Would you expect the required rate rate of returns for a U.S investor in U.S common stocks to be the same as
the required rate of return on Japanese common stocks? what factors would determine the require rate of return for stocks in these countries?

Invstors demand a higher risk-free rate of return (which might correspond, for exmaple, to the 10-year T-bond rate) in countries where the inflation expectation is higher. This rate is currently higher in the US than (for exmaple) Europe and Japan, and our currency value with respect to the world's other major currencies is also falling.

The required rate of return for stocks tends to be higher than that for bonds, because of the higher volatility of stocks. Therefore two factors influencing the relative rate in different countries are 1: inflation expectation for the currency and 2: stock market volatility (usually represented by a "beta" coefficient). Most developing countries have a higher stock market beta than the USA. Japan suffered a major stock market collapse and slow recovery that has lasted over 20 years. Memories of this continue to affect investor confidence in Japan.

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