Testing the hypothesis that: (UIP)
Forward exchange rate is unbiased estimate of future spot rate.
This is equivalent to test the hypothesis of Uncovered Interest Parity.
Due to arbitrage principle, Covered Interest Arbitrage holds in unrestricted capital markets, if we ignore
transaction costs and default risks by depository entities.
The forward rate is equal to:
Forward price for currency i, j= (1+ Interest rate in country i)/(1+interest rate in country j) * spot rate of
currency i, j.
If this doesn’t hold, there will be arbitrage profit, i.e., if the higher interest rate country’s currency price
expressed in forward terms doesn’t depreciate in the time period of our consideration, one can simply
save in higher interest countries (exchange your currency to the higher yielding one) and cover the
proceeds with a forward and earn abnormal return. If, on the other hand, the value of the higher yielding
currency in dollar terms (for example) depreciates (in forward terms) more than the interest rate
differential dictates, then one can borrow the weaker currency and invest in the stronger one and make
abnormal return, this is, of course, suppose that there is same access to borrowing for private person as
well as for institutions.
Forward price are expressed as points. It is valued as 0,0001 for 1 point. In order to get the forward rate,
you need to add back the forward points to the spot rate of your chosen.
Step 1:
Collecting data of spot rate over Swedish Kronor and US dollars, (or Euro and USD if you prefer), forward
points, 3 month forward, for the latest 2 years.
1 Forward point is equivalent to 1/10000 SEK, should be added to the spot rate to get the forward rate.
Step 2: Testing if the Future spot rate differential is equal to the forward differential. F0/S0.
St / S0     ( F0t / S0 )  
or in Ln form: ( to transform st, st-1, F tt-1 simply transform the data using =ln( ) )
𝑡
𝑆𝑡 − 𝑆𝑡−1 = 𝛼 + 𝛽(𝐹𝑡−1
− 𝑆𝑡−1 ) + 𝜀𝑡
If the theory holds true we will have β=1 and α=0.
The result is presented as follows (for your comparison).
Regression result of SEKUSD=R (SEK/$) forward rate vs. future spot rate empirical testing:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.14479
R Square
0.02096
Adjusted R
Square
0.01792
Standard Error
0.04628
Observations
324
ANOVA
df
Regression
Residual
Total
1
322
323
SS
0.01477
0.68970
0.70447
Intercept
Ft-st-1(3m)
Coefficients
0.00140
0.11817
Standard Error
0.00265
0.04500
MS
0.01477
0.00214
F
6.89504
Significance
F
0.00906
t Stat
0.53009
2.62584
P-value
0.59641
0.00906
Lower 95%
-0.00380
0.02963
The forward differential and the future spot rate differential is not equal. Because the coefficient β is
0,118. The forward rate is closely following the current rate, but not an indication to future spot rate. To
say that is to say that the market is random. This means that the forward rate is not an unbiased
predictor of the future spot rate.