The presence of a risk premium in foreign exchange markets for the floating exchange rate period has been examined by some researchers and the results obtained were not successful. In this thesis, we analyse a number of exchange rate models and assess their empirical performance. Using the data from the Group-S members in the post Bretton Woods period, we investigate the presence of the risk premium among different models. Our results are remarkably satisfactory. A 'new' random walk model is tested. It has been found that the null hypothesis of a unit coefficient with or without a constant cannot be rejected for several pairs of the countries. The statistically non-zero constant indicates the existence of the risk premium and/or transaction costs in the foreign exchange markets. Results of testing long run Real Interest Parity (RIP) show that such a condition holds in several cases, and this is explained by the existence of capital and exchange rate controls, and thus by the risk premium, rather than PPP and UIP conditions. One way to detect the existence of the risk premium is to test the significance of the semi-elasticity of bond supplies in a portfolio balance model. It has been shown that such a premium does exist in many cases. Thus the results support the view that the exchange rate is mainly determinated by investors' portfolio behaviour. Finally, a synthesis of monetary and portfolio balance models is also studied. We have been able to uncover evidence in support of the long run model of exchange rate determination for the floating exchange rate period. The evidence supports the synthesis model and a policy reaction function that manages the exchange rate by fully or partially offsetting systematic fluctuations in interest rate differentials.