Non Resident Indians (NRIs) have a plethora of investment options to choose from. Among these include mutual funds, stocks, NRO Fixed Deposits and NRE Fixed Deposits.
Real estate is more a long term bet and can be excluded for the purpose, while NRIs are not permitted to invest in small savings schemes issued by the post office.

The best bet considering the current circumstances for NRIs would be NRE Fixed Deposits. Here is a quick comparison and conclusion on the reasons for the same.
NRE Fixed Deposits vs Shares
A good bank offers an interest rate of 9-9.5 per cent on NRE Fixed Deposits. If you take quarterly compounding the returns over 2-years could work out to a near 10 per cent. The problem with shares at the moment is that they have run-up too much and too fast.
Another problem is that in shares you ending up paying short term capital gains tax, if your holding is less than one year. On the other hand NRE Fixed deposits are tax free.
You do not pay any tax whatsoever on interest earned on NRE Fixed Deposits, making their post tax returns superior to every other instrument. Your capital and interest is protected, while you cannot say that for sure in shares.
NRE Fixed Deposits VS NRO Fixed Deposits
The simple fact is that NRE Fixed Deposits are tax free, whereas NRO Fixed Deposits are taxable. Also, funds from NRE Fixed Deposits, including its interest income is freely repatriable. So, in case of emergency, you can repatriate swiftly and without worries.
NRE Fixed Deposits vs Government Securities
Well, government securities are currently yielding 8.5 per cent, while NRE Bank deposits can yield as much as 10 per cent, as mentioned above. Also, NRE Fixed Deposits are tax free, while interest on government securities attract tax.
NRE Fixed Deposits vs Mutual Fund Schemes
If you invest in an equity mutual fund scheme currently, you are going to buy at a very high net asset value (NAV) as shares have risen and so have the NAV of mutual fund schemes.
What this means is that chances of you bettering returns from Mutual Fund Schemes, could even be lower than NRE Fixed Deposits.
Also, remember that returns from NRE Fixed Deposits is almost guaranteed and you would get a fixed sum on maturity. Equity schemes of mutual funds cannot guarantee you the same.
Conclusion
For tax free and risk free returns NRO fixed deposits are the best bet. Mutual Fund and shares could offer higher returns, but there is always an element of risk, when it concerns protecting your interest and capital.
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