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truthisntstupid (93.47)

Error in start price calculation?

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July 12, 2011 – Comments (10)

OK. 

This bugs me.  I have spent some time understanding how CAPS calculates a new start price every time a stock goes ex-dividend.  In fact, I wrote a blog about it.

http://caps.fool.com/Blogs/dividends-and-capsand-how/591837

 

So I'm puzzled my the drop in my start price for PEP since I last updated my pitch for PEP on June 3rd.

My start price for PEP before June 1st was  $59.76. 

June 1st PEP went ex-dividend, and the opening price on ex-dividend day was $70.58.  The dividend was $0.515.

1 / 1 + ($0.515/$70.58)... times $59.76 = $59.33.

I get that.  It's easy, basic math.

The error is in my favor and all, but I want to know why my start price has dropped from $59.33 to $58.53 since the last time I looked on June 3rd.

PEP hasn't gone ex-dividend since then, and even if it did, it would drop the start price to something in the neighborhood of $58.90, give or take a penny or two.

 Am I overlooking something, or is this an error in CAPS?

10 Comments – Post Your Own

#1) On July 12, 2011 at 1:48 PM, truthisntstupid (93.47) wrote:

By the way, in case I wasn't clear enough about it, $59.33 was my listed start price for PEP on June 3rd.

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#2) On July 12, 2011 at 2:01 PM, portefeuille (99.66) wrote:

1 / 1 + ($0.515/$70.58)... times $59.76 = $59.33

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2 correction factors make sense.

day n = last trading day before the ex-dividend day
day n + 1 =  ex-dividend day

a :=  closing price on the last trading day n,
e := opening price on day n + 1,
d := dividend,
c := d/(a - d),
cf1 := 1 - d/a,
cf2 := 1/(1 + d/e).

The price goes from a to the theoretical "ex-dividend day opening price" a - d, so it is multiplied by (a - d)/a = 1 - d/a = cf1. multiplying the starting price with the same factor ensures that the performance is "continuous at the close of trading on day n".

Using the dividend to buy shares at the open of the ex-dividend date you get d/e shares. As the number of shares is multiplied by (1 + d/e), the starting price is multiplied by 1/(1 + d/e) = cf2.

(For e = a - d you get cf2 = 1/(1 + d/(a - d)) = 1 - d/a = cf1, as it should be.)

cf1 is the correction factor you get if you reinvest the dividend at the close of day n. For 1 share you need to buy c shares at the close.

1/(1 + c) = 1 - d/a = cf1.

(As it should be you can afford to buy exactly those c shares for every share you own at the close, as (1 + c) * d/a = c.)

So whether you prefer cf1 or cf2 depends on whether you assume dividend reinvestment at the close of day n or at the open of day n + 1.

(To buy at the close you would need to know the closing price in advance, which is usually not possible, so using cf2 (as in the "caps" game) might "make more sense" ...)

cf2 -> 0 for e -> 0 (as it should, as the number of shares you buy at the open is d/e which goes to infinity), so if for some reason opening price on day n + 1 is "unreasonably low" it might be more reasonable to switch to the use of cf1 (to not create instant "caps" game score point millionaires ...).

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In the "caps" game cf2 is used.

cf2 = 1/(1 + d/e) = 1/(1 + $0.515/$70.58) ≈ 0.9928,

$59.76 * cf2 ≈ $59.33.

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#3) On July 12, 2011 at 2:08 PM, portefeuille (99.66) wrote:

In the "caps" game cf2 is used.

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Okay, exactly how are we adjusting?
The exact formula is

New Start Price = Old Start Price * Reduction Factor

Where Reduction Factor = 1 / (1 + Dividend / Post-div Price)

--------------------------

(from here)

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#4) On July 12, 2011 at 2:16 PM, portefeuille (99.66) wrote:

#2,3 The use of cf1 = 1 - d/a = 1 / (1 + d/(a - d)) was suggested in comment #6 to that post.

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I'd argue the equation should be:

Reduction Factor = 1/(1+(Div/(Closing Price-Div)))

--------------------------

(from here)

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#5) On July 12, 2011 at 2:16 PM, truthisntstupid (93.47) wrote:

Hi, Porte

Yes, that's how I figure it...cf2.  I know I'm doing it right, and even though the error is in my favor, I just wonder why my start price was adjusted from $59.33 (correct start price) to $58.53 (not correct).

Even when it goes ex-dividend the next time in September, the dividend will be $0.515 unless its raised (and it's already been raised this year).  That would put the new start price close to $58.90 - not $58.53.

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#6) On July 12, 2011 at 2:33 PM, truthisntstupid (93.47) wrote:

Porte

Wouldn't   1/(1+(Div/(Closing Price - DIV)))  end up with the same result as cf2?

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#7) On July 12, 2011 at 2:55 PM, TMFCHarris (99.62) wrote:

Truth -

It looks like we have a PEP dividend that popped up on the feed for June 28th. I'm digging deeper into why that happened, and I'll keep you posted.

Fool on,
Chris

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#8) On July 12, 2011 at 2:58 PM, truthisntstupid (93.47) wrote:

TMFCHarris

Thanks!  

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#9) On July 12, 2011 at 3:08 PM, truthisntstupid (93.47) wrote:

So, then...the dividend of some company that went ex-dividend on June 28th with a quarterly payout of somewhere close to ~$0.80 or so was mistakenly credited to PEP on CAPS.

 Just guessing...

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#10) On July 16, 2011 at 5:14 PM, truthisntstupid (93.47) wrote:

Now my start price for PEP is back where it should be...$59.33.

I'm glad, because in my last pitch reply, I referred to my start price and the fact that the next time it went ex-dividend my start price would drop to around $58.90.  The erroneous dividend attributed to it made it look like I didn't know what I was talking about!

Besides...PEP doesn't need an unfair advantage.  

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