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Foreign Exchange Bid-Ask Spreads
- The SE Asian Interbank Market in 1997
Torbjörn Becker and Amadou Sy1
IMF, Research Department
August 1999
Abstract
An important aspect of financial and macroeconomic stability is how the financial markets
behave in times of crises. This paper studies the interbank markets for foreign exchange, and
in particular, the behavior of bid ask spreads in these markets in times of currency crises. Is it
for example the case that our standard models of bid ask spreads still apply in a crises? In the
Asian crises there were also more general questions of what happened with profits and entry
and exits in the interbank market. The paper addresses these question in two ways, one is a
qualitative description of different players account of the episode, and one is a quantitative
analysis of bid ask spreads covering the pre-crises period as well as the crises period. Some
of the results are that several markets experienced a severe liquidity crunch in the crises
period, which was reflected in the fact that many players left the market, and that the spreads
skyrocketed in the crises. However, this latter observation does not necessarily mean that
spreads were “unreasonable”, since it is also consistent with standard models of bid ask
spreads given the substantial increase in exchange rate volatility in the crises. High profits in
the foreign exchange market can thus partially be rationalized by the increased risk facing the
market participants, and some chose to leave the market to avoid the risk of making losses
while others stayed and could (potentially) make large profits.
Author’s E-Mail Address: Tbecker@imf.org , Asy@imf.org
1
The views expressed are those of the authors and do not necessarily represent those of the
Fund.
Acknowledgements to be added.
2
I. INTRODUCTION
Following the floating of the Thai baht on July 2, 1997 which marked the start of the Asian
crisis, bid-ask spreads on most Asian currencies skyrocketed to levels never seen before. For
instance, mean percent bid-ask spreads widened by factors of between 5 for the Malaysian
ringgit and 14 for the Indonesian rupiah. At the same time, commercial banks experienced
considerable profits on their foreign exchange trading2. These disruptions in the
microstructure of the foreign exchange markets have been, however, overlooked by
economists in spite of their consequences on financial and macroeconomic stability. This
paper addresses three main issues. First, it offers a description of the microstructure of the
Asian foreign exchange markets before and after the Asian crisis. Second, the paper analyzes
the behavior of bid-ask spreads and their determinants during the crisis. Finally, it discusses
whether banks earned “excess returns” during the crisis. Both the focus on emerging markets
and the Asian crisis distinguish this paper from other work in the field.
One interpretation of the increase in foreign exchange bid-ask spreads is that transaction
costs, i.e. the costs associated with converting emerging markets’ currencies into dollars, rose
drastically. For instance, in the aftermath of the Indonesian rupiah devaluation, the average
cost of carrying out a rupiah-dollar transaction on the spot market reached a hefty 1.7
percent, rising on occasion to as much as 10 percent. Such costs do have a significant impact
on various macro- and microeconomic variables. As an illustration, a report by the
Commission of the European Communities3 estimated, in 1990, that the elimination of
spreads following the adoption of a single European currency would result in savings of 0.4
percent of Community GDP per annum (ECU 15 billion), with the small and less developed
European economies gaining around one percent of their GDP (compared to 0.1-0.2 percent
for larger member states). The report also estimated total transaction costs incurred by nonfinancial firms to be on average 15 percent of their profits on turnover in other EC countries.
These figures doubled in the case of small firms, in particular when they were located in nonERM countries.
Transaction costs are not the only type of costs that firms face. In fact, during the crisis, both
bid-ask spreads on spot transactions and on forward contracts rose drastically. Since forward
transactions represented one of the most common form of hedging technique in the region,
the increase in their spreads represented a substantial rise in the cost of hedging, precisely at
the time when it was needed the most.
2
A recent report by the IIF (see IIF, Report of the Task Force on Risk Assessment, March
1999) remarked that, “...a diversity of business lines enabled most banks to offset losses in
Asia with record foreign exchange trading revenues. This enabled most financial firms to
emerge from the East Asian market turmoil without experiencing debilitating losses.”
European Economy, October 1990, No 44, “One market, one money: An evaluation of the
potential benefits and costs of forming an economic and monetary union.”
3
3
In contrast, bid-ask spreads can be interpreted as financial profits since they also represent
exchange margins and commission fees paid to brokers and commercial banks.
Consequently, the abrupt rise in bid-ask spreads during the Asian crisis resulted in record
trading profits for banks. One justification for these record profits is that these gains
represented compensation for the high levels of risk that had to be incurred during such
turbulent times.
Finally, the study of bid-ask spreads and more generally of the microstructure of foreign
exchange markets, is of interest for exchange rate economics since it can complement
traditional exchange rate models to analyze short-run exchange rate behavior, an area where
the conventional macro approach has been less successful4.
[This paper first describes developments in the foreign exchange market structure for
emerging East-Asian currencies during the 1997 Asian crisis. Second, the paper provides a
first study of bid-ask spreads of emerging East-Asian currencies during the currency crisis.]
II. THE FOREIGN EXCHANGE MARKET
A. Overview
The foreign exchange market5 is a largely unregulated, decentralized, quote driven
international market. Its major participants are market-makers at commercial and investment
banks who trade currencies with each other both directly and through foreign exchange
brokers. In the direct interbank market, market-makers typically maintain long or short
positions in a foreign currency (for settlement in two business days in a spot transaction) and
provide bid and ask prices upon demand. In the brokered interbank market, brokers arrange
trades in exchange for a fee, by keeping a book of market makers limit orders - that is,
orders to buy or sell a specified quantity of foreign currency at a specified price - from which
they quote the best bid and ask upon request. Brokered trading allows the rapid dissemination
of orders to other market-makers, anonymity in quoting, and the freedom not to quote to
other market-makers on a reciprocal basis. The other participants in the market are customers
of the market-making banks, who generally use the market to complete transactions in
international trade, and central banks, who may enter the market to move exchange rates or
simply to complete their own international transactions. Finally, nonbank financial
institutions like hedge funds are active players in the foreign exchange market.
4
See Flood and Taylor (1996)
See Flood (1991), “Microstructure Theory and the Foreign Exchange Market”, Federal
Reserve Bank of St. Louis
5
4
Estimates from a recent BIS survey6 of foreign exchange activities in the 43 largest centers
indicate that daily average turnover in traditional7 foreign exchange instruments (spot
transactions, outright forwards and foreign exchange swaps) could be estimated at some $1.5
trillion per day in April 1998, making the foreign exchange market the largest market in the
world. In current dollar terms, the net foreign exchange turnover increased by 26 percent
over April 1995. Compared with the 45 percent rise in 1995, the deceleration reflected the
appreciation of the US dollar, which led to a corresponding decrease in the dollar value of
non-US dollar transactions. Allowing for exchange rate adjustments8, this was an increase of
46 percent from the previous triennial survey, compared with a rate of expansion of 29
percent in the 1992-1995 period. In line with the surge in capital flows, the daily turnover of
global foreign exchange transactions as ratio of world trade continued to expand, from 60
times in 1995 to approximately 70 times in 19989.
Forward instruments (outright forwards and swaps) consolidated their predominant position
with 60 percent of total activity ($900 billion), pushing spot turnover down from 44 percent
in 1995 to 40 percent ($600 billion). Most forward transactions (85 percent) are made up of
foreign exchange swaps, 95 percent of which involve the US dollar.
The predominant market mechanism in the major centers is still the direct inter-dealer
market. In the UK, for example, the proportion of total foreign exchange business transacted
by brokers fell from 35 percent in 1995 to 27 percent in 1998, the remainder being conducted
bilaterally between banks. Electronic brokers increased their share of total foreign exchange
turnover from 5 percent in 1995 to 11 percent in 1998. Consequently, the proportion of
business conducted by traditional voice brokers, who quote prices over telephone lines to
dealing rooms, declined from 30 percent to 16 percent. Electronic brokers now handle almost
25 percent of total spot transactions in London.
The trend towards increased market concentration in the major centers continued. As an
illustration, the combined share of the top 10 dealers in London and in the US, rose from 44
and 48 percent respectively to 50 and 51 percent. The concentration levels are even higher in
medium-sized markets and most of the top players are foreign-owned institutions. In London,
for instance, 85 percent of aggregate turnover in 1998 are undertaken by foreign-owned
institutions.
6
Central Bank Survey of Foreign Exchange and Derivatives Market Activity (April 1998).
7
Daily turnover in the OTC derivatives market, which includes other foreign exchange
derivatives and all interest rate derivatives contracts was at $362 billion, 85 percent higher
than in April 1995. Interest rate products, with 73 percent of total turnover outweighed forex
instruments.
8
Adjusted for differences in the dollar value of non-dollar transactions.
9
See HKMA, November 1998, Quarterly Bulletin.
5
In contrast, global daily turnover in foreign exchange and interest rate derivatives contract
traded over-the-counter, including traditional forex derivatives instruments, was estimated at
$1.3 trillion in April 1998. This represented a growth of 66 percent since April 1995.
A breakdown by currency reveals the predominance of the dollar on one side of
transactions10 with 87 percent of average daily turnover, followed by the Deutsche mark (30
percent), and the Japanese yen (21 percent). A geographical distribution of global traditional
foreign exchange market activity shows that the United Kingdom comforted its leading role
with 32 percent of trading activity, while the United States ranked second with 18 percent of
total activity, widening the gap with Japan whose share was reduced to 8 percent.
Among emerging markets Singapore and Hong-Kong SAR are the major foreign exchange
trading centers. The recent BIS survey estimates the average daily turnover to about $139
billion and 79 billion respectively, comforting Singapore as the fourth largest foreign
exchange center in the world, ahead of Switzerland, Germany and France. Like other
financial centers, most of these figures represent transactions involving the three major
currencies. In Singapore, transactions in the dollar-yen currency pair represented about 22
percent of the total volume while trading in the dollar-mark pair constituted 23 percent. In
contrast, the share of transactions in the Singapore dollar was estimated at 17 percent.
Singapores foreign exchange market remains dominated by foreign exchange swaps and
spot transactions, which made up 54 and 43 percent respectively, of total foreign exchange
transactions. The remaining 3 percent comprised outright forward transactions. Of the total
turnover, 86 percent were transactions between financial institutions while trading with nonbank customers accounted for 14 percent reflecting the growing use of Singapore as a
regional base for corporations to operate their treasury operations.
Because of the consequences of the Asian crisis, the average net daily turnover of Hong
Kong’s spot foreign exchange dropped by 10 percent (to US$79 billion) in April 1998, down
from US$90.2 billion in April 1995. Spot deals fell by 10 percent mainly because of a 32
percent reduction in the trading of US dollar against the Deutsche mark. In contrast, turnover
of US dollar against Hong Kong dollar and US dollar against Japanese yen transactions
experienced robust growth rates of 25 and 30 percent respectively. The increase in Hong
Kong dollar was due to demand for business and financial transactions while the surge in yen
carry trades (driven by the large interest rate differential between US dollar and yen)
encouraged trading in Japanese yen. Net turnover of forward contracts fell by 15 percent, due
largely to a decline in foreign currency swaps.
10
Counting both currency sides of every foreign exchange transaction means that the
currency breakdowns sums to 200 percent of the aggregate.
6
In Hong Kong, about 70 percent of all FX transactions involve the US dollar (against
currencies other than the HK dollar), compared with 78 percent in April 1995. Transactions
involving the Hong Kong dollar accounted for 24 percent rising from 17 percent in 1995. The
dollar-yen is the most heavily traded currency pair with 26 percent of average net daily
turnover. However, the US-Hong Kong dollar pair with 22 percent of average daily turnover
has replaced the US-mark with 20 percent of daily turnover as the second common currency
pair.
In contrast, trading of OTC foreign exchange derivatives rose by 92 percent while that of
interest rate derivatives decreased by 31 percent. Overall, the net daily turnover of total
derivatives fell by 10 percent from $US4.2 billion in April 1995 to $US3.8 billion in April
1998. The HKMA attributes this decline to a reduction in the size of treasury activities of
some foreign institutions, caused partly by restructuring and partly by diminishing appetite
for risk. Forward transactions continued to account for a significant share of transactions with
61 percent of total foreign exchange transactions. Foreign exchange swaps dominated the
forward transactions with 92 percent of the total forward transactions, while outright forward
transactions accounted for 8 percent of the total. In April 1998, OTC interest rate derivatives
comprised the largest proportion of derivatives turnover with a 64 percent market share
compared with 36 percent in foreign exchange derivatives (OTC options and currency
swaps). However, the share of OTC interest rate derivatives fell from the 83 percent share
recorded in 1995.
According to the HKMA, the share of the inter-broker market remains unchanged at 34
percent of all foreign exchange transactions. Foreign exchange transactions with overseas
banks decreased from 71 percent to 69 percent of the net turnover. The share of foreign
authorized institutions fell from 84 percent to 73 percent of all foreign exchange and
derivatives transactions. Market concentration remained high with the top 10 players still
accounting for 51 percent of gross turnover and the top 30 players for 78 percent.
B. Emerging Market Currencies
Prior to the Asian crisis, the Thai baht had been perhaps the most liquid of the Asian
currencies with 1996 survey data11 from Singapore suggesting a total average daily trading
volume on the interbank market of $14 billion. The volume on the spot market was $5
billion compared to $9 billion in the swaps and forward markets. Total volumes for the
Malaysian ringgit and the Indonesian rupiah were respectively $9.5 and $8.5 billion.
Although volumes on the spot market were estimated at $6 and $5 billion, these currencies
had smaller swaps and forwards volumes of about $3.5 billion each. Total daily volume for
the Singapore and the Hong Kong dollar were $7.5 and 4 billion respectively with $3.5 and
$2.0 billion worth of spot transactions each. The less traded currencies of South Korea,
Taiwan POC, India, China and the Philippines had estimated volume ranging between 2.4
billion for the won to 400 million for the peso. The New Taiwan dollar and the rupee both
11
See Singapore Foreign Exchange Market Committee (1996).
7
had estimated daily volumes of $1.1 billion while the figure for the renminbi was about $400
million.
Although the BIS survey does not explicitly collect data on emerging market currencies, it
provides an estimate of market size by approximating total market turnover in local currency
estimate. By April 1998, the most active markets were for the Singapore and the Hong Kong
dollars, and to a lesser degree the Thai baht (see Table 1). The Hong Kong and the Singapore
dollars had daily average turnovers of US$19 and US$18 billion, respectively. In contrast,
turnovers for the Thai baht decreased by about 50 percent to $2.5 billion, while trading for
the rupiah and the ringgit melted by 80 and 90 percent to daily averages of $972 and $660
million, respectively. Because of the reported low levels of liquidity, most of the forward
transactions were short-term and were very often rolled over. The non-deliverable forward
markets were dominated by the New Taiwan dollar, the Korean won, and at a smaller scale,
the peso, the renminbi and the rupiah. In contrast, total turnover for other emerging markets
were lower, ranging from $8.5 and $7 billion, respectively for the Mexican peso and the
South African rand to $1.2 billion for the Chilean peso, (see Table 2).
In the aftermath of the crisis, the number of market participants had decreased and positions
were smaller than before the crisis. The size of deals shrank12, with standard interbank and
interbroker amounts declining, for example for the baht from $10-20 million to $3 million for
spot transactions and from $20 million to $10 million on forward markets. The number of
interbank players declined on average by more than half their previous number with, for
example, the number of institutions trading on the spot market for ringgit down from 25 to 12
and on the forward market form 50 to 20. The composition of the foreign exchange market
had also changed. In fact, because of the high levels of bid-ask spreads, the broker market
was said to be playing an increasing role with currently about 65 percent of the transaction
volume in Singapore, up from 5 percent before the crisis. In the midst of the crisis, a larger
proportion of the transactions were reportedly through the broker market. On the other hand,
the interbank market was said to be dominated by a few core international banks. Finally,
hedgers, mostly equity investors, proprietary trading desks and hedge funds, were reportedly
still active on the other side of the transactions.
Table 1. Foreign Exchange Turnover in Asian Marketsa
(Daily averages in millions of US dollars)
Country
Hong Kong
Singapore
Thailand
South Korea
Taiwan
India
12
1998b
18,711
17,644
2,574
2,289
1,720
1,389
See IMF, “International Capital Markets” (1998)
1996c
4,000
7,500
14,000
2,400
1,100
1,100
Change
368%
135%
-82%
-5%
56%
26%
8
Indonesia
Malaysia
Philippines
China
972
660
492
211
8,500
9,500
400
400
-89%
-93%
23%
-47%
a
Spot, outright forwards, and foreign exchange swap transactions. Net of local inter-dealer double-counting.
Local currency against US$.
b
Source: BIS, May 1999 (Annex Table E-7, Central Bank Survey of Foreign Exchange and Derivatives Market
Activity, 1998).
c
Source: Singapore Foreign Exchange Committee, 1996, Annual Report.
Table 2. Foreign Exchange Turnover Non-Asian Emerging Marketsa
(Daily averages in millions of US dollars)
Country
Argentina
Brazil
Chile
Mexico
South Africa
Czech Republic
Poland
Russia
Saudi Arabia
1998
2,173
5,127
1,212
8,543
7,289
4,169
1,315
4,728
1,422
a
Spot, outright forwards, and foreign exchange swap transactions. Net of local inter-dealer double-counting.
Local currency against US$.
Source: BIS, May 1999 (Annex Table E-7, Central Bank Survey Of Foreign Exchange and Derivatives Market
Activity, 1998).
III. OVERVIEW OF THE LITERATURE
Microstructure theory decomposes bid-ask spreads, the standard measure of transaction costs,
in three different types of costs: (1) order processing costs; (2) asymmetric information costs
and (3) inventory-carrying costs. Order processing costs cover the cost of providing liquidity
services and are negligible in the foreign exchange market given the efficiency with which
transactions are completed and their size. Asymmetric information costs, which are attributed
to the presence of information-motivated traders, are difficult to motivate in the foreign
exchange markets and are far less relevant in the stock markets. However, customer order
flows13 or central bank intervention14 have been recently analyzed. Surveys of individual
13
See Lyons (19XX), Hsieh et Al. (1996).
14
See Bossaerts and Hillion (1991).
9
traders in the interbank market (see Cheung and Wong, 1999) indicate that practitioners
generally follow the market convention to set their interbank bid-ask spreads. The practice is
perceived as a means to maintain an equitable and reciprocal trading relationship between
dealers. Market uncertainty15 is reportedly the most important reason for deviating from the
conventional interbank bid-ask spreads. In this paper, we focus on market makers inventory
carrying costs.
For a bank, maintaining open positions in currencies is costly because of uncertainties in
forecasts of price risk, interest rate costs, and trading activity. The notion of a desired
inventory level for the market-maker underlies all of the theoretical models relating bid-ask
spreads and inventory-carrying costs16. Our study will investigate whether inventorycarrying cost proxies can significantly explain time series variation in spreads in the direct
interbank foreign exchange market.
Greater uncertainty regarding the future spot rate, as associated with greater unexpected
volatility of the spot rate, is likely to result in a widening of the spread, as risk-averse traders
increase the spread to offset the increased risk of losses. GARCH models of the variance
have found that bid-ask spreads depend positively on volatility17. Recently, option-implied
volatility measures18 have been used for the same purpose and confirm the earlier findings.
When holding a currency inventory, a market-maker foregoes the interest rate that can be
earned on less liquid deposits. The alternative to maintaining liquid currency inventories is to
respond to buy and sell orders by settling transactions at another banks ask price or bid
price, effectively paying the bid-ask spreads on its settling transactions. Consequently,
earning a spread on transactions associated with order imbalances requires that the bank be a
net supplier of liquidity to other traders. A measure of the opportunity cost resulting from the
requirement to maintain liquid inventories is the difference between the interest rate earned
on a highly liquid positions and the interest that could have been earned on similar but less
liquid positions.
The third component of inventory-carrying costs involves trading activity. There is evidence
that spreads tend to increase when markets are less active as before the week-end and a
15
The major reasons for deviating from the market convention were: a thin/hectic market,
before/after a major news release, increased market volatility, and an unexpected change in
market activity.
16
See the dynamic optimization models of Bradfield (1979), Amihud and Mendelson (1980)
and Ho and Stoll (1981). See Lyons (19XX).
17
See Glassman (1987), Boothe (1988), Bollerslev and Domowitz (1993), Bollerslev and
Melvin (1994), and Lee (1994).
18
See He and Wei (1994), Jorion (1995)
10
holiday. For example, Glassman (1987) finds that bid-ask spreads widen on Fridays and
Bessembinder (1994) finds that measures of liquidity cost and risk variable are more
pronounced before nontrading intervals. Trading activity is also measured by trading volume
and many authors have documented the positive correlation of bid-ask spreads with volume.
Empirically, however, trading volume is highly autocorrelated, in addition, expected and
unexpected volume can be discriminated. Cornell (1978) argues that spreads should be a
decreasing function of expected volume because of economies of scale leading to more
efficient processing of trades and because of higher competition among market makers. The
theoretical model of Easley and OHara (1992) reaches a similar conclusion. Unexpected
volume, however, reflects contemporaneous volatility through the mixture of distribution
hypothesis and should be positively related to bid-ask spreads.
Boothe (1988) treats volume as an omitted variable and performs misspecification tests.
While estimators are less efficient and potentially inconsistent, the direction of potential
coefficient bias is such that hypothesis tests regarding the importance of uncertainty are
rendered more conservative. Hartmann (1998) reviews the limitations of the different
methods to measure trading volumes used in the literature. In a recent paper, the same author
uses the only long time-series of daily spot foreign exchange trading volume currently
available, that of the dollar-yen. Hartmann (1999) shows that, in line with standard spreads
models and volume theories, that unpredictable foreign exchange turnover increases with
spreads, while predictable turnover decreases them.
Finally, Huang and Masulis (1999) have recently measured competition in the FX markets
for major currencies by the number of dealers active in the market and find that bid-ask
spreads decrease with an increase in competition, even after controlling for the effects of
volatility. The expected level of competition is time varying, highly predictable, and displays
a strong seasonal component that in part is induced by geographic concentration of business
activity over the 24-hour trading day.
Most research in market microstructure presumes the existence of a single market
mechanism. Dealers can trade directly with each other on a bilateral basis, or can place
orders through interdealer brokers. Recently, however, Saporta (1997) has analyzed the
determinants of agents’ choice of market mechanism. She shows that sufficient increases in
asset volatility, in the customer’s liquidity needs and in the aversion of dealers to risk can
cause a shift of inter-dealer trading from the direct inter-dealer market to the brokered market
and vice-versa.
IV. DATA AND ESTIMATION
Theories about the determinants of the bid ask spread suggest that a number of variables
should be included in a study of spreads: exchange rate risk/volatility (with a positive sign),
expected (-) and unexpected (+) volume, a measure of the alternative/liquidity cost (+),
weekday dummies and year/time dummies. In this section the measures and data used for
these concepts are discussed. Throughout the paper, the following notation will be used at
11
different occasions: At is the ask price and Bt is the bid price of a currency, ASt is the absolute
spread given by ASt  At  Bt , the midpoint Mt is given by M t  Bt  At 2 , and the
percentage spread PSt is defined as PSt  ASt M t .
b
g
The currencies studied are the Thai baht (THB), the Indonesian rupiah (IDR), the Korean
won (KRW), the Malaysian ringgit (MYR), the Philippine peso (PHP), the Singapore dollar
(SGD), the Hong Kong dollar (HKD), and the Japanese yen (JPY). In general, daily data
covering the period 1/1/1990 to 11/2/1998 is used, although in some cases data is available
only for a shorter period, which is evident in the graphs of the exchange rates versus the US
dollar in Figure 119. The five first currencies (THB, IDR, KRW, MYR, PHP) in the graph
are currencies with (relatively) fixed exchange rates that were floated during the Asian crises.
The next two are first the relatively flexible SGD and secondly, the HKD that is under a
currency board regime (note the scale on the HKD graph). Finally, the JPY is included as a
reference to a major mature market world currency with Asian origin.
The Asian crises is evident in the graphs of the first five currencies, in terms of sharp
depreciations starting in July 1997 for the Thai baht, the Philippine peso and the Malaysian
ringgit, in August for the Indonesian rupiah, and in November for the Korean won. Also the
Singapore dollar and the Japanese yen depreciated during the Asian crises, while the Hong
Kong dollar remained under a currency board regime despite pressure that was particularly
severe in late October (see for example the ICMR September 1998 Box 2.12 for a
chronology of the Asian crises).
19
More specifically, data for THB starts 5/6/91, for IDR 11/19/90, for KRW 5/30/90 and for
PHP 5/18/92.
12
Figure 1. Daily Exchange Rates versus US Dollar
(Bid-Ask Midpoint)
60
50
16000
2000
14000
1800
12000
1600
10000
1400
40
8000
1200
6000
30
1000
4000
800
2000
20
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
0
1/ 01/ 90
12/ 02/ 91
THB
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
600
1/ 01/ 90
12/ 02/ 91
I DR
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
10/ 02/ 95
9/ 01/ 97
KRW
5. 0
50
2. 0
4. 5
45
1. 9
4. 0
40
3. 5
35
3. 0
30
2. 5
25
2. 0
1/ 01/ 90
20
1/ 01/ 90
1. 8
1. 7
1. 6
12/ 02/ 91
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
1. 5
1. 4
12/ 02/ 91
MYR
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
PHP
7. 82
1. 3
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
SGD
180
7. 80
160
7. 78
140
7. 76
120
7. 74
100
7. 72
7. 70
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
HKD
10/ 02/ 95
9/ 01/ 97
80
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
JPY
A. Bid-Ask Spreads
This section characterizes bid ask spreads in the Asian interbank market, looking at both time
series and cross sectional aspects of bid ask spreads20. Figure 2 contains the absolute spreads
on a daily basis since 1990 (see footnote 19 for data availability and for the scaling of
spreads, see note “a” in Table 3). It is clearly evident that for the first five currencies there
were dramatic increases in the spreads concurrent with the abandonment of the fixed
exchange rates in the crises. One interesting observation to make though, is that in Korea, the
increase in the bid-ask spreads occurred before the currency was actually floated, suggesting
that the uncertainty of the exchange rate was felt prior to the float. This increase started in
September 1996, long before both the won and the baht were floated.
Note that we are using average daily interbank spreads from Reuters’ database, which are
narrower than indicative intra daily quotes on the Reuters screen (see, e.g., Bessembinder,
1994 and Lyons, 1995).
20
13
Figure 2. Interbank Bid-Ask Spreads
1200
140000
1000
120000
5000
4000
100000
800
3000
80000
600
60000
400
1000
200
0
1/ 01/ 90
2000
40000
20000
12/ 02/ 91
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
0
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
THB
10/ 02/ 95
9/ 01/ 97
0
1/ 01/ 90
12/ 02/ 91
I DR
1000
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
10/ 02/ 95
9/ 01/ 97
KRW
3000
80
2500
800
60
2000
600
1500
40
400
1000
20
200
0
1/ 01/ 90
500
12/ 02/ 91
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
0
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
MYR
10/ 02/ 95
9/ 01/ 97
PHP
80
0
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
SGD
100
80
60
60
40
40
20
0
1/ 01/ 90
20
12/ 02/ 91
11/ 01/ 93
HKD
10/ 02/ 95
9/ 01/ 97
0
1/ 01/ 90
12/ 02/ 91
11/ 01/ 93
10/ 02/ 95
9/ 01/ 97
JPY
Table 3 contains the empirical frequency distributions of the absolute spreads. The table
shows that the clustering of bid ask spreads observed in mature markets (see, e.g.,
Bessembinder,1994 and Bollerslev and Melvin, 1994) is evident also in these emerging
markets21. The most common spread accounts for anywhere between 18 to 84 percent of the
observations before the crises (with a cross-country average of 53%), while the cumulative
frequency of the 3 most common spreads range from 40 to over 90 percent (80%). It is
interesting to note that the strong clustering observed in relatively calm times is reduced
during the crises period. This is not too surprising given the substantial increase in
uncertainty and level change of the exchange rates. The cross-country average is down to 36
percent for the most common and 70 for the three most common spreads during the crises.
21
The clustering occurs when the exchange rates are stated in the European way, that is,
home currency per US dollar, which is the conventional way of quoting these currencies.
14
Excluding HKD and JPY the reduced clustering in the crises period becomes even more
evident.
Although absolute spreads are not suitable for comparison between countries or when
exchange rates change dramatically, it is still of some interest to note that for the first five
currencies the mean absolute spread increase roughly by a factor 10 in the crises period. For
the rupiah, the increase is around 60 times, while for the peso only around two times. The
peso, however, had experience a steady decline in spreads in the years before the crises, and
if compared with only the year before the crises, the mean spread increased by almost a
factor 10 in the crises, comparable with the other countries.
Table 3. Frequency Distributions of Absolute Spreadsa,b
Currency
THB
IDR
KRW
MYR
PHP
SGD
HKD
JPY
Pre-crises
3
Mean
30
21.9
(92)
200
329
(68)
30
62
(74)
1
20
(66)
300
(23)
10
(42)
2
10
(86)
100
(46)
20
(64)
10
(68)
500
(18)
10
(74)
10
(81)
20
(81)
100
(34)
20
(81)
5
(88)
15
(86)
400
(45)
5
(87)
20
(92)
5
(49)
10
(85)
7
(97)
14
278
11
10
7
Crises
3
Mean
100
274
(72)
3000 20734
(49)
300
522
(62)
Max
300
(0.1)
1500
(0.1)
1500
(0.1)
1
200
(33)
30000
(20)
400
(28)
2
300
(56)
20000
(39)
500
(46)
100
(0.2)
1000
(3)
50
(0.7)
74
(0.1)
100
(32)
500
(15)
20
(32)
10
(76)
50
(45)
1000
(30)
30
(58)
5
(88)
95
(57)
400
(42)
10
(82)
20
(93)
105
100
(0.1)
5
(50)
10
(95)
7
(98)
7
595
23
10
Max
1000
(2)
125000
(0.3)
4000
(1)
810
(0.3)
2700
(0.3)
70
(0.3)
50
(0.6)
10
(45)
a
The absolute spreads have been scaled to make the smallest absolute spread observed an integer, so THB is
multiplied by 1000, IDR by 100, KRW by 100, MYR by 10000, PHP by 1000, SGD by 10000, HKD by 10000,
and JPY by 100.
b
The table contains the 3 most common spreads with cumulative frequency in parenthesis. The Max spreads are
with frequency in parenthesis.
Table 4 provides some summary statistics for percentage spreads, which can be used to
compare the transaction costs between countries and time periods, since it takes into account
the level of the exchange rate (or put differently, it converts the spreads to dollars). The time
series dimension indicates that it became substantially more expensive to get in and out of
15
one of the first six currencies on the list in the crises period compared with the pre-crises
years. For some currencies (IDR, MYR, PHP), the year ahead of the crises had been a year of
declining spreads, while for Thailand and especially Korea, the trend was towards greater
spreads. These developments for the baht and the won are consistent with a build up of
uncertainty regarding these exchange rates well ahead of the actual float.
Comparing the different countries in the region, we see that spreads in HKD, which operates
under a currency board, were extremely small compared not only to the emerging markets’
currencies but also to the yen. At the other end of the spectrum were IDR and PHP during the
crises period, with percentage spreads of more than 100 times the spreads in HKD. Note also
that MYR had the smallest spreads of the emerging markets, excluding HKD, both before
and after the crises, and even smaller than JPY in the pre-crises period. PHP experienced the
most significant reduction of spreads leading up to the crises, with spreads down to 23
percent in the year before the crises compared to 106 percent for the entire pre-crises period.
In the crises, however, spreads came back up to levels well above the pre-crises mean.
Table 4. Mean Percentage Spreadsa
THB
IDR
KRW
MYR
PHP
SGD
HKD
JPY
a
Pre crises
0.087
0.159
0.075
0.052
1.062
0.071
0.013
0.062
96/97
0.131
0.088
0.345
0.040
0.237
0.069
0.012
0.060
Crises
0.683
2.159
0.422
0.283
1.635
0.140
0.014
0.057
Full sample
0.193
0.495
0.128
0.087
1.181
0.081
0.013
0.061
Unscaled absolute spreads divided by the midpoint of the exchange rate
As a first cursory investigation of the relationship between spreads and the volatility of the
exchange rate, Table 5 presents the ratio of spreads to exchange rate volatility, measured as
the standard deviation of exchange rate returns (i.e., the first difference of the logarithm of
the exchange rate)22. The most obvious observation is that volatility increased for all of the
currencies in the crises period, with a factor of anything between marginal increases to forty
fold increases depending on country and reference period. Moreover, dividing absolute and
22
The returns are used to compute the volatility measure since in general, a unit root in the
level exchange rate series cannot be rejected at normal significance levels. Hong Kong is the
only case where the null of a unit root can be rejected, but the same volatility measure is used
for comparability.
16
percentage spreads with volatility seems to “explain” a fair amount of the spread explosion in
the crises period in the sense that these ratios are not higher in the crises period than in other
periods. Instead, volatility adjusted percentage spreads are in all cases except for THB lower
in the crises period compared with earlier periods. For IDR this is not the case when absolute
spreads are used in the numerator, due to the substantial depreciation of the currency,
although for the other currencies the fall in the ratio is observed also for the absolute spread
volatility ratio.
Table 5. Exchange Rate Volatility and Spreads
Pre crises
96/97
Crises
Full sample
a
Volatility
THB
IDR
KRW
MYR
PHP
SGD
HKD
JPY
THB
IDR
KRW
MYR
PHP
SGD
HKD
JPY
36.46
11.61
17.19
20.80
38.46
23.51
3.45
68.33
87.37
14.10
26.86
16.63
4.51
15.80
1.71
62.84
197.1
485.7
255.4
165.8
143.3
79.87
3.97
98.28
89.62
19.96
102.9
67.39
73.75
37.90
3.53
73.63
6.0
2836.4
361.8
0.65
72.5
0.48
2.97
10.6
AS/Volatility
3.8
13.9
1478.0
4269.4
1108.7
204.5
0.61
0.64
137.9
41.5
0.62
0.29
5.47
2.72
11.0
7.4
7.5
1882.9
128.2
0.41
46.7
0.34
2.92
9.8
PS/Volatility
THB
0.238
0.149
0.346
0.215
IDR
1.365
0.623
0.445
0.248
KRW
0.436
1.284
0.166
0.124
MYR
0.248
0.243
0.171
0.129
PHP
2.762
5.244
1.141
1.602
SGD
0.300
0.435
0.176
0.214
HKD
0.383
0.706
0.351
0.378
JPY
0.091
0.096
0.058
0.083
a
Volatility is measured as the standard deviation of the exchange rate
return in percent.
17
In the contagion literature, a great deal of attention has been given to how returns are
correlated across different market before and during a crises. In Table 6, the correlations
between spreads for the different currencies are displayed before and during the crises. The
overall impression is that there is some correlation, but perhaps less than expected. However,
this is only contemporaneous correlations based on daily data, so there may be lagged
responses that are not picked up here. As for the comparison between pre-crises and crises,
there are relatively little change in the picture except for THB and JPY, with the former
displaying a clear increase in correlations while in the latter case all the pre-crises correlation
seems to vanish in the crises period.23
Table 6. Correlations Between Absolute Spreadsa
THB
IDR
KRW
MYR
PHP
SGD
HKD
JPY
THB
IDR
KRW
378
0.07
0.11
0.09
0.03
0.04
0.05
0.10
0.07
93201
-0.08
0.10
0.27
0.12
0.11
0.05
0.11
-0.08
21689
-0.08
-0.28
0.00
-0.01
0.08
MYR
PHP
Pre-Crises
0.09
0.03
0.10
0.27
-0.08
-0.28
63
0.24
0.24
53760
0.41
0.13
0.19
0.09
0.14
-0.00
Crises
THB
28494
0.12
0.07
0.18
0.33
IDR
0.13
4.8E10
0.09
0.24
-0.14
KRW
0.07
0.09 194043
0.17
0.10
MYR
0.18
0.24
0.17
9954
-0.07
PHP
0.33
-0.14
0.10
-0.07 153597
SGD
0.31
0.47
0.07
0.32
-0.05
HKD
0.23
-0.06
0.03
0.09
0.14
JPY
0.08
-0.05
-0.02
-0.05
0.04
a
Above 10% in light gray, above 20% in dark gray.
SGD
HKD
JPY
0.04
0.12
0.00
0.41
0.13
13
0.39
0.20
0.06
0.11
-0.01
0.19
0.09
0.40
11
0.15
0.10
0.06
0.08
0.15
-0.01
0.20
0.15
6
0.31
0.47
0.07
0.32
-0.05
136
0.06
0.04
0.23
-0.06
0.03
0.09
0.14
0.06
30
-0.00
0.08
-0.05
-0.02
-0.05
0.04
0.04
-0.00
6
B. Exchange Rate Risk
23
[Discuss problem with correlation measure with large differences in variances, a la
contagion literature]
18
In Table 5, volatility was measured as the standard deviation over a certain time period. Such
measure can serve as a first check of the relevance of volatility, but suffers the obvious
limitation of being constant over the period it is measured, while changes in spreads and
exchange rate volatilities may be high frequency events. To produce high frequency
measures of the (perceived) exchange rate risk, GARCH models are estimated for the
midpoint of the exchange rates, and then used to compute time varying conditional variances
for the exchange rates. Following the literature in this area, the estimations are based on first
differences of the logarithm of the exchange rate series, which is done to remove the unit root
in the original level series24. Furthermore, the transformed series have the interpretations of
being one day returns on holding the currency. The estimated model used for all exchange
rates is a GARCH(1,1) model with dummies for weekdays and floating of the exchange rate
in the variance specification (Di ,Df)25. The dummy for the float is also included in the mean
equation. Formally, volatility is measured by the conditional variance obtained from the
GARCH(1,1) model
Rt   M  Df   t

4
2
R ,t
      i Di   5 Df  2t 1   2R ,t 1
(1)
i 1
c h
where Rt  10,000 log M t and  t It ~ N 0,  2t 1 . The conditional variance  2R ,t is the one
period ahead forecast of the variance given information at time t-126. The ’s, , ’s, , and 
are the parameter to estimate.
24
Simple ADF and PP tests of the level data confirm that the null of a unit root cannot be
rejected for 7 of the 8 series. For the HKD, the null can be marginally rejected, however, the
first difference of the log series is still used to conform to the estimation for the other
countries. Furthermore, as a test, GARCH in levels were also estimated and the resulting
conditional variance series was perfectly (to the third decimal) correlated with the series from
the first difference GARCH.
25
Since the specification test of the standardized residuals sometimes suggested that the
model needed to be extended to include MA or AR components in the mean, these more
elaborated models were also estimated and the resulting conditional variance series were
compared to the ones obtained by the basic GARCH(1,1). In all the cases, the correlation
between the series were between .99 and 1, and to maintain as much comparability as
possible, the basic model was used in the remainder of the investigation.
26
In Bessembinder (1994), the author includes the conditional variance led one period in the
spread equation (see p. 328), which seems to suggest that the author allows the traders to
include information at time t for the forecast for time t. In this paper, time t information about
volatility is not assumed to be known for the spread decision at time t. In other words, we use
 2t rather than  2t1 as the volatility forecast in the spread equation.
19
Table 7 present the mean of the estimated conditional variances. Comparing these numbers to
the cruder volatility measure presented in Table 5, we see that the numbers correspond
almost perfectly if the standard deviations in Table 7 are multiplied by a factor 10. However,
the GARCH model also produces a daily series of potentially changing conditional variances,
which is used in the estimation section below.
There are obviously other ways to measure the perceived exchange rate risk, and this is only
one measure. In section [] realized volatility is used, while implied volatility from options
prices has not been investigated further, since it suffers from both computational problems,
lack of data and worst of all, is based on models that assume a constant volatility, such as
Black and Scholes. For a more detail account of the pros and cons of theses measures, see for
example [Jorion ?, Diebold et al ?].
Table 7. Mean Conditional Variancesa
Pre crises
96/97
Crises
Full sample
10.9
59.9
441.6
87.8
THB
3.3
7.7
21.0
9.4
1.57
2.01
2583.4
435.8
IDR
1.3
1.4
50.8
20.9
3.7
8.1
701.1
114.2
KRW
1.9
2.8
26.5
10.7
4.7
3.4
276.9
45.9
MYR
2.2
1.8
16.6
6.8
21
4.1
255.8
69.6
PHP
4.6
2.0
16.0
8.3
5.8
3.5
69.2
15.4
SGD
2.4
1.9
8.3
3.9
0.15
0.04
0.28
0.17
HKD
0.4
0.2
0.5
0.4
46.9
40
96.5
54.4
JPY
6.8
6.3
9.8
7.4
a
Mean Standard deviations in italics for comparison with
volatility in Table 5.
In Table 6 the correlation between spreads were displayed for the pre-crises and crises
period, with a reference to the current contagion literature. In Table 8, the correlations
between conditional variances are presented. The pattern of increasing correlations that is
found in the contagion literature (see, e.g., Rigobon and Goldfajn) shows up quite strongly
here. During the crises period, almost all the currencies’ conditional variances become
positively correlated and relatively strongly so, with the striking exception being JPY, where
the correlations with the first five currencies become negative in the crises period.
20
Table 8. Correlations Between Conditional Variancesa
THB
IDR
KRW
MYR
PHP
SGD
HKD
JPY
THB
IDR
KRW
19.2
0.07
-0.02
0.10
-0.05
-0.02
-0.00
0.19
0.07
2.2
0.26
0.05
-0.04
0.28
0.18
0.06
-0.02
0.26
5.9
-0.05
-0.15
0.16
-0.07
0.13
MYR
PHP
Pre-Crises
0.10
-0.05
0.05
-0.04
-0.05
-0.15
8.3
-0.06
-0.06
34.7
0.17
0.07
0.03
-0.01
0.02
-0.15
Crises
668
0.17
0.14
0.23
0.14
THB
0.17
3163
0.32
0.65
0.45
IDR
0.14
0.32
1661
0.12
0.43
KRW
0.23
0.65
0.12
308
0.51
MYR
0.14
0.45
0.43
0.51
161
PHP
0.13
0.42
0.06
0.48
0.32
SGD
0.11
0.41
0.07
0.34
0.25
HKD
-0.16
-0.07
-0.14
-0.21
-0.29
JPY
a
Above 10% in light gray, above 20% in dark gray.
SGD
HKD
JPY
-0.01
0.28
0.16
0.17
0.07
5.0
0.26
0.41
-0.00
0.18
-0.07
0.03
-0.01
0.26
0.31
0.14
0.19
0.06
0.13
0.02
-0.15
0.41
0.14
22.1
0.13
0.42
0.06
0.48
0.32
53
0.33
0.21
0.11
0.41
0.07
0.33
0.25
0.33
0.39
0.03
-0.16
-0.07
-0.14
-0.21
-0.29
0.21
0.03
57
C. Volume Measures
Measures of expected and unexpected volume are problematic for several reasons. First,
there is no daily data available on interbank forex transactions, and even if there was such
data, the issue of simultaneity between spreads and the volume would have to be dealt with.
In this study, we use the daily volume in the stock market as a proxy/instrument for the
volume in the interbank market. The reason that stock market volumes are used is that the
data exists readily and that we postulate that some of the foreign exchange trade is motivated
by transactions in the local stock markets that investors want to convert into different
currencies. The next issue that arises irrespective of the series used is how it should be
decomposed into an expected and an unexpected component. In other studies this has been
achieved by fitting univariate ARIMA models to the levels or differences, and let the
predicted value represent the expected volumes and the residuals be the unexpected
component.
21
The strategy employed here is to fit the smallest possible ARIMA model that passes the
standard residual test, but in the case there are indications of ARCH effects, these are
included in the estimation process and thus a slightly more general model is used for the
volume decomposition. Since ADF tests of all the series rejected the null of a unit root in the
series, the ARMA model for the means are based on the series in levels. In general, the series
could be well described by the ARMA(2,1)-GARCH(1,1) model according to
Vt   0  1Vt 1   2Vt 2   t   t 1
 V2 ,t   0   1 2t 1   2 V2 ,t 1
(2)
Using a ARMA-GARCH model also allow us to use an alternative measure of the
uncertainty regarding volumes, namely the conditional variance of the residual, rather than
the residual itself27. This is potentially a more appealing measure of the uncertainty in
volume compared to using a single residual to measure the uncertainty in volumes, since it is
based on more information and has a natural forward looking property making it suitable for
forecasting the uncertainty, not only notice it when it has happened, which is the case when
the residual itself is used.
D. Measures of Alternative Cost
In the literature it is argued that an interest differential should enter the analysis of spreads to
account for the alternative cost of performing the service of creating liquidity in the foreign
exchange market and thus forego a more attractive alternative use of funds. The measure
used by Bessembinder (1994) is the interest differential between overnight deposit rates
(''short'') and one month deposit rates (''long'') in the Eurodollar market, the motivation being
that the longer maturity return is foregone and only the shorter maturity return is received for
the stock of foreign exchange. To make this a cost in a narrow business/accounting sense, we
have to (at least) make the assumption that the long rate is always higher than the short,
which is already a restrictive assumption that clearly is incorrect in certain periods. More
27
Missing observations creates a problem of non-continuous samples that makes the
GARCH and MA estimation break down in Eviews. This has been handled by extrapolating
the existing data in a relatively ad hoc way; if there is one point missing, the previous data is
repeated, if there are two points missing, the last and then the next data points are used, and
in the few cases of more consecutive missing observations, the last strategy is complemented
by a simple linear extrapolation between the points. To check that the series has not been
damaged too much by these ad hoc fixes, a simple AR(1) is run on both the original and
continuous series, to check that at least these parameter estimates are the same for both
series. Since the volume series have more missing observations, it is no surprise that the only
statistically different results are obtained for two of these series, the one for Japan and
Philippines. The Philippines series look very strange before 11/19/96, so that was no surprise.
After that date the adjusted series does not display any difference to the original in this AR(1)
sense.
22
importantly is that from an economic perspective this is a measure that hinges on the
preferred investment horizon, what is perceived as the natural alternative to holding foreign
exchange (could be domestic currency, stocks,...). In the current study, four interest
differentials have been used in the empirical models (to the extent data is available), first the
standard Eurodollar short-long differential, secondly the domestic currency short-long
differential, and finally the differential between foreign and domestic rates, both for short and
long maturity.
E. Estimating the Spread Equation
The previous discussion has focused on description of the how the independent variables are
constructed. It is now time to consider different measures of the dependent variable, and how
this translates into the estimation strategy. There are three candidates that have been used,
absolute spreads, percentage spreads and finally, grouping absolute spreads into a relatively
small set of classes.
The most straightforward measure is the absolute spread itself. However, this measure has
some problems; one is that the spread is likely to be a function of the level of the exchange
rate, which motivates normalizing the spread by dividing by the level and thus create a
percentage spread measure. However, if exchange rate variations are not very large and we
concentrate the attention on a single market, using percentage spreads may actually hide
some regularities in the data. Another observation regarding absolute spreads are that they
often are clustered around certain values, like 5, 10 or 25 basis points (see Table 3). This
observation has made some researchers use ordered probit/logit models where the dependent
variable is reclassified into a relatively small number of categories, for example ''small,
medium or large'' spreads.
In this study, we investigate which results are robust to these different measures of the
dependent variable and associated estimation techniques. We thus estimate the spread
equation using both absolute and percentage spreads by the means of OLS, with Newey-West
robust standard errors (which is equivalent to the GMM estimation employed by
Bessembinder 1994). These estimations form the basis for the remainder of the paper, while
the result of the ordered probit estimation is omitted. The reason for this is that the purpose of
the paper is to investigate spreads in a crises period and in doing so, comparing these spreads
to spreads in tranquil times. Ordered probit models then run into the problem that the
classification of for example “small, medium and large” spreads change between these time
periods. In other words, the spreads in the crises period are generally so large that they have
not been observed in the pre-crises period, which basically would lead an ordered probit
model with an open last class to contain all the crises observations in this class, and there
would be no variation to explain in the crises period. This is the case for all the emerging
market currencies that we are primarily interested in, and only the ordered probit model for
JPY seem to be performing slightly better in sample with an ordered probit model. To
conserve space, we have therefore omitted the ordered probit results, and will not discuss
these models further.
23
The type of equations that are estimated by using OLS with robust standard errors are of the
form
St   0   1St 1   2
2
R ,t
  3 it   4Vt  3   5
3
2
V ,t
   i 5 Di ,t   9 T   t
(3)
i 1
where the dependent spread variable St is either the absolute or the percentage spread. The
 ' s are the coefficients to be estimated,  2R ,t is the conditional variance from equation (1),
it is the alternative cost, Vt-3 is the proxy for expected volume,  V2 ,t is the proxy for
unexpected volume from equation (2), Di,t are the dummies for weekdays, T is a time trend,
and  t is the error term. The volume variable is lagged three days to allow for a normal
settlement in the stock market, that is, the stock market transaction is assumed to be
translated into an FX transaction only after it is settled. The time trend is included to allow
for the fact that some financial markets develop over time, which could influence the spreads.
V. RESULTS
This section summarizes the results in Tables x-y and Figures z-zz. The table for each
country consists of 6 columns, each representing a different model that differs in terms of the
dependent variable and the included independent variables. Models (1) – (3) use absolute
spreads as the dependent variable and models (4) – (6) uses the percentage spread. In the
tables, the first lines are the coefficient estimates and corresponding t-statistics, followed by
the number of observations in the sample and the adjusted R2. In addition to these relatively
simple measures of model performance, we also investigate if there is evidence of structural
breaks concurrent with the crises and how the pre-crises models perform in terms of
forecasting in the crises period.
A. General Results
The most robust result is that the conditional variance of the exchange rate that is used to
measure exchange rate risk enters with a positive and statistically significant coefficient in
the spread equation in almost all cases. This confirms empirical results obtained for mature
market currencies (see, e.g., Bessembinder 1994), and is also in line with the theoretical
models.
Another variable that is always positive and often significant is the lagged spread. This
result is also consistent with findings in mature markets. In some instances when percentage
spreads are used, the coefficients are greater than one, indicating problems with nonstationarity for those specifications.
The interest rate differential that turns out to have a significant effect in most cases is the
difference between foreign and domestic rates, while the Eurodollar short-long differential
24
hardly turns up significant in any estimated equation. Irrespective of the measure used,
however, the signs are mixed and the coefficients are seldom significant.
Expected volumes seem to add some explanatory power in certain markets but not in others,
and the (point estimates of) signs are not always consistent with what the previous
considerations would suggest. For MYR, the coefficient is negative as predicted by theory,
but it is positive for SGD. The volatility in volumes should be positive according to theory,
and there are a number of cases with significant positive coefficients, but the general
impression is more mixed.
Weekday dummies are significant and negative on Mondays in many cases and significant
and positive for Fridays. This is in line with the idea that costs are higher over the weekend,
both due to increased uncertainty since there are two non-trading days and to longer periods
of foregone alternative investment opportunities. The Friday effect was also documented in
Bessembinder, while others have found evidence of a Wednesday rather than Friday effect
explained by Wednesday contracts being the ones settled on the day after the weekend (see
reference in Bollerslev and Melvin). Here there are no significant Wednesday effects.
B. Which Model Works Best?
Since we have estimated the spread equation in some different forms, including various sets
of explanatory variables, it is interesting to try to establish what model actually works
reasonably well according to some alternative standards. Below we discuss performance in
terms of adjusted R2, structural breaks, and out of sample forecast performance.
Adjusted R2
In terms of in sample performance, adjusted R2 for the models is anywhere from 0 to 73
percent. For the pre-crises period with the simplest specification, which includes only the
conditional variance of the exchange rate, the average is 12 percent both for the models using
absolute and percentage spreads, while it increases to over 25 percent if the entire sample is
used. This observation suggest that the jump in spreads that takes place in the crises is
accompanied by a jump in at least some of the explanatory variables, and this variance is (at
least to some extent) picked up by the model.
Adding the lagged dependent variable to the explanatory variables increases the adjusted R2
with around 20 percent on average to between 36 to 47 percent. Adding the whole battery of
other explanatory variables adds another 7 percent on average if the entire sample is used, but
reduces it slightly if only the pre-crises samples are used. The overall picture seem to suggest
that the model with absolute spreads work only marginally better than the percentage spread
models, and that the bulk of the in sample explanatory power comes from the conditional
variance and lagged dependent variable. As mentioned in the previous section, there are
several cases where the other variables have significant coefficients, however, the impact on
adjusted R2 seems limited.
25
Structural Breaks
To investigate the stability of the parameter estimates over different sub-periods, each model
was estimated for three sub-samples: pre crises, crises and full sample. The Tables x-y report
formal test of structural breaks, namely the standard Chow test and a Wald test (with pvalues) where the null is no structural break. The Wald test is added to the standard Chow
test, since the Chow test assumes equal variances in the sub-samples, while the Wald test
does not impose this constraint. Since the test can yield different results, both are reported.
In almost all cases there is evidence of a structural break at the time of the crises, and the
only cases where the null of no structural breaks can not be rejected is for PHP, HKD, and
JPY in the most simple specifications using absolute spreads. Looking at the individual
parameter estimates, the pattern that emerges is that the constant increases dramatically at the
same time as the coefficient of the conditional variance is reduced. In other words, the fixed
part of the transaction cost went up in the crises period, while the compensation for the
exchange rate risk went down. This could potentially signal that the conditional variance
measure does not capture the uncertainty as well in the crises period as in the pre-crises
period, so that the overall risk in the crises is perceived as being constantly high rather than
frequently adjusting to changes in the conditional variance. Although the stability of the
relationship can be rejected statistically, it is interesting to note that the signs remain
unchanged for both the constant and the conditional variance and that the point estimate for
the latter is of the same order of magnitude in the two sub-samples, with the full sample
estimate being somewhere between the estimates from the two sub-samples. This latter
observation is not true for many of the other coefficients, which suggest that the more
parsimonious model may be preferred from a stability and forecasting perspective.
Forecasting
This section investigates the ability of pre-crises models to forecast in the crises sample. Two
types of forecast are presented, static and dynamic, where the static uses actual observations
of the lagged dependent variable while the dynamic uses the previous forecasted values of
the lagged dependent variable28. Models (3) and (6) runs into problems with missing
observations which due to the use of estimated lagged variables in the forecast limits the
sample in many cases to such small number that dynamic forecasts are meaningless,
therefore only the static forecasts are presented for these models.
The statistics that are presented in Tables x-y dealing with forecast properties are: Root
mean square error (RMSE the S or D is appended to note if it is from the Static or Dynamic
forecast) which is used to compare forecast performance of different models for one specific
dependent variable. Mean absolute error (MAE), which can be used as RMSE but uses
28
Since models (1) and (4) do not include lagged dependent variables, these results should be
the same for both types of forecasts and are only displayed to makes sure the estimation
works.
26
absolute number instead of squares. Mean absolute percentage error (MAPE), is a scale
invariant measure that can be used to compare forecast also for different variables (or
countries). Theil inequality coefficient (TIC), is also scale invariant and is between 0 and 1,
where 0 is perfect fit.
The statistics do not present a strong case for using a particular model for forecasts, since
both the MAPE and TIC statistics are fairly similar for both the absolute and percent spread
equations, with the cross-country mean of the TIC being between 0.3-0.4 for all the models.
The average MAPE statistic slightly favors the use of absolute spreads, but the overall
picture suggests that most of the specifications generate similar results. In terms of dynamic
forecasts, there is obviously some deterioration of forecast performance since lagged
forecasts rather than actual spreads are used. However, given the large changes in spreads,
the deterioration in forecasts seem to be fairly marginal in most cases (on average, TIC
increases by 8 percentage points).
As a further investigation into what is going “wrong” with the forecasts, the mean square
forecast error can be divided into three parts: The bias proportion (Bias), which measures
the difference in means between the forecasted and actual series (ideally zero). The variance
proportion (Var), which measures the difference in variance between actual and forecast
(ideally zero). Finally, the covariance proportion (Cov) measures remaining unsystematic
errors in the forecast (ideally equal to one). These three proportions should obviously sum to
one. For a more detailed discussion of these measures, see, for example, Pindyck and
Rubinfeld (1998).
On average, the models do fairly well in terms of these statistics with the Cov always above
50 percent and in some cases up to 70 percent. The bias proportions is in general fairly small
varying between 6 and 20 percent for the cross-country average. However, looking at
individual countries, there is a great deal of variation in the bias proportion, which ranges
from 0 to 70 percent over all countries and models. Most of the high bias proportions can be
found for the models using percentage spreads and using a large set of explanatory variables.
This suggests that it may be preferable to use a simple absolute spread model if the aim of the
forecast is to track the mean of the actual spread, which is also closely related to statements
about excessive spreads in the crises period.
In addition to the tables discussed above, some graphs depicting the forecast performance of
the various models are presented in Figures z-xx. For each country there are two graphs: The
first series of graphs (Figures z-zz) contain the actual series plotted together with the
confidence interval for the forecasted series. The graph is organized such that in the upper
left hand corner is the first models static forecast followed by the other models static
forecasts (the first number which is either 1 or 2 indicates static or dynamic forecast, the
second number indicate which model was used to estimate the parameters), and then the
dynamic forecasts follow. As mentioned above, there are no dynamic forecasts for models
(3) and (6). A relatively narrow forecast interval that manage to track the actual variable is
obviously desirable, while wide intervals in combination with actual values outside the
interval indicates a less useful model for forecasting purposes.
27
The graphs in Figures z-zz does not suggest that one model outperforms the others in all the
cases. Rather, they all seem to have their benefits and limitations. In the case of HKD and
JPY, the models do not pick up much of the limited variation, while in the other countries,
the models seem to pick up at least some of the variation in spreads. Another impression for
the first five currencies is that the number of observations that lie above the confidence
interval seem to be greater than the number of observations that lie below. This suggests that
spreads may have been higher than one would expect in the crises period.
The second set of graphs (Figures x-xx) contain the residuals in the forecast interval (i.e., the
difference between the actual and forecasted value). These should preferable look like any
residual, and in particular have mean zero unless the bias proportion discussed above is non
zero, which indicates that the forecast cannot track the mean of the actual variable. These
graphs in combination with the bias proportion serve as a way of identifying “excess”
spreads in the crises period.
The Figures indicate that the residuals are positive in some cases and negative in others, thus
not providing a robust conclusion with respect to excess spreads in the crises period.
Similar results are obtained by calculating the mean of the residuals in the crises period, and
only IDR yields the same result for all models, namely that the mean is positive. For most of
the other countries, the sign of the mean varies depending on whether absolute or percentage
spreads are used.
C. Were Spreads in the Crises “Unreasonable”?
[INCOMPLETE]
The way this paper addresses this potentially controversial question is by comparing the
spreads in the crises with spreads predicted by the models estimated in the pre-crises period.
By using pre-crises estimates, the answer to the question does not depend on how the crises
episode affect the coefficient estimates, rather, the only thing that is allowed to change crises
spreads are actual changes in the explanatory variables. From Table 7 it is evident that the
conditional variance of the exchange rates increases quite dramatically in the crises period,
and given the positive coefficient this variable has in the spread equations, this suggests that
the spreads should also increase. However, the question is if this is enough to explain the
massive increase in spreads or if there is evidence that supports the view that spreads were
excessive in the crises period.
The quantitative analysis presented indicate that, in general, the spreads observed in the
crises period were consistent with models of bid-ask spreads estimated in the pre-crises
period.
VI. CONCLUDING REMARKS
[INCOMPLETE]
28
Volatility in exchange rates important determinant of bid ask spreads also in the emerging
markets of SE Asia, both before and after the crises. A significant part of the spreads can be
attributed to the increased risk carried by the participants in the market. This lead to high
profits for some of the participants while other decided to exit the interbank market.
29
REFERENCES
Amihud, Y., and H., Mendelson, 1986, “Asset Pricing and the Bid-Ask Spread,” Journal of
Financial Economics, 17, pp.223-249.
Andersen, T., and T., Bollerslev, 1997, “Answering the Critics: Yes, ARCH Models Do
Provide Good Volatility Forecasts,” NBER, Working Paper 6023.
Bank for International Settlements, 1999, Central Bank Survey of Foreign Exchange and
Derivatives Market Activity, 1998, Basle, May.
Bessembinder, H., 1994, “Bid-Ask Spreads in the Interbank Foreign Exchange Markets,”
Journal of Financial Economics, 35, pp.317-348.
Bollerslev, T., and I., Domowitz, 1993, “Trading Patterns and Prices in the Interbank Foreign
Exchange Market,” Journal of Finance, 48, 4, pp. 1421-1443.
______, and M. Melvin, 1994, “Bid-Ask Spreads and the Volatility in the Foreign Exchange
Market,” Journal of International Economics, 36, pp. 355-372.
Boothe, P., 1988, “Exchange Rate Risk and the Bid-Ask Spread: A Seven Country
Comparison,” Economic Inquiry, pp.485-492.
Bossaerts, P., and P., Hillion, 1991, “Market Microstructure Effects of Government
Intervention in the Foreign Exchange Markets,” Review of Financial Studies, 4,
pp.513-541.
Bradfield, J., 1979, “A Formal Dynamic Model of Market Making,” Journal of Financial
and Quantitative Analysis,” pp. 275-291.
Cheung, Y., and C., Wong, 1999, “A Survey of Market Practitioners’ Views on Exchange
Rate Dynamics,” forthcoming Journal of International Economics.
Cornell, B., 1978, “Determinants of the Bid-Ask Spread on Forward Foreign Exchange
Contracts Under Floating Exchange Rates,” journal of International Business Studies,
9 (33), pp. 33-41.
Easley, D., and M., OHara, 1992, “Adverse Selection and Large Trade Volume: The
Implications for Market Efficiency,” Journal of Financial and Quantitative Analysis,
27, pp.185-208.
European Economy, 1990, “One Market, One Money: An Evaluation of the Potential
Benefits and Costs of Forming an Economic and Monetary Union,” No 44, October.
30
Flood, R., and M. Taylor, 1996, “Exchange Rate Economics: What’s Wrong with the
Conventional Macro Approach?” The Microstructure of Foreign Exchange Markets,
edited by J. A. Frankel, G. Galli, and A. Giovannini, University of Chicago Press, pp.
261-302.
Flood, M., 1991, “Microstructure Theory and the Foreign Exchange Market,” Federal
Reserve Bank of St. Louis, 73, pp.52-70.
Frankel, J. and A. Rose, 1995, “Empirical Research on Nominal Exchange Rates,” Handbook
of International Economics, Vol. III, G. Grossman, and K. Rogoff (Eds.), pp. 16891729.
______, G., Galli, and A., Giovannini, 1996, The Microstructure of Foreign Exchange
Markets, University of Chicago Press.
Glassman, D., 1987, “Exchange Rate Risk and Transaction Costs: Evidence from Bid-Ask
Spreads,” Journal of International Money and Finance, 6, pp. 479-490.
Goldfajn and Rigobon
Hartmann, P., 1998, “Do Reuters Spreads Reflect Currencies’ Differences in Global Trading
Activity?” Journal of International Money and Finance, 17, pp. 757-784.
______, 1999, “Trading Volume and Transaction Costs in the Foreign Exchange Market:
Evidence from Daily Dollar-Yen Spot Data,” Journal of Banking and Finance, 23,
pp.801-824.
Ho, T., and H., Stoll, 1981, “Optimal Dealer Pricing Under Transactions and Return
Uncertainty,” Journal of Financial Economics, 9, pp. 47-73.
Hong Kong Monetary Authority, 1998, Quarterly Bulletin, November.
Hsieh, D., and A., Kleidon, 1996, “Bid-Ask Spreads in Foreign Exchange Markets:
Implications for Models of Asymmetric Information,” The Microstructure of Foreign
Exchange Markets, J. A. Frankel, G. Galli, and A. Giovannini (Eds.), University of
Chicago Press, Chicago, IL, pp. 41-72.
Huang, R., and R., Masulis, 1999, “FX Spreads and Dealer Competition across the 24-Hour
Trading Day,” Review of Financial Studies, 12 (1), pp. 61-93.
Institute of International Finance, 1999, Report of The Task Force on Risk Assessment,
Washington, D.C., March.
International Monetary Fund, 1998, International Capital Markets: Developments,
Prospects, and Key Policy Issues, Washington, D. C., September.
31
Jorion, P., 1996, “Risk and Turnover in the Foreign Exchange Market,” The Microstructure
of Foreign Exchange Markets, J. A. Frankel, G. Galli, and A. Giovannini (Eds.),
University of Chicago Press, Chicago, IL, pp. 19-37.
Lee, T., 1994, “Spread and Volatility in Spot and Forward Exchange Rates,” Journal of
International Money and Finance, 13 (3), pp.375-383.
Lyons, R., 1995, “Tests of Microstructural Hypotheses in the Foreign Exchange Market,”
Journal of Financial Economics, 39, pp. 321-351.
______, 1996, “Foreign Exchange Volume: Sound and Fury Signifying Nothing?” The
Microstructure of Foreign Exchange Markets, J. A. Frankel, G. Galli, and A.
Giovannini (Eds.), University of Chicago Press, Chicago, IL, pp. 183-208.
Mac Donald, R., 1998, “Economics of Exchange Rates: Theories and Evidence,” IMF
Institute Economics Training Program, June 22-24.
Peiers, B., 1997, “Informed Traders, Intervention, and Price Leadership” A Deeper View of
the Microstructure of the Foreign Exchange Market,” Journal of Finance, 52, pp.
1589-1614.
Pindyck and Rubinfeld (1998) Econometric Models and Economic Forecasts, 4th edition,
McGraw-Hill
Saporta, V., 1997, “Which Inter-Dealer Market Prevails? An Analysis of Inter-Dealer
Trading in Opaque Markets,” Bank of England, Working Paper.
Singapore Foreign Exchange Market Committee, 1996, Annual Report.
Wei, S., 1994, “Anticipation of Foreign Exchange Volatility and Bid-Ask Spreads,” NBER,
Working Paper No. 4737.
32
Appendix
[INCOMPLETE]
VII. LOWER FREQUENCY DATA
By using lower frequency data, the empirical study presented above can be complemented
not only in terms of alternative frequency, but also in terms of alternative measures.
A. Realized Volatility
An alternative measure of exchange rate risk is realized volatility, with one advantage being
that the measure is model free. To compute it, high(er) frequency data is used, and there are
some different alternatives available. The most straightforward way is to use (the average of)
the sum of squared or absolute returns. In this way, daily data can be used to compute, for
example, monthly realized returns.
B. Volume Data
Another advantage with using a lower frequency is that volume data is available on a
monthly basis for some countries. In this illustration, Malaysian data will be used.
C. Results
The general result that bid ask spreads to a large extent can be explained by exchange rate
risk is reinforced when monthly data for Malaysia is studied. In addition, the impact of actual
foreign exchange volumes indicate that [].
33
THB
(1)
(2)
(3)
(4)
(5)
(6)
Sample pre
Crises full
pre
crises full
pre
crises full
pre
crises full
pre
crises full
pre
crises full
Constant
19.36 229.52 47.19 11.78 124.47 12.19 -0.74 770.73 -108.66 76.42 557.49 141.73
48.10 403.76
69.91
9.20 3812.1
-254.77
t-stat
33.83 11.69
7.21
5.38
4.62
4.77 -0.06
2.44
-3.97 34.23 14.26
9.57
5.66
7.60
10.37
0.20
4.54
-3.84
2
0.28
0.10
0.23
0.19
0.04
0.04
0.18
0.03
0.04
1.09
0.28
0.59
0.76
0.19
0.20
0.75
0.15
0.21

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
6.32
2.29
2.71
5.88
0.39
3.36
1.46
0.49
4.27
1.07
0.77
12.17
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1603
0.45
0.24
0.17
0.59
0.43
0.31
0.00
0.69
0.24
0.17
0.59
0.43
0.31
0.00
0.69
348
348
348
0.15
1950
0.37
834.52
0.00
123.15
0.00
1599
0.49
0.19
0.12
0.41
0.32
0.15
0.00
0.85
0.23
0.16
0.57
0.41
0.25
0.01
0.74
347
347
347
0.32
1945
0.70
62.63
0.00
44.72
0.00
5.55
0.40
2.46
15.18
1.21
0.04
1.17
1.04
0.37
3.17
-9.63
-0.15
0.13
1.02
1.15
0.63
8.44
4.00
0.25
0.09
1.66
0.00
0.00
-0.84
-3.92
-1.74
1.54
0.33
4.82
1.71
0.00
0.80
802
0.49
0.19
-7.62
-0.25
11.97
0.39
10.75
0.47
-0.29
-2.00
261
0.22
0.20
0.14
0.43
0.32
0.15
0.00
0.85
261
7.41
5.99
1.46
2.38
51.53
1.23
0.13
1.15
3.20
0.40
1.87
27.58
0.18
0.33
1.11
2.69
1.21
7.16
21.44
0.58
0.14
0.99
0.00
0.00
0.00
0.00
-0.26
-5.91
-0.71
2.27
0.26
4.88
0.70
0.08
4.81
1062
0.68
9.04
0.00
66.29
0.00
-0.71
-14.89
-1.66
2.71
0.18
19.51
1.73
0.01
0.64
802
0.54
-0.20
3.08
0.05
39.91
0.52
29.53
0.58
-1.58
-4.03
261
0.26
-0.73
-7.66
-0.38
6.72
0.30
18.24
1.03
0.21
5.23
1062
0.63
19.53
0.00
108.22
0.00
1603
0.50
0.66
0.37
0.48
0.39
0.04
0.24
0.73
0.66
0.37
0.48
0.39
0.04
0.24
0.73
348
348
4.40
348
0.22
3.51
1950
0.42
690.21
0.00
154.19
0.00
6.77
1.46
3.22
1599
0.54
0.58
0.32
0.46
0.32
0.03
0.21
0.77
0.58
0.32
0.46
0.32
0.03
0.21
0.77
347
347
4.70
0.71
3.87
347
0.28
2.62
1.59
10.16
1945
0.65
80.49
0.00
69.27
0.00
0.62
0.35
0.50
0.32
0.03
0.17
0.81
261
34
IDR
(1)
(2)
(3)
(4)
(5)
(6)
Sample Pre
crises
full
Pre
crises full
pre
crises
Full
pre
crises full
pre
crises full
pre
crises Full
Constant
331
14636
1647
138
6393
560
-163
-126137
-16704
15
156
28
6.36
104
20.9 -3.49
-546 -216.9
t-stat
20.74
5.45
4.57 10.08
4.04
3.71 -0.84
-3.10
-2.54 19.98
8.13
9.44
9.45
7.03
11.73 -0.45
-1.50 -2.94
2.35
2.85
4.85
1.36
0.75
1.15
2.38
1.22
1.03
0.08
0.03
0.05
0.03
0.01
0.02 0.08
0.01 0.02
2
R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
1.86
3.45
5.65
1.26
0.58
16.20
1.25
0.63
7.45
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1754
0.03
252.21
172.35
2.50
0.61
0.39
0.32
0.30
252.21
172.35
2.50
0.61
0.39
0.32
0.30
317
317
317
0.18
2070
0.45
279.57
0.00
34.53
0.00
1750
0.35
167.40
100.15
5.72
0.31
0.11
0.15
0.74
234.04
157.82
3.33
0.53
0.32
0.29
0.39
316
316
316
0.48
1.86
0.72
9.36
1.83
0.52
3.49
7.18
1.59
0.13
0.48
0.02
1.19
0.47
2.82
102.01
0.94
-12.16
-1.20
0.17
1.13
0.53
3.55
220.66
2.76
-13.61
-1.48
0.18
1.40
-18.54
-1.15
-12.81
-0.60
4.97
0.22
0.11
0.98
2065
372
0.71
0.64
45.55
0.00
25.16
0.00
1.51
-4272.08
-1.95
1993.36
0.80
2451.26
0.75
62.62
3.09
220
0.55
1.71
-1796.69
-2.12
824.10
0.84
759.07
0.62
9.39
2.35
591
0.70
3.07
0.00
29.40
0.00
173.86
99.33
0.77
0.30
0.03
0.10
0.87
220
1.76
1754
0.01
2.24
1.34
7.37
0.35
0.00
0.09
0.92
2.24
1.34
7.37
0.35
0.00
0.09
0.92
317
317
4.69
317
0.24
6.67
2070
0.51
395.88
0.00
53.41
0.00
0.79
0.03
16.85
1750
0.35
7.65
5.11
28.20
0.59
0.43
0.42
0.16
7.65
5.11
28.20
0.59
0.43
0.42
0.16
316
316
3.30
0.00
5.73
316
0.41
3.90
0.01
8.55
2065
0.68
121.57
0.00
196.83
0.00
1.84
0.02
3.51
0.25
1.55
0.01
0.63
0.00
1.81
0.00
2.62
-0.39
-0.34
-0.05
-0.50
0.00
2.36
0.00
2.93
1.06
1.43
-0.03
-0.42
0.00
1.21
1.37 1.88
-0.68 -31.79 -11.89
-1.07
-1.49 -1.47
-0.44 17.44 6.36
-0.53
0.74 0.71
0.34 24.97 9.53
0.38
0.88 0.89
0.00
0.31 0.13
0.67
1.69 2.84
372
220
591
0.62
0.44 0.69
2.56
0.00
43.65
0.00
7.39
4.86
2.53
0.59
0.42
0.43
0.15
220
35
KRW
(1)
(2)
(3)
(4)
(5)
(6)
Sample pre
crises
full
pre
crises full
pre
crises
full
pre
crises full
pre
crises full
pre
crises full
Constant 54.02
467.25 115.88 11.87 326.12 40.96 -42.73 -1275.40
-59.45
6.66 34.17 11.79
1.91 23.28
5.06 -3.89 -132.63
-3.64
t-stat
6.28
9.75
10.21
3.96
5.26
4.32 -3.46
-0.71
-3.64
6.98
9.33 10.89
5.52
5.11
5.80 -2.86
-0.93
-2.09
2
7.10
0.10
0.19
1.49
0.08
0.07
0.51
0.17
0.15
0.75
0.01
0.01
0.11
0.00
0.00
0.01
0.01
0.01

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
5.50
2.94
7.17
2.10
0.78
16.01
1.46
0.30
1.66
1.93
0.64
7.62
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
1938
Rbar2
0.16
Chow
p-val
Wald
p-val
Forecast
RMSES 121.58
MAES
49.73
MAPES
11.67
TICS
0.92
BiasS
0.16
VarS
0.79
CovS
0.05
RMSED 121.58
MAED
49.73
MAPED
11.67
TICD
0.92
BiasD
0.16
VarD
0.79
CovD
0.05
#obsS
231
#obsD
231
231
0.10
2168
0.16
362.77
0.00
94.95
0.00
1929
0.69
23.54
9.60
2.41
0.68
0.13
0.60
0.27
104.73
44.02
10.31
0.91
0.17
0.76
0.07
217
217
217
0.17
2145
0.51
125.31
0.00
43.52
0.00
1.02
0.77
13.96
-11.16
-0.99
0.27
1.42
-0.03
2.11
0.46
3.43
59.92
0.81
-2.71
-2.16
0.31
2.25
0.60
9.00
-4.04
-0.30
-0.50
-1.18
0.18
-0.72
7.72
1.00
-7.52
-1.26
7.08
0.86
0.05
4.18
1518
0.73
2.25
-55.05
-0.54
-66.31
-0.84
-67.03
-1.03
0.75
0.92
200
0.28
1.78
-3.13
-0.22
-14.17
-1.40
-3.91
-0.40
0.09
5.47
1717
0.61
9.68
0.00
27.33
0.00
6.69
3.78
1.11
0.38
0.11
0.08
0.81
200
5.60
1938
0.14
12.92
5.39
18.86
0.94
0.17
0.79
0.04
12.92
5.39
18.86
0.94
0.17
0.79
0.04
231
231
2.18
231
0.06
6.29
2168
0.08
235.32
0.00
77.15
0.00
1.74
0.09
16.65
1929
0.68
1.97
0.90
3.38
0.71
0.19
0.57
0.24
1.97
0.90
3.38
0.71
0.19
0.57
0.24
217
217
1.02
0.02
1.69
217
0.15
0.30 0.17
0.06 0.09
7.40 14.08
-1.03
-0.81
0.02
0.90
0.00
1.91
0.03
3.44
7.88
1.29
-0.23
-2.51
0.02
1.35
0.05
7.03
1.51
0.89
-0.11
-2.74
0.00
-0.87
0.90
1.01
-0.90
-1.33
0.73
0.82
0.01
4.04
1518
0.72
2.41
-2.61
-0.34
-4.17
-0.73
-5.52
-1.17
0.07
1.13
200
0.27
0.57
0.14
0.11
-1.10
-1.28
-0.41
-0.45
0.01
5.14
1717
0.56
32.86
0.00
94.18
0.00
2145
0.47
192.43
0.00
29.99
0.00
0.45
0.29
1.26
0.36
0.20
0.00
0.80
200
36
MYR
(1)
(2)
(3)
(4)
(5)
(6)
Sample pre
crises
full
pre
crises full
pre
crises
full
pre
crises full
pre
crises full
pre
crises full
Constant 12.04
66.26
17.03
8.33
45.49 10.10 10.70
-590.55
-21.11 463.84 1872.8 608.62 327.16 1355.9 430.76 402.4 -9322.6 -418.06
t-stat
29.16
6.87
13.17 16.26
4.52
5.65
8.05
-5.22
-3.73 30.15
7.56 17.84
16.81
5.16
9.12 7.87
-2.98
-2.75
2
0.30
0.15
0.23
0.20
0.11
0.14
0.15
0.09
0.12
11.20
3.59
5.62
7.41
2.69
3.46
5.47
2.12
3.03

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
3.76
3.89
6.58
3.51
0.31
8.86
3.02
0.29
2.64
3.52
0.39
3.52
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1960
0.08
0.01
0.01
2.25
0.35
0.01
0.00
0.99
0.01
0.01
2.25
0.35
0.01
0.00
0.99
340
340
340
0.21
2299
0.47
208.01
0.00
31.63
0.00
1956
0.17
0.01
0.01
1.75
0.32
0.01
0.05
0.94
0.01
0.01
2.24
0.35
0.02
0.02
0.96
339
339
339
0.28
2294
0.56
57.40
0.00
22.91
0.00
3.10
0.21
3.74
-0.01
-0.12
-0.01
-1.11
0.00
2.87
0.08
1.36
-1.69
-0.69
-0.16
-1.60
0.01
3.78
0.27
3.27
1.98
2.67
-0.09
-2.85
0.01
0.27
-0.38
-0.65
-0.31
-0.72
0.97
2.02
0.00
-2.68
982
0.17
2.58
-5.33
-0.55
-3.16
-0.36
-5.28
-0.50
0.32
5.48
225
0.40
2.20
0.05
0.03
-0.33
-0.16
-0.37
-0.18
0.02
4.98
1206
0.67
38.46
0.00
95.36
0.00
0.01
0.01
0.44
0.32
0.23
0.06
0.71
225
3.67
1960
0.08
0.33
0.19
3.18
0.37
0.05
0.09
0.86
0.33
0.19
3.18
0.37
0.05
0.09
0.86
340
340
3.52
340
0.20
6.06
2299
0.45
203.36
0.00
32.81
0.00
3.42
11.49
8.60
1956
0.16
0.28
0.16
2.52
0.33
0.08
0.03
0.90
0.28
0.16
2.52
0.33
0.08
0.03
0.90
339
339
2.75
7.14
2.55
339
0.27
3.27
10.09
3.50
3.02
2.39
7.72
2.20
3.80
1.28
0.27 -33.26
0.06
-0.49
-0.36
-4.30
-1.19
-1.55
0.01
0.33
3.32
6.82
3.10
39.78
2.20
-2.08
-2.53
0.20
0.22
2.43
-14.08 -161.01
-0.63
-0.59
-12.80 -93.15
-0.78
-0.39
38.27 -126.67
2.06
-0.44
-0.04
5.54
-1.94
3.43
2294
982
225
0.54 0.15
0.31
57.67
0.00
19.34
0.00
2.34
-3.81
-0.07
-16.05
-0.29
5.46
0.10
0.61
5.05
1206
0.65
30.71
0.00
83.39
0.00
0.20
0.12
0.42
0.28
0.01
0.01
0.99
225
37
PHP
(1)
(2)
(3)
(4)
(5)
(6)
Sample Pre
crises
full
pre
crises full
pre
crises
full
pre
crises full
pre
crises full
pre
crises full
Constant 242.16
230.01 245.92 14.68 131.94 49.83 32.67
2909.46
47.21 912.59 560.93 947.17
45.52 194.20 194.77 148.4 13437 814.26
t-stat
13.82
5.15
14.72
4.58
4.75
5.86
0.70
5.21
0.75 13.64
3.17 14.43
3.00
1.50
5.55 0.86
7.29
3.02
2
1.70
1.44
1.41
0.07
0.64
0.24
3.26
0.71
0.85
6.99
4.22
3.36
0.76
1.26
-1.14
12.90
1.16
1.62

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
3.84
6.62
9.60
1.05
0.94
67.77
5.00
0.51
8.18
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1336
0.06
0.32
0.23
0.57
0.22
0.06
0.13
0.81
0.32
0.23
0.57
0.22
0.06
0.13
0.81
341
341
341
0.35
1676
0.34
1.37
0.25
0.60
0.74
1329
0.89
0.30
0.18
0.38
0.21
0.00
0.00
1.00
0.38
0.23
0.49
0.30
0.04
0.45
0.51
340
340
340
0.50
3.78
0.81
24.32
1.06
0.51
7.31
4.50
0.79
0.01
1.28
0.00
4.82
0.33
4.64
-105.45
-1.37
-0.22
-0.87
-0.01
6.90
0.52
9.74
-29.86
-1.06
-0.03
-1.52
0.00
-0.58
6.33
1.79
-20.53
-1.37
-50.38
-1.17
0.00
-0.03
1668
495
0.75
0.28
65.64
0.00
47.74
0.00
-2.12
-66.95
-1.91
32.83
0.64
63.64
1.42
-1.24
-4.86
260
0.54
-2.97
-22.07
-1.63
4.74
0.24
7.55
0.46
0.01
0.25
754
0.78
14.70
0.00
72.56
0.00
0.81
0.66
1.26
0.36
0.62
0.10
0.28
260
4.07
1336
0.07
1.56
1.27
1.25
0.31
0.47
0.01
0.52
1.56
1.27
1.25
0.31
0.47
0.01
0.52
341
341
4.67
341
0.29
5.51
1676
0.17
23.43
0.00
11.11
0.00
2.69
3.58
49.44
1329
0.88
1.31
0.97
0.84
0.27
0.33
0.03
0.65
1.31
0.97
0.84
0.27
0.33
0.03
0.65
340
340
2.86
1.89
6.94
340
0.49
-4.31
3.09
22.13
1.12
2.65
1.98
1.20
7.34
4.17
16.99 -384.00
0.78
-1.84
0.02
-0.92
1.21
-1.11
0.00
-0.03
3.77
1.94
8.80
-78.35
-1.00
-0.14
-2.09
0.00
-0.73
-1.88
24.56 -227.73
1.80
-2.03
-80.83 111.35
-1.44
0.70
-199.4 192.34
-1.24
1.41
-0.02
-5.93
-0.19
-7.06
1668
495
260
0.72 0.29
0.58
108.84
0.00
101.74
0.00
-3.08
-74.29
-1.64
19.78
0.31
26.68
0.52
-0.33
-2.14
754
0.73
22.13
0.00
78.09
0.00
3.87
3.31
2.32
0.48
0.71
0.11
0.18
260
38
SGD
(1)
(2)
(3)
Sample pre
crises
full
pre
crises full
pre
crises
full
Constant
9.74
17.82
10.82
6.48
11.94
6.65
7.20
-42.17
t-stat
38.41
8.28
26.05 10.56
6.48 15.39 10.85
-2.61
2
0.25
0.08
0.14
0.14
0.05
0.08
0.05
0.04

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
5.36
2.41
4.71
4.36
0.34
5.34
1.89
0.34
5.96
3.50
0.39
7.96
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1951
0.05
0.001
0.001
0.54
0.26
0.07
0.01
0.92
0.001
0.001
0.54
0.26
0.07
0.01
0.92
348
348
348
0.11
2298
0.29
84.75
0.00
15.31
0.00
1946
0.16
0.001
0.001
0.43
0.22
0.02
0.02
0.97
0.001
0.001
0.49
0.25
0.03
0.00
0.97
347
347
347
0.21
2292
0.39
27.35
0.00
11.90
0.01
(4)
(5)
(6)
pre
crises full
pre
crises full
pre
crises full
3.58 633.48 1117 687.5
455.3 789.1
454.5 354.4 -1854.2 220.4
2.86 45.15
9.37 28.95
11.69
7.52
17.28 8.32
-1.90
3.27
0.06 12.35
4.10
7.99
6.75
2.44
4.84 4.03
2.18
3.23
2.09
0.29
6.65
-0.73
-1.46
-0.01
-0.76
0.00
1.55
0.21
3.27
1.52
0.64
0.09
2.49
0.01
2.71
0.30
5.89
-0.31
-0.47
0.04
2.08
0.01
1.54
-0.78
-3.39
-0.31
-1.62
0.70
2.58
0.00
-1.11
1062
0.12
1.91
-1.44
-1.03
1.45
1.07
3.55
1.89
0.02
3.05
265
0.33
3.27
-0.96
-2.71
0.05
0.16
1.25
2.97
0.00
2.25
1326
0.55
11.78
0.00
28.82
0.00
0.001
0.001
0.32
0.26
0.21
0.29
0.51
265
5.23
1951
0.03
0.08
0.05
0.46
0.25
0.01
0.00
0.99
0.08
0.05
0.46
0.25
0.01
0.00
0.99
348
348
2.41
348
0.10
4.71
2298
0.27
86.69
0.00
16.59
0.00
3.95
18.85
4.63
1946
0.13
0.07
0.05
0.37
0.22
0.00
0.09
0.91
0.07
0.05
0.37
0.22
0.00
0.09
0.91
347
347
1.88
19.26
5.73
347
0.19
3.52 2.33
21.71 19.32
7.33 6.90
-47.95
-1.43
-0.81
-1.44
0.07
1.60
11.69
3.07
97.01
0.69
5.14
2.39
0.35
2.64
17.04
5.73
-21.01
-0.53
1.99
1.63
0.36
1.56
2.12
-53.01 -80.86
-3.43
-0.96
-20.06 85.66
-1.59
1.06
47.23 211.66
2.56
1.89
0.08
1.19
5.45
2.45
2292 1062
265
0.37 0.13
0.29
30.53
0.00
14.29
0.00
3.30
-59.21
-2.72
1.48
0.08
80.58
3.10
0.16
4.25
1326
0.51
7.77
0.00
22.08
0.01
0.06
0.04
0.33
0.21
0.03
0.20
0.78
265
39
HKD
(1)
(2)
(3)
(4)
(5)
(6)
Sample pre
crises
full
pre
crises full
pre
crises
full
pre
crises full
pre
crises full
pre
crises Full
Constant
9.54
9.77
9.57
8.14
7.24
7.95
8.01
21.97
8.12 123.14 126.21 123.55 105.21 93.36 102.63 103.7 284.59 105.20
t-stat
65.04
21.97
65.33 15.10
9.86 16.80 10.12
3.12
12.30 65.33 21.92 65.55
15.16
9.83
16.85 10.14
3.13 12.32
2
4.53
3.65
4.34
3.71
2.51
3.44
5.59
2.26
4.69
58.31
47.22
55.96
47.86
32.42
44.39
71.78
29.09
60.29

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
7.79
1.76
6.23
5.57
0.15
2.50
1.60
0.26
3.51
5.00
0.17
3.32
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1952
0.09
0.0005
0.0003
0.27
0.23
0.00
0.50
0.51
0.0005
0.0003
0.27
0.23
0.00
0.50
0.51
348
348
348
0.06
2299
0.08
0.72
0.49
0.26
0.88
1948
0.11
0.0005
0.0003
0.27
0.23
0.00
0.50
0.50
0.0005
0.0003
0.27
0.23
0.00
0.52
0.48
347
347
347
0.12
2294
0.11
1.92
0.12
1.57
0.67
3.83
0.12
2.21
1.00
1.40
0.00
-0.97
0.00
0.85
0.20
2.08
0.53
2.13
0.00
0.41
0.00
3.27
0.16
3.27
0.35
1.44
0.00
0.08
0.00
-0.71
0.04
0.16
0.00
0.02
0.63
2.72
0.00
0.41
1067
0.22
1.08
-0.44
-0.47
-0.77
-0.88
0.71
0.82
-0.01
-2.30
256
0.20
1.19
-0.05
-0.21
-0.14
-0.61
0.67
2.71
0.00
-1.57
1322
0.22
3.09
0.00
16.58
0.08
0.0006
0.0004
0.40
0.22
0.08
0.16
0.76
256
7.78
1952
0.09
0.0069
0.0033
0.27
0.23
0.00
0.50
0.50
0.0069
0.0033
0.27
0.23
0.00
0.50
0.50
348
348
1.76
348
0.06
6.22
2299
0.08
0.69
0.50
0.26
0.88
5.58
1.91
2.50
1948
0.11
0.0067
0.0033
0.27
0.23
0.00
0.50
0.50
0.0067
0.0033
0.27
0.23
0.00
0.50
0.50
347
347
1.60
3.43
3.52
347
0.12
5.00
2.22
3.33
2294
0.11
1.96
0.12
1.61
0.66
3.82
1.53
2.21
12.89
1.40
-0.02
-0.96
0.00
0.85
2.53
2.09
6.85
2.14
0.03
0.42
0.00
3.26
2.07
3.28
4.55
1.45
0.00
0.09
0.00
-0.70
0.49
0.16
0.06
0.03
8.20
2.72
0.00
0.36
1067
0.22
1.08
-5.73
-0.47
-9.99
-0.88
9.24
0.82
-0.10
-2.30
256
0.20
1.20
-0.69
-0.21
-1.82
-0.60
8.68
2.71
-0.01
-1.61
1322
0.22
3.08
0.00
16.62
0.08
0.007
0.004
0.40
0.22
0.08
0.17
0.76
256
40
JPY
(1)
(2)
(3)
(4)
(5)
(6)
Sample pre
crises
full
pre
crises full
pre
crises
full
pre
crises full
pre
crises full
pre
crises full
Constant
6.86
6.85
6.97
6.19
6.70
6.34
3.59
17.97
4.97
5.43
5.23
5.85
5.25
4.84
5.65 6.15 23.61
7.29
t-stat
34.14
25.59
47.71 16.41
13.64 20.20
4.89
2.95
15.03 34.10 19.65 48.60
24.62 11.43
30.07 8.90
4.80 22.67
0.008
0.004
0.005 0.007
0.004 0.004 0.008
0.009
0.004 0.016 0.005 0.005
0.016 0.005
0.005 0.013 0.012 0.009
2
R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
2.05
1.78
2.50
2.11
0.10
2.30
1.77
0.02
0.43
2.57
0.09
2.46
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs
Rbar2
Chow
p-val
Wald
p-val
Forecast
RMSES
MAES
MAPES
TICS
BiasS
VarS
CovS
RMSED
MAED
MAPED
TICD
BiasD
VarD
CovD
#obsS
#obsD
1952
0.00
0.03
0.02
0.41
0.16
0.02
0.68
0.31
0.03
0.02
0.41
0.16
0.02
0.68
0.31
348
348
348
0.01
2299
0.00
0.43
0.65
1.52
0.47
1948
0.01
0.03
0.02
0.41
0.17
0.01
0.63
0.36
0.03
0.02
0.41
0.16
0.02
0.66
0.32
347
347
347
0.00
2294
0.01
0.60
0.61
2.84
0.42
2.75
0.06
2.09
0.24
2.29
0.00
1.79
0.00
3.42
-0.02
-0.36
0.37
0.40
0.00
-0.18
0.00
2.78
0.05
1.74
0.07
1.15
0.00
1.49
0.00
0.30
-0.43
-2.35
-0.09
-0.47
1.73
8.94
0.00
2.63
1057
0.13
-0.13
0.40
1.00
-0.36
-0.95
0.72
1.69
0.00
-2.54
315
0.03
0.13
-0.23
-1.36
-0.17
-1.04
1.52
8.37
0.00
2.32
1371
0.10
3.26
0.00
26.83
0.00
0.03
0.02
0.44
0.17
0.09
0.32
0.60
315
5.51
1952
0.02
0.03
0.02
0.54
0.19
0.26
0.21
0.53
0.03
0.02
0.54
0.19
0.26
0.21
0.53
348
348
1.91
348
0.01
2.56
2299
0.00
19.67
0.00
36.44
0.00
5.53
0.03
1.19
1948
0.02
0.03
0.02
0.53
0.19
0.26
0.21
0.53
0.03
0.02
0.53
0.19
0.26
0.21
0.53
347
347
1.91
0.06
1.25
347
0.02
2.55
0.03
1.38
2294
0.00
13.09
0.00
38.48
0.00
4.15
0.05
1.81
-0.35
-3.38
0.00
0.81
0.00
5.75
0.00
0.06
0.63
0.87
0.00
-0.05
0.00
5.65
0.04
1.83
-0.49
-7.37
0.00
0.63
0.00
0.40
-0.35
-2.02
-0.06
-0.34
1.68
8.87
0.00
-2.58
1057
0.15
-0.25
0.24
0.74
-0.26
-0.88
0.49
1.48
-0.01
-5.02
315
0.10
0.02
-0.22
-1.44
-0.13
-0.83
1.43
8.45
0.00
-8.10
1371
0.14
3.61
0.00
35.23
0.00
0.02
0.02
0.46
0.18
0.08
0.24
0.68
315
41
MEAN
(1)
(2)
(3)
(4)
(5)
(6)
Sample pre
Crises full
pre
crises full
pre
crises full
pre
crises full
pre
crises full
pre
crises full
Constant 85.61 1958
262 25.81
880 86.83 -18.06 -15540
-2103
279
553
319
124
371
160
127
712
31.72
t-stat 30.18 11.84 23.62 10.29
6.65
9.59
3.78
0.26
2.13 31.19 11.67 25.66
11.49
6.90
13.35
4.12
1.55
3.71
2
2.06
1.05
1.42
0.90
0.52
0.65
1.52
0.57
0.87
11.35
7.43
9.20
7.96
4.88
6.47
11.88
4.34
8.55

R ,t
t-stat
St-1
t-stat
it
t-stat
Vt-3
t-stat
4.56
3.14
5.64
3.23
0.45
15.29
2.18
0.35
4.26
2.90
0.50
8.84
 V2 ,t
t-stat
Mon
t-stat
Wed
t-stat
Fri
t-stat
Trend
t-stat
#obs 1805
Rbar2
0.12
Chow
p-val
Wald
p-val
Forecast
RMSES 46.80
MAES 27.81
MAPES
2.35
TICS
0.40
BiasS
0.13
VarS
0.30
CovS
0.57
RMSED 46.80
MAED 27.81
MAPED
2.35
TICD
0.40
BiasD
0.13
VarD
0.30
CovD
0.57
#obsS 327.63
#obsD 327.63
327
0.15
2132
0.27
221.52
0.17
37.74
0.26
1800
0.36
23.93
13.76
1.47
0.31
0.06
0.24
0.70
42.43
25.28
2.26
0.39
0.11
0.34
0.56
325.00
325.00
325
0.26
2124
0.47
48.30
0.09
25.04
0.14
2.65
0.36
5.24
2.02
0.59
0.05
0.41
2.23
0.26
2.55
5.95
0.34
-1.88
-0.26
3.00
0.38
5.61
24.11
0.80
-1.76
-0.21
0.00
0.06
0.05
0.08
0.91
-1.24
-551
-0.79 -0.71
-5.00 246.13
-0.71 -0.02
-3.68 307.29
2.23
0.69
0.02
7.77
0.64
0.10
919
250
0.35
0.32
0.88
-228
-1.12
102.04
-0.21
96.33
1.91
1.20
2.61
1168
0.54
11.63
0.00
45.40
0.01
22.70
12.99
0.64
0.29
0.19
0.14
0.67
250.25
5.13
3.19
5.19
3.81
4.68
12.88
2.50
4.06
3.91
2.11
4.85
7.97
2.81
2.52
4.02
2.26
5.25
2.32
4.08 -34.71
-0.07
0.31
-0.13
0.00
0.14
-0.23
0.01
1805
0.12
2.23
1.08
4.05
0.38
0.13
0.24
0.64
2.23
1.08
4.05
0.38
0.13
0.24
0.64
327.63
327.63
327
0.15
2132
0.25
206.91
0.06
47.75
0.11
1800
0.36
1.49
0.94
4.57
0.36
0.16
0.26
0.58
1.49
0.94
4.57
0.36
0.16
0.26
0.58
325.00
325.00
325
0.24
2124
0.44
75.82
0.01
58.94
0.08
3.13
3.65
4.98
-3.94
-0.30
-0.03
-0.56
0.08
0.07
0.05
0.88
-7.13 -63.30
-0.73
-0.64
-14.04 18.35
-0.73
0.02
-10.43 42.01
2.24
0.68
0.01
-0.06
0.81
-1.21
919
250
0.35
0.31
0.69
-19.70
-0.98
1.91
-0.20
18.77
2.04
0.10
1.33
1168
0.51
15.28
0.00
60.18
0.01
1.58
1.12
1.03
0.33
0.20
0.16
0.64
250.25