The Forex Reserve of a country remains in the locker of its central bank and does not earn any interest for that country. What are the measures that the central bank of a country can take to overcome this and other related demerits. Further due to this demerit,does a country really have a saturation/limitation level beyond which it is uneconomical to pile up its Forex Reserve?
The foreign exchange reserves of a country are normally invested in short-term government bonds in countries with liquid currencies (or trade partners). It is a portfolio of assets, and so the reserves may be diversified. On average, it should earn the risk-free short-term rate of the reserve currencies.
The cost to the country holding reserves is that they have to issue currency/bank reserves as the flip side of holding the forex reserves. These excess reserves will need to be drained, and so in some cases needs to issue bonds or bills to do so. In other words, the country needs to pay the domestic interest rate in order to hold the forex reserves; you can think of them borrowing to finance the position. (They could raise reserve requirements, forcing local banks to effectively loan money to the central bank to finance the reserve. This pushes the interest cost onto the domestic banking industry.)
Since a central bank can create its own currency costlessly, it appears that this might be a good deal. But creating a very large reserve position is effectively a huge bet, and any losses are effectively a cost to the taxpayer. (The Swiss attempt to limit Franc strength versus the euro ultimately failed as the position was not politically viable.)
Furthermore, the countries where you hold the reserves may not be amused with the country holding its exchange rate at too low a level. The country may become the target for corrective trade policies if reserves are "too large."
Finally, the reserves are lent to another government. If relations with that country deteriorate, those reserves are at risk of being seized.