Exchange Rate Variability of the Korean Won Against US Dollar: An Approach from the Randomized Complete Block Design

Yunsu Park; Seunghyuk Han; Sunbin Kim; Taewon Kim; Seungin You; Ajiboye Babalola; Yunsu Park; Seunghuk Han; Sunbin Kim; Taewon Kim; Seungin You; Ajiboye Babalola

doi:10.3998/umurj.9827

1. Introduction

The mainstay of most powerful countries have been defined by their economic prowess. Gauging from the perspectives of the popular economics of Eastern Asian countries, many investors and scholars may argue that the best economies to invest in are Japan and China. According to the World Bank [10], the worldwide Gross Domestic Product (GDP) of China in 2022 was at a benchmark of 12,720 USD per capita. In contrast, in the same year, the GDP in South Korea reached USD 32,423 per capita, or 1,674 trillion USD for the nation. This is strange for a country badly hit by the pandemic in 2020/21 and for the most part of 2022, Most economies had plunged into recession, with most income per capita at an all-time low. However, South Korea managed to stay afloat due to its economic policies, while managing to be one of the world’s largest economies. It is currently ranked at 13th globally. From a microeconomic perspective, one notable observation is that, despite operating under a capitalistic system similar to the West; the concentration of its economy appears to be dominated by three major countries. Additionally, it has consistently remained resilient in the face of its northern neighbour, North Korea, and within its own political spectrum. Several countries that have implicitly or explicitly fixed their exchange rates to the currency of another country (such as the US dollar) or anchored a unified exchange rate (examples include iCentral Europe) and their inflation rates are slightly higher than that of the foreign country they benched marked their monetary value on. The idea often leads to devaluation and this weakens the domestic economy. Devaluation often invites recession, inflation and thus pushes the economy into a conundrum of an inflation-devaluation cycle. This causes a setback in economic development and immense pressure on the home currency. This affects the prospects for high economic growth, and has been the strength of most economies in the East. Successful exports generate economic surpluses, resulting in a nominal appreciation pressure on the currency unless the central bank intervenes in the foreign exchange market and accumulates their fiscal balance surplus. Even if the central bank’s intervention maintains a fixed exchange rate, unsterilized intervention results in inflation, causing the real exchange rate to appreciate.

Throughout the financial history of the Korean economy, it has never stopped growing and improving. To truly understand its resilience, one must identify the moments where its growth stalled. These instances have only occurred three times: during the Asian Financial Crisis in 1997, the global recession in 2008, and the global pandemic of 2019/2020. During the Asian Financial Crisis, South Korea implemented a flee-floating exchange rate regime on December 12th, 1997 [11] and revised the Bank of Korea Act in 1998 [1], both required by the International Monetary Fund (IMF) as conditions for its bailout. These domestic reforms granted the central bank greater independence [12] and significantly enhanced the resilience and stability of the Korean economy. During the global recession, it was impossible to achieve growth due to all currencies experiencing downturns. However, during the global pandemic, this was felt most severely by Asian economies. Due to the influence of the USD, the US economy hardly felt the shock, which forms the basis for this measurement.

From 2020 to 2021, the COVID-19 pandemic triggered significant liquidity expansion, followed by a transition toward endemic conditions and aggressive monetary tightening by the U.S. Federal Reserve from 2022 to 2023. This sequence constitutes an economic cycle that reflects the influence of external factors on exchange rate dynamics.

This study aims to statistically identify seasonal patterns embedded in exchange rate data and time-specific (monthly and weekly) volatility concentration in exchange rate data of Korean won against the U.S. dollars from 2020 to 2023. It further interprets these patterns in a socio-economic and policy context based on underlying external causes such as U.S. Federal Reserve policy.

2. Literature Review

The Korean economy emerged from the harsh economic realities of the 1960s, a time when the country was at a disadvantaged position politically and was struggling to navigate the plain fields with internal resources and external forces. Within all of these difficulties, it managed to build its success through sacrifices and the avoidance of waste. The country over the years opened up key sectors such as manufacturing, construction, transportation and electric power. The combination of these sectors have provided a foundational path on which the country has thrived through the years. See Park Park [8], Seok et al Seok, Lee, and Pyo [9]. The work Cho [2] which focused on the dwindling foreign exchange, motivated this study due to it being focused on the global financial crises in 2008 and how it affected the spending power of the Korean won in the global market. Cho established his results using the analysis of variance that the financial setback faced by the Korean won was a result of short-term setbacks and long-term setbacks. The work argued that the former was driven by scarcity, high rents, and other cataclysms, while the latter was more influenced by the US market. We consider the data-driven works of Park [8] which may also be of interest, because the author tried to establish no significance between the variation before the 2008 crisis and afterwards. An interesting study by Kim [6] studied this issue on a microscale, focusing on large companies that failed. While it is may appear easy to attribute these failures it to both short-term and long-term variations, it is difficult to isolate the confounding variables from those countries’ internal resources or the disruption of the financial market caused by stakeholders as clearly outlined by Goodfriend [4] and Clarida, Galí, and Gertler [3]. Our work is focused on understanding when these two variations occur and their significance., our work is based on the perspectives of the previously mentioned research and the monetary policy report from the Bank of Korea [1].

3. Research Design

3.1 Research Question

We will be studying and looking at the trend data of South Korea’s exchange rate with the US (USD) to determine if there is a statistically meaningful difference in the price of 1 USD in KRW across different weeks and months from a specific period, from 2020 to 2023. The analysis will aim to identify any long-term trends, seasonal patterns, or cyclical fluctuations in the exchange rate data. Furthermore, we will explore whether any specific events can be causally linked with changes in the exchange rate. Before proceeding with, processing and testing data, we will establish a hypothesis.

3.2 Hypothesis

Our primary hypothesis centers on whether there is a statistically meaningful difference in the price of 1 USD in KRW across different weeks and months over the established period: . The following hypotheses are formulated to guide our analysis:

Null Hypothesis $H 0$

There is no statistically significant difference in the average exchange rate of 1 USD to KRW across different months and weeks from 2020 to 2023. Any observed differences are due to random variation rather than systemic changes.
Alternative Hypothesis $H 1$
There is a statistically significant difference in the average exchange rate of 1 USD to KRW across different months and weeks from 2020 to 2023. The observed differences reflect underlying systemic changes influenced by factors such as US monetary policy, global economic conditions, and specific events during the study period.

3.3 Data Collection

This study investigates the value of 1 US Dollar (USD) in the South Korean legal tender South Korean Won (KRW) over the course of four years. The record was taken from 2020 to 2024. According to investing.com [5], the value of the 1 US Dollar to the KRW on the date (May 15th, 2024) that the data was collected is 1,359 KRW.

Table 1:

First six rows of the USD/KRW historical dataset

Date	Price	Open	High	Low	Change
12/29/2023	1,295.06	1,289.88	1,301.36	1,284.02	0.41%
12/28/2023	1,289.80	1,294.02	1,295.00	1,285.34	-0.34%
12/27/2023	1,294.18	1,295.85	1,297.28	1,292.30	0.01%
12/26/2023	1,293.99	1,296.39	1,300.15	1,291.82	-0.11%
12/25/2023	1,295.43	1,298.72	1,299.45	1,296.12	-0.14%
12/22/2023	1,297.25	1,296.95	1,303.93	1,295.80	0.18%

Each Date shows the value of one USD in KRW in price, the opening price, or the starting price of that day, the highest and the lowest price it was exchanged for. The Change.. is in relation to the difference between the columns Price and Open, such that when the price is greater than open, Change.. is positive and vice versa. we can say that the value in Change.. is a consequence of both Price and Open.

Table 2:

First six rows and four columns of the reshaped dataset

Jan	Feb	Mar	Apr
Week1 Day1	1,154.02	1,189.79	1,189.61	1,236.20
Week1 Day2	1,157.35	1,182.90	1,180.50	1,227.35
Week1 Day3	1,164.95	1,183.40	1,184.73	1,235.61
Week1 Day4	1,166.94	1,185.28	1,188.72	1,224.60
Week1 Day5	1,167.30	1,191.39	1,188.70	1,214.93
Week2 Day1	1,162.25	1,187.17	1,200.88	1,215.76

Table 2 follows with the restructuring of Table 1; this is done in such a way that all active days of each week are classified under each month of the year for the value “Price.” According to implication, day 1 week 1 may not necessarily be January 1, but the first business day upon which transaction/trading starts in the year.

This arrangement mimics the structure of the Randomized Complete Block Design (RCBD) with interactions where weeks are treated as “Blocks”, months as “Treatment” and the days as the interaction between Treatment and Block [7].

3.4 Data Overview

Consequently, upon Table 2, we have a box plot to illustrate the variability of the data as arranged by columns (months). The data that makes up Figure 1 are the values for week 1–16 for all five active days of each week. This means that we have 80 days (80 data points) for each month.

Figure 1.

Boxplot of the distribution of the price of 1 USD in each Month.

Figure 1 shows the price (or value) of 1 USD in KRW on the vertical axis and months on the horizontal axis. From the Figure presented, we see that the month with the lowest interval is January which is 1,080 and 1,285. The box plot for February has values close to the mean but has a few outliers., According to the data, the October box plot is the widest; with values far from its mean and a margin of over 300 KRW. It is appropriate to say that there is a stronger instability between August and November and it gradually stabilizes in December. When the year begins, the variation is minimal, and the trend continues until August-November.

Table 3:

Outliers in February

Date	Price
02/28/2023	1323.02
02/27/2023	1317.40
02/24/2023	1314.45
02/22/2023	1302.65
02/21/2023	1305.75

Table 3 shows the outliers detected in February explicitly. As shown in the table, the outliers are all clustered in the year 2023. Although the explanation to this phenomenon may need further investigation, the continuous incline of the value of 1 USD in KRW as shown in Investing.com [5] may be a contributing factor. The outliers could be a result of the continuous increase in the exchange rate, rather than the consequence of unusual events.

As discussed earlier, the value of a dollar and the variability of its values do not remain stable throughout the year. Figure 2 visualizes the distribution of the exchange rate for each month with the notable similarities, differences, and fluctuations in the exchange rate. For January and February, there are several peaks indicating high volatility, which suggests a considerable exchange rate with instability and high frequency for these two months. It is clear to see that there are two peaks in February, which suggests that exchange rates are significant during that particular time. For March and April, there are fewer peaks; these are less pronounced as indicated in Figure 2 when comparing the first two facets. March and April appear less volatile or more stable. May and July also show greater stability compared to the first four months. In contrast, volatility seems to increase in August, marked by a dip at the midpoint of the graph. This trend continues from September to November before stabilizing in December.

Figure 2:

Histogram in separate grids visualizing the distribution of the price of 1 USD in each Month.

Regardless of the inconsistent variance within the months, Figure 3 reveals a notable pattern that occurs in almost every treatment group. As highlighted in Figure 3, at Week 4, Week 8, and Week 12, the line graphs illustrate a vertical shift, implying an abrupt change in the exchange rate. This vertical shift is observed in all treatment groups except for September at Week 4, in every group at Week 8, and in seven out of twelve groups at Week 12. In essence, from 2020 to 2022, the exchange rate has experienced sudden changes at the end of each month. This pattern suggests a potential interaction between the exchange rate and the final week of the month, which warrants further investigation, though it is not the primary focus of our current research.

Figure 3.

Abrupt shifts in the line graph.

4. Experimentation and Computational analysis

The graphical representations of the data reveal several notable patterns in the exchange rate fluctuation. However, the discovered patterns do not directly relate to the research question, and thus a Randomized Complete Block Design is required to statistically test whether any observed differences in the exchange rate across the treatments and the blocks are due to random variation, or reflect systemic changes.

4.1 ANOVA Test

To determine if there are any significant differences in the exchange rate across the months and weeks, an ANOVA (Analysis of Variance) test is conducted. The ANOVA test is a statistical method used to compare the means of multiple groups to ascertain whether at least one group mean is statistically different from the others. This helps in understanding the effect of different factors on exchange rate variability.

In this study, we consider two main factors:

Treatments (Months): Corresponds to the 12 months of the year, from January to December
Blocks (Weeks): Corresponds to the 16 weeks (4 weeks per year) within each month over the period from 2020 to 2023

We employ a Randomized Complete Block Design (RCBD) to control for the variability between weeks while assessing the impact of different months on the exchange rate and to isolate the time-based volatility concentration.

Table 4:

Analysis of Variance Table

	Df	Sum Sq Mean Sq	F value	Pr(>F)
treat	11	685860.95 62350.9958485129	1189.03012272127	<2e-16
block	15	4661332.60 310755.506871104	5926. 09072947267	<2e-16
treat:block	165	1424379.39 8632.60238875568	164. 623261232979	<2e-16
Residuals	768	40272.79 52.4385334374988
Total	959	6811845.75

Table 4 presents the results of the ANOVA test. As shown in the table, the test statistics F-value for both treatments (Months) and blocks (Weeks) yield a p-value of less than 0.05. This indicates that there is a statistically significant difference in the exchange rate across the months and weeks. The results suggest that the exchange rate is influenced by the month and week, rather than random variation.

Table 5:

Post-hoc analysis of treatment using two methods

	mean	Tukey’s HSD	Fisher’s LSD
10	1275.792	a	a
9	1268.618	b	b
8	1246.398	c	c
11	1240.711	d	d
5	1237.381	d	e
7	1233.271	e	f
6	1224.960	f	g
4	1224.930	f	g
12	1219.327	g	h
3	1218.285	g	h
2	1195.350	h	i
1	1174.924	i	j

Table 6:

Post-hoc analysis of block using two methods

mean	Tukey’s HSD	Fisher’s LSD
16 1307.632	a	a
13 1306.276	a	a
15 1305.259	a	ab
14 1303.238	a	b
12 1294.916	b	c
11 1291.310	bc	d
10 1289.867	c	de
9 1287.907	c	e
4 1181.916	d	f
3 1180.900	d	f
1 1179.872	d	f
2 1174.901	e	g
8 1146.804	f	h
7 1146.480	f	h
6 1143.649	f	i
5 1138.649	g	i

4.2 Post-Hoc Analysis

To further investigate the differences in the exchange rate across the months and weeks, a post-hoc analysis is conducted. The post-hoc analysis helps to identify which specific months and weeks exhibit significant differences in the exchange rate. In this study, we utilize two post-hoc methods: Tukey’s HSD (Honestly Significant Difference) test [7] and Fisher’s LSD (Least Significant Difference) test [7]

Table 5 and Table 6 present the results of the post-hoc analysis for the treatments (Months) and blocks (Weeks), respectively, using Tukey’s HSD and Fisher’s LSD tests. These tables display the mean exchange rates for each treatment and block, along with the groups identified by each post-hoc method. For instance, the mean exchange rates for month 6 (July) and month 4 (April) are statistically indistinguishable according to both methods. Conversely, the difference in mean exchange rates between month 1 (January) and month 2 (February) is significant under both methods. Similarly, the statistical significance of differences in mean exchange rates across weeks is assessed using the same two post-hoc methods. Although the group classifications vary slightly between the two methods, the overall results reinforce the extreme probability values shown in Table 4, confirming that the mean exchange rates of USD to KRW are significantly different across both treatments and blocks.

Figure 4 demonstrates the interaction between months and weeks. If the effect of the week on the exchange rate were consistent across all months, the lines would be parallel. However, as illustrated in Figure 4, the slopes of the lines vary notably across different months, with multiple intersections. This variation suggests that the exchange rate is influenced by both the month and the week, indicating a significant interaction between these two factors.

Figure 4.

Interaction plot demonstrating the interaction between months and weeks

The interaction between months and weeks is further visualized in Figure 5. Ideally, if there were no interaction, the line graph within each facet would display a similar pattern, with minimal variation in slopes at each point. For instance, the line graphs for January and March exhibit mostly parallel trends. In contrast, the line graphs for January and November show significantly different patterns, indicating that the effect of the week on the exchange rate is not consistent between January and November. This observation highlights a significant interaction between the month and the week, corroborating the extreme probability values from Table 4.

Figure 5.

Faceted interaction plot demonstrating the interaction between months and weeks

5. Summary and conclusion

This study utilizes a Randomized Complete Block Design (RCBD) with months as treatments and weeks as blocks to statistically test the variability in the exchange rate of the Korean Won (KRW) against the United States Dollar (USD) from 2020 to 2023. The extremely small probability values from the ANOVA result indicate significant differences in the exchange rate across both months and weeks. The subsequent post-hoc analysis isolates these differences and confirms the meaningful interactions between treatments and blocks. This analysis explains how US Federal Reserve monetary policy implemented in 2022 affected Korean won/dollar exchange rate volatility through interest rate differentials and capital flows [12]

The exchange rate is highly influential on the domestic pricing of imported and exported goods, and the inconsistency of the exchange rate may lead to greater uncertainty in pricing, affecting inflation and economic stability. Moreover, the fluctuations in the exchange rate in recent years suggest the need for businesses and investors to develop better risk management and hedging strategies to prevent potential financial losses.

In conclusion, the study identified the volatility concentration in 2022 which reflects the aggressive interest rate increase by the US Federal Reserve (often referred to as “Giant Step”) implemented in 2022.The KRW stands out as the most stable in the first quarter of every year and gradually grows unstable as the year runs out; for which we can only speculate as of now. The strength of the USD appears to have progressed in the last four years, which may be due to foreign or domestic policies including monetary tightening; a measure of the US government to shrink inflation to the barest minimum Although the KRW appears weak compared to the USD; the prices of commodities have been relatively stable. For the further research, the true measure of the differences in means for months and weeks can be valid if a comparative multivariate analysis is conducted, and the performance of the Korean won is measured on a multidimensional scale across different currencies that factors their respective policies within the measurement period.

References

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[11] Bank of Korea. “Exchange Rate System”. Accessed: 2026–02–08. url: https://www.bok.or.kr/eng/main/contents.do?menuNo=400186.https://www.bok.or.kr/eng/main/contents.do?menuNo=400186

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