TWR Yield for Reinvested and Distributed Distributions

[El Wealtho]

When one retrieves data from the Yahoo Historical server there is the option of retrieving with Distributions either "Distributed" or "Reinvested".

1) Why would one choose one over the other?

I have observed that retrieving the data each way results in the exact same TWR Yield figures (along the top of the graph).

2) Shouldn't the yield be different for distributions Distributed or Reinvested?

[Mark]

Hi El Wealtho,

1) You would choose "Distributed" if you didn't reinvest, or were trying to model a case where you didn't reinvest. Choose "Reinvested" otherwise.

2) No. TWR will be the same in both cases. TWR factors out external cash flows, and only evaluates the performance of the underlying object, ignoring external additions/withdrawals within the yield term. The distribution itself is factored into the TWR, but how much you had invested during various parts of the yield term are ignore for TWR. This is different than ROI, which does factor in how much you had invested. ROI is time and money weighted.

[El Wealtho]

2) ... TWR factors out external cash flows, and only evaluates the performance of the underlying object, ignoring external additions/withdrawals within the yield term. The distribution itself is factored into the TWR, but how much you had invested during various parts of the yield term are ignore for TWR.

Well, not according to your definition of TWR here:

https://www.fundmanagersoftware.com/hel ... s_twr.html

External flows are accounted for in TWR calculations.

Additionally, using your Example Calculation on that page, if the dividend is "reinvested" rather than "paid in cash", shouldn't BMV3 = 2550? If so, this will affect the TWR calculations - and they should differ between Yahoo downloads for "Reinvested" vs. "Distributed" distributions.

[Mark]

Hi El Wealtho,

That definition doesn't say they are "accounted" for, it factors them out. It does this by creating multiple time periods between each external flow, and calculating the returns of each of these periods, and then combining all the periods together. Each Ri term is created between external cash flows, so they are factored out. Let's take an example:

Started with 10 shares at $100/share
Received a distribution of $100 dividend for $1/share while share price was still $100/share
Say the end price ends up at $115/share

Look at 2 cases, one where you took out the dividend, and one where you reinvested it:

1) Distributed:

You had an external cash flow, so there will be 2 components:

Cash Flow Period 0:
BMVi: 1000.000000 EMVi: 1100.000000 Yieldi: 10.00
Cash Flow Period 1:
BMVi: 1000.000000 EMVi: 1150.000000 Yieldi: 15.00
Total Yield: 26.50

2) Reinvested:

There was no external flow, everything stayed in the investment, so there only needs to be 1 component:

Cash Flow Period 0:
BMVi: 1000.000000 EMVi: 1265.000000 Yieldi: 26.50
Total Yield: 26.50

Notice, the resulting Total Yield is the same, either way. Also, notice in case 1, the EMVi for the first period included the value of the distribution, before it was removed. The BMVi for the second period, excluded the value of the distribution, after it was removed. All the BMV/EMV for each period have no external flows in them, so the BMV to EMV changes are due only to performance, and not any money being added/removed.