Assumptions
Interest rate parity rests on certain assumptions, the first being that capital is mobile - investors can readily exchange domestic assets for foreign assets. The second assumption is that assets have perfect substitutability, following from their similarities in riskiness and liquidity. Given capital mobility and perfect substitutability, investors would be expected to hold those assets offering greater returns, be they domestic or foreign assets. However, both domestic and foreign assets are held by investors. Therefore, it must be true that no difference can exist between the returns on domestic assets and the returns on foreign assets. That is not to say that domestic investors and foreign investors will earn equivalent returns, but that a single investor on any given side would expect to earn equivalent returns from either investment decision.
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