The document analyzes the uncovered interest rate parity (UIP) puzzle using standard UIP regressions and carry trade portfolios for 46 countries from 2002-2016, with a focus on Singapore. UIP holds for Singapore based on the regression results. Carry trade portfolios sorted by interest rate differentials show that the highest differential portfolio earns a positive average excess return while the lowest differential portfolio earns a negative return, contrary to expectations if UIP held. Singapore is most frequently allocated to the middle portfolios and its excess returns were stable before 2008 but more volatile afterwards.

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Assignment 3
Xinyu Wei
Xi Zhang
During this assignment we are going to check the UIP puzzle by using standard UIP regression
and carry trade portfolios. We use 46 countries, and we focus on Singapore.
Data
We select 47 countries, include the United States, from 2002 to 2016. We use the monthly data.
Interest rate of OECD countries are from OECD website, household consumption is from IMF,
and other data from Bloomberg. We select period of 2002-2016 because 12 European countries
began to use Euro in 2002. And those countries which join Euro after 2002 are not include in our
sample.
Standard UIP Regression
Because our interest rates are 3-month rates and we want to check the monthly pattern, so we need
to transfer them to 1-month rates firstly. Then we regress the change of natural logarithm of
exchange rate on the interest rate differential. Table 1 shows the results for each country. From the
results we found that UIP holds in many developed countries, like Norway and Denmark, and UIP
does not hold in some developing countries, like South Africa and Sri Lanka.
UIP holds in Singapore. The coefficient of interest differential in Singapore is 1.314, and the p-
value of the test coefficient equals to 1 is 0.8046. So we think UIP holds in Singapore. There are
three main assumptions for UIP holding, investors being risk neutral, perfect capital mobility and
same default risk for foreign and domestic investment. Singapore has highly developed market
economy and very few capital control, which makes it possible for global capital to flow freely
into and out of country border. For default risk, both Singapore and U.S. rate Aaa on Moody's
ratings. So we believe that Singapore and U.S. have similar default risk level. We think these are
the main reason why UIP holds in Singapore.
Table 2 shows the panel regression for all countries. The result shows that the UIP does not hold
for panel data.
Carry Trade Portfolios
We construct 5 portfolios, first four all include 9 countries, and the number in last group is various.
The first portfolio has lowest interest rate differential and fifth portfolio has highest interest rate
differential. The portfolios are rebalanced every month. They are ranked from low to high interest
rates, portfolio 1 being the portfolio with the lowest interest rate currencies and portfolio 5 being

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the one with the highest interest rate currencies. By building portfolios, we filter out currency
changes that are orthogonal to changes in interest rates. Figure 1 shows the allocation for all
countries, the darker color means the higher interest rate differential. Because we use 46 countries,
the standard deviation of the excess return for each portfolio is quite small. Portfolio 1 has the
largest standard deviation, 0.018, and smallest standard deviation is 0.0029 which is in portfolio
2. Table 3 shows the summary of the excess return for each portfolio. We report average excess
return, standard deviation, Sharpe Ratio, interest rate differential, and change of the natural
logarithm of exchange rate. We know that the excess return is composed by interest rate differential
and the change of the natural logarithm of exchange rate. And if there were no average risk
premium, the sum of these should be zero. Table 2 shows they are not. And from figure 2, we
found that investors earn large negative excess return on the first portfolio because the low interest
rate currencies in the first portfolio depreciate on average by 2.7 basis points, while the average
foreign interest rate is 0.19 percentage points higher than U.S. On the other hand, the higher interest
rate currencies in the fifth portfolio appreciate on average by 2.6 percentage points, but the average
interest rate difference is on average 0.345 percentage points.
Table 4 shows the times and frequency of allocation in portfolio of Singapore. Most time Singapore
is in portfolio 2 and 4, less time in fifth portfolio. Compare to other countries in our sample,
Singapore doesn’t have high interest rate differential. Figure 6 shows the excess return in
Singapore. Before 2008 the excess return in Singapore is in the range from -0.02 to 0.02. But after
2008 the excess return fluctuates heavily. This may be the result of the financial crisis in 2008.
Portfolio Regression
In this section, we derive a linear factor model whose factors are US household consumption
growth Δc, word GDP growth rate, and volatility of global equity markets. Table 5 to table 8 show
the result of the regressions. As in this section we use annual data, from 2002 to 2015. The most
coefficients are not statistically significant may because of the short period in this sample. These
three factors may have long-term effect on excess return. So in the further work, we should use
longer period. For consumption growth, the first portfolio’s coefficient is 0.000533, and the fifth
portfolio’s coefficient is -0.000106, shown in Table 8. For world GDP growth rate, the coefficient
decreases with the increasing of the interest rate differential. Table 6 reports that in fifth portfolio
the coefficient is -0.025, which means that in the highest interest rate portfolio one percent increase
in world GDP growth rate decreases 2.5 percent in interest rate differential. World GDP growth
rate measures the whole economic environment, higher growth rate better investment environment.
So when the investment environment improving, the risk of invest in foreign countries will
decrease, which decreases the risk premium. Then the interest rate differential will decrease. Table
7 reports the coefficient on volatility, we use the Morgan Stanley World Capital International Index
to calculate the volatility of global equity markets. The coefficient increases with the increasing of
the interest rate differential.

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Table 1 regression result for each country
AUS AUT BEL CAN CHE CHL CHN COL
din 7.373**
2.035 2.035 4.593 0.394 1.142 0.612 2.745
(2.87) (0.87) (0.87) (1.59) (0.17) (0.71) (1.05) (1.60)
p-value 0.0141 0.6596 0.6596 0.2153 0.7978 0.9296 0.5084 0.3101
_cons 0.0206**
0.00194 0.00194 0.00284 0.00309 0.00253 0.00381 0.00844
(2.96) (0.82) (0.82) (1.16) (0.99) (0.65) (1.6) (1.16)
N 170 170 170 170 170 144 57 169
CZE DEU DNK ESP FIN FRA GBR GRC
din 1.871 2.035 1.246 2.035 2.035 2.035 2.995 2.035
(0.84) (0.87) (0.62) (0.87) (0.87) (0.87) (1.44) (0.87)
p-value 0.6954 0.6596 0.9023 0.6596 0.6596 0.6596 0.3402 0.6596
_cons 0.00301 0.00194 0.00201 0.00194 0.00194 0.00194 0.00271 0.00194
(1.04) (0.82) (0.82) (0.82) (0.82) (0.82) (1) (0.82)
N 170 170 170 170 170 170 170 170
HKG HUN IDN IRL ISL ISR ITA JPN
din -0.0346 1.435 -2.349**
2.035 0.798 1.003 2.035 1.879
(-0.22) (1.31) (-2.68) (0.87) (0.67) (0.98) (0.87) (1.38)
p-value 0 0.6908 0.0002 0.6596 0.8655 0.9979 0.6596 0.5195
_cons 0.0000254 0.0054 -0.0154**
0.00194 0.00352 0.00241 0.00194 -0.00132
(0.23) (1.04) (-2.73) (0.82) (0.47) (1.06) (0.82) (-0.51)
N 169 170 169 170 170 170 170 166
KOR LKA LUX LVA MEX MYS NGA NLD
din 0.507 0.153 2.208 0.0113 -0.711 2.299*
-0.237 2.035
(0.23) (0.58) (0.94) (0.02) (-0.47) (2.33) (-0.42) (0.87)
p-value 0.826 0.0014 0.6094 0.0881 0.2626 0.1904 0.0323 0.6596
_cons 0.0016 -0.00154 0.00184 0.000267 -0.00661 0.00261 -0.00601 0.00194
(0.36) (-0.75) (0.77) (0.11) (-1.04) -1.36 (-1.32) -0.82
N 170 168 169 170 170 170 104 170
NOR NZL PER PHL POL PRT QAT RUS
din 1.005 9.308**
1.147 0.626 1.371 2.035 0.0366 -0.904
(0.62) (2.85) (1.44) (1.09) (0.82) (0.87) (1.21) (-1.45)
p-value 0.9977 0.0119 0.8534 0.516 0.8238 0.6596 0 0.0027
_cons 0.00187 0.0283**
0.0012 0.00224 0.00424 0.00194 0.0000082 -0.0105*
(0.55) (3.02) (0.9) (1.37) (0.78) (0.82) (0.25) (-2.19)
N 170 170 170 150 170 170 135 169

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SGP SWE TUR TWN VEN ZAF
din 1.314 0.634 -1.79 0.223 -0.269 -3.970*
(1.04) (0.36) (-1.37) (0.23) (-0.35) (-2.14)
p-value 0.8046 0.8373 0.0347 0.4271 0.1001 0.008
_cons 0.000806 0.00161 -0.0209*
0.0002 -0.0182 -0.0210*
(0.54) (0.6) (-2.10) (0.16) (-1.67) (-2.14)
N 169 170 101 161 170 170
t statistics in parentheses
* p < 0.05, ** p < 0.01, *** p < 0.001
p-value is the test result of the coefficient equals to 1.
Table 2 result for panel data
-1
Δln(exchange rate)
din 0.624***
(5.62)
p-value 0.0007
_cons 0.00120**
(2.75)
N 7470
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001
p-value is the test result of the coefficient equals to 1.

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Figure 1 Portfolio Allocation by Country
Figure 2 Average excess return for each portfolio

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Figure 3 Standard deviation of excess return
Figure 4 Sharpe Ratio of excess return

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Figure 5 Average excess return of portfolio
Figure 6 Singapore excess return, 2002-2016

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Table 3 Summary of Portfolios
portfolio 1 2 3 4 5
Mean -0.02511 -0.0062 0.003246 0.012003 0.029838
Standard deviation 0.017894 0.002937 0.003079 0.003324 0.011697
Sharpe Ratio -1.40297 -2.10987 1.054431 3.611066 2.550866
Interest differential 0.0019 0.00139 0.00112 0.00165 0.00345
Δln(exchange rate) -0.02712 -0.00758 0.00213 0.010355 0.026384
Note: Mean and interest differential are in decimal format.
Table 4 Allocation of Singapore in portfolios
Portfolio 1 2 3 4 5
Times 22 62 25 53 7
Frequency 0.130178 0.366864 0.147929 0.313609 0.04142
Table 5 Regression result of average excess return on consumption growth
group1 group2 group3 group4 group5
Δc 0.000533**
0.000232 0.000192 0.000098 -0.000106
(3.81) (1.66) (1.19) (0.62) (-0.49)
_cons -0.475***
-0.146*
-0.0188 0.114 0.403***
(-8.21) (-2.52) (-0.28) (1.74) (4.49)
N 13 13 13 13 13
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001

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Table 6 Regression result of average excess return on world GDP growth rate
group1 group2 group3 group4 group5
world GDP growth rate 0.0173 -0.00253 -0.00707 -0.00929 -0.025
(0.75) (-0.15) (-0.38) (-0.53) (-1.07)
_cons -0.348**
-0.0534 0.0772 0.183*
0.454***
(-3.62) (-0.74) (0.99) (2.52) (4.68)
N 14 14 14 14 14
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001
Table 7 Regression result of average excess return on volatility
group1 group2 group3 group4 group5
volatility -0.00161**
-0.000519 -0.000152 0.000239 0.00109
(-3.21) (-1.08) (-0.28) (0.47) (1.73)
_cons -0.148**
-0.0204 0.0623 0.128*
0.267***
(-3.06) (-0.44) (1.18) (2.61) (4.38)
N 14 14 14 14 14
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001
Table 8 Result of portfolio regression
group1 group2 group3 group4 group5
Δc 0.000307 0.000218 0.000397 0.000437 0.000429
(1.20) (0.82) (1.33) (1.60) (1.21)
world GDP growth rate -0.0148 -0.0158 -0.00759 0.000741 -0.00173
(-0.72) (-0.74) (-0.32) (0.03) (-0.06)
volatility -0.00108 -0.000221 0.000765 0.0014 0.00217
(-1.12) (-0.22) (0.68) (1.37) (1.63)
_cons -0.241 -0.0595 -0.13 -0.134 0.0264
(-1.11) (-0.26) (-0.51) (-0.58) (0.09)
N 13 13 13 13 13
t statistics in parentheses
*
p < 0.05, **
p < 0.01, ***
p < 0.001