CFA CFA Level 1 Confused between TWR and Geometric mean

# Confused between TWR and Geometric mean

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This may be a silly question but I’ve just started my CFA level 1 learning and I’m currently doing quantitative methods. I’m a bit confused by the concepts of time-weighted returns and the geometric mean.

I’m being told that they are the same thing and calculated using the same formula but this isn’t the case from what I can see.

For example, I was doing a practise question earlier which asked me to calculate the annualized time-weighted return for a fund that returned 14% and 8% over the previous two years.

I used the TWR formula which would have been written as:

(1 + 0.14)(1 + 0.08) – 1

I ended up getting that question wrong and found in the explanation that it wanted me to use the geometric mean formula which would have been written as:

[(1 + 0.14)(1 + 0.08)] ^1/2 – 1

These two formulas obviously return very different answers but I keep seeing TWR and geometric being labelled as the same thing and being used interchangeably as with my example question which stated TWR but the answer used the geometric mean formula.

Is there something I’m missing that is causing this confusing? Thanks in advance.   