It is sometimes asserted that investors who hedge their foreign currency bond or stock returns remove the foreign exchange risk associated with the investment, reduce the volatility of their domestic currency returns, and thus get a "free lunch"

because the mean return in domestic currency remains the same as the mean return in the foreign currency. Is this true or false? Why?

If forward rates are unbiased predictors of future spot rates, hedging foreign currency investments does not change their expected returns and effectively removes a source of volatility. Some would say that this provides a "free lunch" because volatility is reduced without a reduction in mean. By hedging foreign investments, you can increase your Sharpe ratio for this particular asset class, which allows you to lever the return to the same volatility and get more return. But, there is no "free lunch" because in this case the foreign exchange risk is not a priced risk. If there is a risk premium in the foreign exchange market, the statement is wrong. Hedged foreign bond and equity investments would have different expected returns than unhedged investments.