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I am attempting to write a function that will calculate the annualized rate of return for individual dividends made by illiquid investments. These dividends are paid at varying intervals and the illiquid investment does not have an observable market price.

I have looked at using:

    [(1 + YTD ROR)1/(#of days/365)] – 1

However, this does not seem valid if this dividend is one of many that have been made this year.

Below are 3 sample cases:

A Investment
$10 / 1 unit
    1/31/2011 - $0.11 div / 1 unit  - 1.1% ROI - 4.4% annualized ROI
    4/30/2011 - $0.08 div / 1 unit  - 0.8% ROI - 3.2% annualized ROI
    7/31/2011 - $0.10 div / 1 unit  - 1.0% ROI - 4% annualized ROI

For investment A the assumption is being made that each dividend paid was being paid on a quarterly basis

B Investment
$10 / 1 unit
    1/31/2011 - $0.11 div / 1 unit  - 1.1% ROI - 13.2% annualized ROI
    2/27/2011 - $0.10 div / 1 unit  - 1.0% ROI - 12% annualized ROI
    3/30/2011 - $0.10 div / 1 unit  - 1.0% ROI - 12% annualized ROI

For investment B the assumption is being made that each dividend paid would be paid monthly.

C Investment
$10 / 1 unit
    5/30/2011 - $2.00 / 1 unit - 20% ROI - 48.6% annualized ROI (assuming 365 days in a year)
    6/30/2011 - $0.10 / 1 unit - 1.0% ROI - 12% Annualized ROI (assuming monthly dividend)

So the problems I'm coming across are:

  1. I won't always know what dividend schedule the current dividend is. For example, is this a monthly or quarterly dividend, or a special one time return of capital, etc.
  2. Sometimes more than 1 dividend is paid per year and sometimes not. Should extra weight be given to those that are the first to occur in that year (which effectively is what happens when using the formula at the top)?

Use Case:

All of this is to reconcile an investment's actual performance with its stated/projected performance. If in the prospectus it is estimated this investment will pay an 8% dividend each year, I need to quantify each paid dividend in annual terms to see if it meets, exceeds, or falls short of the projected performance.

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For calculating the statistics, I believe you'd want to look up the formula for a time weighted return. –  John Jun 12 '12 at 22:43
    
John, thanks for the comment. When I perform a mid-point Dietz return for the first dividend of the first investment I get a return of -67%. Formula used was (($10+($10+0.11)/2)-($10-($10+0.11)/2))/($10+($10+0.11)/2) Since there is no marketable value (so no ending value/closing value) the assumption was made that the original unit price is the ending value. –  w00tw00t111 Jun 13 '12 at 13:49
    
Try this instead: en.wikipedia.org/wiki/True_time-weighted_rate_of_return –  John Jun 13 '12 at 19:59
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3 Answers 3

Can we make the assumption that the amount of each dividend is directly correlated to the amount of time between dividends? This would be the case if there were a fixed dividend payout ratio, or whatever the equivalent vocabulary is for this instrument.

If so, you could annualize each dividend by the number of days since the previous dividend.

The reason this is sound is that if the dividend payout ratio is fixed, then each dividend only represents income earned since the last dividend was paid. Since we know with certainty the length of the period in which the income was generated, we can annualize on that basis.

The fact that you mention a "special one time return of capital" makes me think this assumption might not be valid for all dividends, but perhaps it will apply to some.

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jlowin, thanks for your answer - yes, for most (let's say 99%) of dividends your theory would be correct. However, on the instances where a special payment is made i.e. something in the portfolio is sold off and investor capital is returned, using the time since last dividend would greatly overstate the annualized dividend rate. The only thing I can think of would be to setup a trigger that if the standard deviation is (x) amount higher then the avg, alert me to see if this was a special payment. –  w00tw00t111 Feb 5 '13 at 16:49
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I believe you will have to conjecture from observations what the correct frequency of dividend payment is, then annualize in the standard manner, by assuming the same dividend is paid out for the rest of the year at the presumed frequency. If over time your conjecture is proven wrong, or the company changes its policy, then adjust your estimate. Without more information, it is impossible to completely answer your question.

Alternatively, once a year has passed, you could always take the trailing twelve month dividend yield.

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Tal, thanks for your comment. I was afraid that would be the case. These calculations need to be automated (hence the reason for seeking a formula) and my "gut intuition" cannot come into play as to what frequency this payment is. If I understand correctly, there is not a formula to determine the correct annualized ROI without inputting the dividend frequency (thus dividend frequency must be known). –  w00tw00t111 Jun 19 '12 at 19:48
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You have to know the payout schedule. If you don't know, then take the TTM (trailing twelve months) of total dividends, and use that as a moving average.

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Chloe, thanks for the answer- that works but only if there is 12months of history...which if this is a new investment there won't be. –  w00tw00t111 Feb 5 '13 at 16:49
    
Continue to use 12 months of history. Count the months with missing dividends as $0.00. You could, theoretically, predict future dividends, but predicting doesn't always work out well in finance. –  Chloe Feb 6 '13 at 16:47
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