Time weighted return with one period of 100% loss being, along, period, returns, investment

spartanag07

If an investment has the returns listed below (the final period being 100% period loss) and pays out one dividend along the way is the time weighted return -100%?

Assume $100 investment

Q1: 10%
Q2: -10%
dividend of $30 (not reinvested)
Q3: -20%
Q4: -100%


cumulative return = (1.1)(0.9)(0.8)(0.0)-1

=-100%

luckygiftvn

Eh no.



Edited 1 time(s). Last edit at Thursday, June 23, 2011 at 08:54AM by soddy1979.

Carson

If the dividend is not be reinvested, it is still held as cash.

So you can't have -100% unless you've lost all the cash too. If you have lost the cash (money market went belly up, government defaulted 100%, whatever), then the calculation is correct.

A more interesting question is what if you have a -100% quarter in the middle of a longer streak (say 10 quarters of returns, but you lost 100% in quarter 5). If you didn't have any external cash flows in and out of the fund, then there would be nothing to invest come quarter 6, but if you had external investors who still invested, you could have a money weighted return that was positive and a time weighted return from quarter 6 forward that is positive. I'm not sure what they right way to do this is other than to footnote that you've lost everything and started over at quarter 6.

chunty

holden1176 Wrote:
-------------------------------------------------------
> If an investment has the returns listed below (the
> final period being 100% period loss) and pays out
> one dividend along the way is the time weighted
> return -100%?
>
> Assume $100 investment
>
> Q1: 10%
> Q2: -10%
> dividend of $30 (not reinvested)
> Q3: -20%
> Q4: -100%
>
>
> cumulative return = (1.1)(0.9)(0.8)(0.0)-1
>
> =-100%

In calculations of time-weighted return, the assumption is made that all cash is reinvested as you want to take out the cash flow timing component out, etc. Therefore, your example is not valid (though, time-weighted return would be -100%). With that said, you can try to modify standard time-weighted return calculation to get to a meaningful number. For example, you can assume that you started the year with $100 and ended with $30 (assume interest rate of 0). Then your cumulative return would be -70%. Or you can use modified Dietz method. To summarize: time-weighted return would not be appropriate for your example, an alternative approach should be used.

yodacaia

My thought was that my example of TWR was not correct. The removal of c/f influences on TWR tripped me up. Obviously I was not including the dividend in my calc above which is a problem.

I am working in a daily valuation environment and the performance reporting service is calculating the return correctly, so there are no issues. The only issue was in my trying to replicate the calculation.

My understanding has improved thanks to bchadwick and maratikus. I appreciate the help.

thommo77

MathMan Wrote:
-------------------------------------------------------
> Time weighted return ignores cash flows. So
> whether a dividend was paid of not, the assumption
> for twr needs to be that the dividend is
> reinvested. If you don't reinvest the dividend,
> you are technically reallocating your portfolio.

Dividend reinvestment isn't a requirement. What happens to the dividend doesn't matter at all, as long as you account for it. If the dividend is NOT reinvested, the calculation treats it as positive income AND a withdrawal. So in essence, it is the same as RECEIVING the dividend, and immediately withdrawing it from the account. The amount of the dividend itself is included in total investment gain.

The return formulas don't have a specific variable for income, but this is how it is handled in practice. Dividends are always treated as part of investment gain and then either stay in cash (as part of account value), get reinvested, or are "withdrawn" from the value immediately.

The timing of the withdrawal (be it from dividends, or general cash flows) can be handled in many ways, and is the driver between different TWR and approximated TWR calculations.



>
> So, the asset with the -100% return actually has a
> time weighted return of -100%
>
> But, your portfolio, which includes whatever you
> did with the 30 bucks that came out of the -100%
> asset, will have a return greater than that.
>
> What maratikus did seems like the best estimate.



Edited 1 time(s). Last edit at Thursday, June 23, 2011 at 10:36PM by McLeod81.

Chuckrox

And whenever you have a -100% return, that's a hole you cannot dig out of unless you contribute additional capital. A 100% loss means there's nothing left. Once you add funds, the cash flow is included in the next periodic return calculation.

bolligerallstar

holden1176 Wrote:
-------------------------------------------------------

Is your screen name taken from the Aussie car brand?

Zestt

MathMan Wrote:
-------------------------------------------------------
>
> This is false...just look at the calculation. The
> div is a negative CF, withdrawl, you are clearly
> adding the dividend back. It is AS IF it is
> reinvested. What you do with it in reality
> doesn't matter.
>
> 1 + r = (V1 - CF)/V0 = (V1 + D)/V0


Actually MathMan... The dividend IS treated as a negative cash flow (as you correctly stated), which shows that it clearly IS being treated as a withdrawal (since it is no longer in the account).

I think you misunderstood what I was saying. I was speaking from a practical sense, explaining how the dividend is treated in an actual portfolio. If the dividend is NOT reinvested, it is treated as a withdrawal, since it is no longer included in the account value.

Using the formula you quoted:

1 + r = (V1+D)/V0

This is a formula you could use if the dividend was NOT reinvested. If it WAS reinvested, it would already be included in V1, so you would not need to add it back in. There is no explicit reinvestment assumption involved here. It doesn't matter whether or not a dividend is reinvested, as long as you account for it in the calculation (through the negative cash flow).



Edited 1 time(s). Last edit at Friday, June 24, 2011 at 10:08PM by McLeod81.