Why is TWR negative even though an account has positive $ gains?
Since TWR is essentially aggregating daily % returns over time, there can be instances where the % return and the $ return have opposite signs if there are significant cashflows within a period.
One common scenario is when an earlier period has negative % returns on a smaller balance, and then a later period has positive (but smaller) % returns on a larger balance. In this scenario, the total TWR over both periods is still negative, even though the $ returns can be slightly positive.
If there are no cashflows, TWR and $ returns are guaranteed to have the same sign.
It has its own quirks, but IRRs are guaranteed to always have the same sign as $ returns.
Why is client-level TWR higher or lower than any of the account TWRs?
To calculate client-level TWR, we don't simply aggregate TWR performance across accounts. Instead, we aggregate daily performance across accounts, then accumulate them over time. As a result, it is possible to have a client-level TWR that is higher or lower than any of the underlying accounts.
The usual scenario where this might happen is when accounts are opened or closed within a period, resulting in account histories do not line up exactly. For example, a client my have:
- Older accounts that have positive returns early on, then have relatively lower returns afterwards.
- Newer accounts that are larger and that earn high returns.
In that scenario, it's very likely that the client-level TWR will be higher than any account TWR.
Why is client-level IRR higher or lower than any of the account IRRs?
Since IRRs assume a constant % return over the full period, there can be instances where the IRR for a group of accounts can be even larger than the IRR of any account.
One common scenario is when there is a new account funded that earns a positive return. Because the new account is treated as a contribution in the middle of the period when calculating aggregated IRR, the $ gains are applied against both the earlier lower balance period and the later higher balance period. That lower balance period requires a higher % return (IRR) to achieve the same $ return.
It is a known issue with using IRRs when there are cashflows, as also mentioned by other investment firms.