I am trying to calculate cross-currency basis on the 3-month horizon for a certain set of currencies. The formula should be $ccb = F/S (1+y_{foreign currency}) - (1+y_{USD})$ where $y_{USD}$ is Libor 3months in USD, S is the spot rate and F is the forward rate (both expressed as the price of foreign currency) and y_foreign currency is the 3-months Libor in the foreign currency. Now, before 2008 I should obtain cross-currency basis close to 0 for almost all the currencies, but that is not the case. For example Japan in 26/11/2004 had an interest rate differential equal to -.0239 (-2.3%). The ratio between spot and forward, however, is not giving me the expected result. What am I doing wrong?
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$\begingroup$ y_{usd} = 2.4% y_{f} = 0.053% S= 103 FP( forward points) = -61bps. The ccb should be close to 0 in bps. $\endgroup$– umbecdlOct 14, 2019 at 8:32
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1 Answer
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Since we are dealing with quarterly returns we have to use the returns over one quarter (one period) not the annualized returns that are commonly quoted and that you used in your formula. So the formula is
$$ccb/4 =\frac{F}{S}(1+y_f/4)-(1+y_{usd}/4)$$
Now the calculation. If the conventional quotation (i.e. in USDJPY terms) S is 103.00 and the forward points are -61, then F is 102.39. But in this formula we need the rates in the opposite direction S=1/103 and F=1/102.39. So F/S is 1.0059576. Since yf is 0.00053, 1+yf/4 is 1.0001325. So (F/S)*(1+yf/4) is 1.0060909. This is not too different from 1+y/4 which is 1.006. So unless I made a mistake (entirely possible) we are on target for essentially no currency basis.
Now try it for a date during the Global Financial Crisis and there should be cross currency basis.
