications of the low and high exchange rate volatility regimes. They used kernel regression to model misspecification and possible nonlinearities. Again, it is not clear from their study how to model the transition from linear to nonlinear for the exchange rate volatility regime.

Peltomaki (2010) determined that carry trade activity is popular during times of low exchange rate implied volatility. This study did not provide the exchange rate implied volatility pattern to quantify the implied volatility regime for maximum profit taking.

Christiansen & Ranaldo (2010) caution that the distinction between low and high risk environments should be taken into account when engaging in carry trade activity. They found that in turbulent times or periods of financial crisis, carry trade’s systematic risk tends to increase and exposures to other risky allocations are also affected. This leads to an increase in exchange rate volatility. Higher exchange rate volatility results in a stronger correlation between stock market and carry trade strategy and the risk exposures of the carry trade strategy are much more pronounced during volatile periods than during the calm periods (Christiansen et al., 2009).

Studies by Chinn & Meredith (2004), Gynteberg & Remolona (2007), Galati et al. (2007), Hacker et al. ( 2010), Bansal & Dahlquist (2000), Beyaert et al*.* (2007) confirmed that the UIP hypothesis as a framework for carry trade activity does not hold in the short-term because of the inverse relation between the bilateral exchange rates and the interest rate differential. According to Galati et al. (2007), carry trade investment is speculatively used to take advantage of the interest rate differentials and the low exchange rate volatility against the background that the UIP is not expected to hold in the short to medium term.

Drakos (2003) investigated the link between the pattern of the deviation of the UIP and term structure of the cross-currency interest rate spread. The author found that the risk premium is not uniform across maturities. Clearly, the term structure of the interest rate is another pertinent issue to be investigated further. Francis et al. (2002) in their study found that the UIP in emerging markets is systematic in nature and that the significant part of the emerging market currency excess returns is associated with the time-varying risk premium.

Bekaert et al. (2007) studied the UIP and expectation hypotheses of the term structure at long and short horizons. For the UIP and the expectation hypotheses to hold, the following conditions must be met (1) if the UIP holds in the short-term, it should also hold in the long-term provided that the expectation of the term structure of the interest rates holds; and (2) the long-term interest rates must be equal to the average expected future of the short-term interest rates over the life of the bond. The authors found that the UIP and the changes in the exchange rates are weak and negatively correlated with the interest rate differentials and that there is no clear pattern. They concluded that the UIP and expectation hypotheses depend more on currency pair than the horizons.

The following issues have implications for carry trade investment in the South African currency: (1) the deviation pattern of the UIP; (2) the term structure of the interest rates; (3) the UIP and expectation hypotheses for the interest rates; (4) the volatility of the exchange rates, and (5) the currency pairs as opposed to the horizons.

The following section develops the approach to determine the impact of these factors in the context of the South African Rand as the target currency for carry trade activity.

**Research Questions**

In order to understand the profitability of currency carry trade investment fully, the following research questions are posed:

- Does the exchange rate volatility have any impact on currency carry trade investment?
- Does the profitability of currency carry trade investment depend on the type of currency?
- Does the profitability of currency carry trade investment depend on time horizon?
- Does the profitability of currency carry trade investment depend on the interest rate differential between the two trading countries?
- Is there a link between interest rate differential and the changes in the exchange rate movements?
- Does the UIP hold in any time horizon?
- Does the forward rate maturity affect the profitability of currency carry trade investment?

**Hypothesis Development**

The UIP hypothesis forms a fundamental approach in testing the profitability of carry trade activity. It has been extensively tested under the linear model. The hypothesis for this research is generalised for testing the UIP under the linear regime, transition regime and nonlinear regime. This research tests the following hypotheses:

H_{o}: α = 0 and β=1

H_{1}: α ≠0 and β≠1

This generalised hypothesis for testing the UIP was extended to the development of the following sub-hypotheses:

**Hypothesis 1: **Exchange rate volatility does not have an impact on the profitability of carry trade investment.

**Alternative hypothesis: **Exchange rate volatility affects the profitability of carry trade investment.

Hypothesis 1 is tested by considering the Sharpe ratio as the transition variable in the LSTR model. The model is tested for intercept of zero and the slope coefficient of one.

**Hypothesis 2: **The profitability of carry trade investment does not depend on the type of currency.

**Alternative hypothesis: **The profitability of carry trade investment depends on the type of currency.

Hypothesis 2 is tested by selecting a different currency as the funding currency. Three currencies are under consideration (British Pound, US Dollar and Japanese Yen).

**Hypothesis 3: **The profitability of carry trade investment does not depend on the time horizon.

**Alternative hypothesis**: The profitability of carry trade investment depends on the time horizon.

Hypothesis 3 is tested for the short-term horizon only. The short-term horizon is defined as a maturity period of less than five years. For this research, this hypothesis is tested with forward rate maturities of less than one year.

**Hypothesis 4: **The profitability of carry trade investment does not depend on the interest rate differential between the two trading countries.

**Alternative hypothesis: **The profitability of carry trade investment depends on the interest rate differential between the two trading countries.

Hypothesis 4 is as a result of the speculative investors who only focus on the interest rate differential to make a profit out of the carry trade investment. As stated elsewhere in the literature review, interest rates might not necessarily be the only determinant of the profitability of carry trade investment.

**Hypothesis 5: **There is no link between the interest rate differential and the changes in the exchange rate movements for the two trading countries.

**Alternative hypothesis: **There is a link between interest rate differential and the changes in exchange rate movements for the two trading countries.

As stipulated by the UIP hypothesis, there is a direct correlation between the interest rate differential and changes in exchange rate movements. It has, however, been proven that the UIP hypothesis does not hold in the short-term horizon. This research intends to determine if indeed the UIP does or does not hold for the South African Rand as the target currency.

**Hypothesis 6: **The UIP hypothesis does not hold in the short-term horizon.

**Alternative hypothesis: **TheUIP hypothesis holds in the short-term horizon.

It has been stated in the preceding chapters that the UIP hypothesis does not hold in the short-term horizon and therefore investors are able to make profit out of the carry trade investment for the short-term horizon. The research intends to prove whether or not this hypothesis is valid. The LSTR model will be tested with the short-term forward rate maturities of up to one year.

**Hypothesis 7: **Forward rate maturity does not affect the profitability of carry trade investment.

**Alternative hypothesis: **Forward rate maturity affects the profitability of carry trade investment.

Investors have a choice in deciding on the maturity of the forward rate to invest in. The question that needs to be answered is whether or not the forward rate maturity has any impact on the FPP. The LSTR model will be tested under different forward rate maturities.

**Summary**

This chapter discussed the problem statement associated with investment in carry trade. The following issues that have an impact on carry trade investment were identified: (1) thedeviation pattern of the UIP; (2) the term structure of the interest rates; (3) the UIP and expectation hypotheses for the interest rates; (4) the volatility of the exchange rates, and (5) the currency pairs as opposed to the time horizons. Hypotheses were then developed. The following chapter will discuss the research design and it will provide a plan on how to address the research hypotheses.

CHAPTER 1: ORIENTATION

1.1. Introduction .

1.2. Background and Context

1.3. Problem Statement

1.4. Research Objectives

1.5. Importance/Significance of the Study

1.6. Ethical Considerations

1.7. Limitations and Delimitations

1.8. Summary

1.9. Thesis Layout

CHAPTER 2: THEORETICAL FOUNDATION

2.1. Introduction

2.2. Interest Rate Parity

2.3. Summary

CHAPTER 3. LITERATURE REVIEW

3.1. Introduction

3.2. Carry Trade Activity

3.3. The Forward Premium Puzzle

3.4. UIP Horizons for Carry Trade Activity

3.5. Carry Trade Activity and Inflation

3.6. Currency Carry Trade Returns and Exchange Rate Volatility

3.7. Exchange Rate Volatility Regimes and Carry Trade Activity

3.8. Summary

CHAPTER 4. PROBLEM STATEMENT AND HYPOTHESES

4.1. Introduction

4.2. Problem Statement

4.3. Research Questions

4.4. Hypothesis Development

4.5. Summary

CHAPTER 5. RESEARCH DESIGN AND ANALYSIS

5.1. Introduction

5.2. Research Objectives

5.3. Research Design

5.4. Model Selection

5.5. Motivation for Using the LSTR Model

5.6. Model Specification

5.7. Data Sources

5.8. Data Analysis

5.9. Econometric and Statistical Issues

5.10. Summary

CHAPTER 6. DISCUSSION OF THE RESULTS

6.1. Introduction .

6.2. Unit Root Test

6.3. Results for using the Sharpe ratio as the Transition Variable

6.4. Risk Adjusted Forward Rate as the Transition Variable

6.5. Delay Parameter for the Transition Variable

6.6. Robustness Checks

6.7. Summary

CHAPTER 7. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

7.1. Introduction

7.2. Summary

7.3. Hypothesis Tests

7.4. Contribution to the Body Of Knowledge

7.5. Limitation of the Study

7.6. Recommendations/Implications

REFERENCES

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AN EMPIRICAL STUDY OF THE EXCHANGE RATE VOLATILITY REGIME FOR CARRY TRADE INVESTORS