Jim Whitney   March 16, 2011

Comparing domestic and foreign returns in practice

Comparing annual rates of return on domestic and foreign 3-month government bonds, as of mid-October 1997:
U.S. interest rate: 5.50%  
  Britain France Germany Japan
Interest rates (i*) 7.19% 3.32% 3.40% 0.48%
Covered interest arbitrage:
(1) Exchange rates (E & E*) Pds/$ $/Pd Fr/$ $/Fr DM/$ $/DM Yn/$ $/Yn
   Spot (s) .6160   5.8610 0.1706 1.7475   121.1  
   3-mo. Forward (f) .6184   5.8286 0.1716 1.7383   119.5  
(2) Expected %DE*   0.586%    
(3) Annual exp.%DE*   2.34%    
(4) Overall U.S. annual return on foreign bonds   5.66%    
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Uncovered interest arbitrage:
(1) Exchange rates (E & E*) Pds/$ $/Pd Fr/$ $/Fr DM/$ $/DM Yn/$ $/Yn
   mid-October 1997 .6160   5.8610 0.1706 1.7475   121.1  
   mid-January 1998 .6137   6.1365 0.1630 1.8320   129.8  
(2) %DE*   -4.455%    
(3) Annual %DE*   -17.82%    
(4) Overall U.S. annual return on foreign bonds   -14.50%    
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    Formulas:
    (1) E* = $/currency = 1/(currency per $)
    (2)  %DE* = 100·((Ef* - Es*)/Es*)
    (3) Annual %DE* = 4·%DE*
    (4) Overall U.S. annual return on foreign bonds = i* + Annual %DE*