Please help me determine which of the following statements about ETFs are correct.

  1. ETFs are passive investment instruments.

  2. Does an ETF’s price move in exact correlation with its index? For example, will a Nifty 50 ETF rise proportionately when the Nifty 50 index spikes?

  3. The key advantage of investing in an ETF over a mutual fund is liquidity—ETFs can be bought and sold instantly, whereas mutual funds typically take two days to process redemptions.

None of these statements are unconditionally true for all ETFs.
Whether they are true will depend on the specific ETF under consideration.

Depends on the ETF.
If an ETF is tracking a passive index, then yes.

Depends on the ETF.
The amount of deviation is measured as the tracking error.

Depends on the ETF.
One should check the typical daily traded volumes of an ETF in the markets/exchanges, relative to the amount one wishes to invest, to get a sense of how liquid one’s investment in the ETF would be.

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