Hi,
Based on what I had understood from the computation methodology for Total Returns Index variant, it seems that the only difference when compared to the underlying index is that, in the case of TRI, the dividends paid are re-invested back into the index (similar to compounding).
The inference is that the weights of the constituents of TRI are the same as that of the underlying index. This can also be ascertained by comparing the %change in the indices, on days when no dividends were paid by the index constituents.
Since the weights are the same in the case of both indices, it makes sense that a newly launched ETF’s NAV will be closer (if not the same) to the underlying index rather than the TRI in its initial days. The divergence of the NAV from the underlying index kicks in, once the index constituents start paying dividend (which is reinvested in the case of ETF).
To test my assumption, I took the example of ICICI Prudential NIFTY ETF which was launched on 21-Mar-2013. The NAV as on the launch date was Rs. 56.61 (for reference, NIFTY50 closed at 5,658.75 on 21-Mar-2013). The NAV of the ETF was Rs. 159.04 as on 10-May-2021 (which would have been higher, if not for the dividend of Rs. 2.20 per unit paid by the fund on 29-Apr-2016) while NIFTY50 closed at 14,942.35.
This is to say that the NAV of the ETFs tend to diverge from the underlying index over time, provided the fund does not distribute any income/capital to the unitholders. However, it might seem that the NAV is closer to the underlying index rather than the TRI, because of the higher base of the TRI [both the ETF and the TRI move at more or less the same rate, but in absolute terms the change in TRI might seem higher due to the base effect].