Comparing account performance to benchmark

Is it appropriate to use the money weighted return to calculate a clients return and then compare it to a time weighted return benchmark calculation? I do not think it is the accepted practice. Can anyone help me out? Also, am I correct that a money weighted return always have a positive dollar return when there is a percentage gain and vice versa (negative dollar return when there is a percentage loss)? And that this relationship does not necessarily hold true for a time weighted returns. I.E. you could have a positive percentage with a dollar loss.

Time weighted returns are pretty much the better choice for everything except when you want to track the size of assets-under-management. For benchmark comparisons, I can’t think of any situation in which a money-weighted return would be more appropriate. If there is a percentage loss on the invested assets, but there is a net cash inflow that is larger than the loss in the same holding period, then you could register a money-weighted AUM gain when in fact there is a time-weighted investment loss from bad/unlucky investment decisions.

Thank you. If there are no cash flows other than an intial cash flow into an account and 60% is invested in one asset (equity index fund) and 40% invested into another asset (money market fund) is it possible to have a different MWR and TWR for the account? Or I am likely doing to calculations incorrectly? For the account I end up with a small dollar loss (remember no cash flow), a positive TWR and a negative MWR.

That’s very odd. Are you including transaction costs in your MWR that you aren’t in your TWR? If there are no deposits or withdrawals in the holding period, and your begin value already includes the initial deposit, then TWR=MWR.

Transactions costs are included in both. I am using daily valuations, though I do not think this changes the fact that, like you said, the TWR should equal the MWR.

That is strange. Can you give us a better sense of how you are doing each calculation? Also, if you are doing (TWR - Benchmark Return), you can get a positive relative return (you beat the benchmark) if the benchmark went down by, say 5%, and your fund went down 3%. That would give a MWR of -3% but (TWR-BM) = +2%. However, that is comparing apples to oranges, because benchmark comparisons should always be relative to TWR, so you shouldn’t be using MWR for that. (I suppose you could simulate identical cash flows going into the benchmark and then compare MWR of each, but I don’t think anyone actually does that).

I agree with your orange v. apple comparison. It needs to be TWR actual v. TWR benchmark. What is happening however is that the actual account TWR is a small +%, and the benchmark TWR is a small +%, but the acutal account and benchmark in dollar terms both lose a small amount of money. This seems counterintuative. Here is how I am calculating the account TWR. I have two assets. A taxable money market (MM) and a equity index fund (EQ). They start at weights 47% EQ and 53% MM. There are no cash flows. If one had the daily returns for each and calculated a daily blended return DB1=[(EQ)r*(EQ)w]+[(MM)r*(MM)w, where r=daily return and w=daily weight. To calculate the cumulative return by day two it would be CR2= [(1+DB1)*(1+DB2)], where DB1=daily blend day one and CR2=cumulative return by day two To calculate the cumulative return by day three it would be CR3= [(1+DB3)*(1+CR2)]-1 I assume this math is correct. Over the course of 2008 and 2009 the weightings become skewed and by 3/9/09 the weighting is now 32.5% EQ and 67.5% MM. This then reverses close to the original weightings by 2010. Could the fact that the weights change daily lead to a positive TWR % gain but actual dollar loss in the account? Seperately, does it matter in the MWR that the EQ and MM weights change gradually over time?

Strange. I cannot edit my last post. Anyways, I figured out what was going on in this two asset account that had no cash flows outside of the initial cash flow. The BENCHMARK TWR was being calculated by weighting the two benchmarks daily based on the returns of the benchmark. This math is found in the my post above this one. The ACTUAL ACCOUNT TWR return of the account was being calculated by the value of the daily value of the account. There was no look through to the underlying assets. In otherwards there was no weighting of the underlying assets. When I “weight” the actual accounts the result make much more sense and seems comparable to the weighted benchmark that was already being calculated. Also, when I “unweight” the actual returns it seems much more comparable to the unweighted benchmark. My question now is how wrong is to weight the benchmarks daily but not weight the assets at the account level? What is the GIPS compliant method? It seems like you cannot use one method for the account cumulative return and another for the benchmark cumulative return. At the very least you should use one or the other.