Why frequency of distribution is important

[OhNoNotimAgain]

As this board knows maths is not my strong point. So I do try and learn more.
Reading "The Art of More" by Michael Brooks I came across this vignette which I think is worth sharing.

In 1863 Jacob Bernoulli was working on the problem of how often a bank should add interest to your account.

Brooks uses the analogy of someone with a $1,000 earning interest at 100% a year.

If added yearly the investor would have $2,000 at the end of the year.

If added every six months he/she would have $2,2250 by year end.

If added quarterly the net result would be $2,414 at the year end.

If added monthly the result is $2,613 after 12 months.

But, strangely, moving to daily calculations only adds another $102 to take the the total to $2,715.

That's because the total heads towards a limit where there is virtually no change and into the realm of the Euler number which is above my pay grade.

However, the exercise does demonstrate the importance of getting the optimal distribution frequency as one mechanism to enhance returns.

Its better for dividends to sit in your account ASAP rather than in the funds managers' account.

[absolutezero]

Its better for dividends to sit in your account ASAP rather than in the funds managers' account.

Mind blowing stuff follows:
It might be even better if the company didn't pay a dividend at all.

[Dod101]

No doubt you just transposed the numbers but the date was actually 1683.

Generally the calculation shows the power of compound interest, but that it has a limit.

Dod

[Charlottesquare]

As this board knows maths is not my strong point. So I do try and learn more.
Reading "The Art of More" by Michael Brooks I came across this vignette which I think is worth sharing.

In 1863 Jacob Bernoulli was working on the problem of how often a bank should add interest to your account.

Brooks uses the analogy of someone with a $1,000 earning interest at 100% a year.

If added yearly the investor would have $2,000 at the end of the year.

If added every six months he/she would have $2,2250 by year end.

If added quarterly the net result would be $2,414 at the year end.

If added monthly the result is $2,613 after 12 months.

But, strangely, moving to daily calculations only adds another $102 to take the the total to $2,715.

That's because the total heads towards a limit where there is virtually no change and into the realm of the Euler number which is above my pay grade.

However, the exercise does demonstrate the importance of getting the optimal distribution frequency as one mechanism to enhance returns.

Its better for dividends to sit in your account ASAP rather than in the funds managers' account.

When you get to the point of considering earning interest on dividends received you are down to the smallest of differences to total income.

If you say have a div yield of 4% and instead of receiving the div once a year at year end you instead get it as 1% 4 times a year at quarter ends, that 1% will earn what ?

Say 1% at 9/12 at say 1.5%= 0.01125%
Say 1% at 6/12 at say 1.5%=0.0075%
Say 1% at 3/12 at say 1.5%=0.00375%

Total increase 0.0225% , applied to a dividend income of say £30,000 pa I think that is £6.75 to the good. (may have lost a few decimals but looks roughly right)

[bluedonkey]

That's 3 pints in 'spoons.

[richfool]

Though it might not be appropriate for this board, it should be borne in mind that more frequent payment of dividends not only provides for the compounding affect of the (earlier) reinvestment of dividends and the income arising from them, but also provides the potential for capital gains arising from those (earlier) reinvested dividends.

[Lootman]

That's 3 pints in 'spoons.

And extra tax reporting each year,

I prefer 1 payment a year and a good sum I can do something with.

Or none.

[GrahamPlatt]

That's 3 pints in 'spoons.

And extra tax reporting each year,

I prefer 1 payment a year and a good sum I can do something with.

Or none.

100 mathematicians walk Into a ‘spoons. The first one orders a pint. The second a half, the third a quarter. As the fourth one steps up and asks for an eighth, the barman, plonking two pints on the counter, announces “that’ll be all gentlemen, I know your limits”.

[Dod101]

As this board knows maths is not my strong point. So I do try and learn more.
Reading "The Art of More" by Michael Brooks I came across this vignette which I think is worth sharing.

In 1863 Jacob Bernoulli was working on the problem of how often a bank should add interest to your account.

Brooks uses the analogy of someone with a $1,000 earning interest at 100% a year.

If added yearly the investor would have $2,000 at the end of the year.

If added every six months he/she would have $2,2250 by year end.

If added quarterly the net result would be $2,414 at the year end.

If added monthly the result is $2,613 after 12 months.

But, strangely, moving to daily calculations only adds another $102 to take the the total to $2,715.

That's because the total heads towards a limit where there is virtually no change and into the realm of the Euler number which is above my pay grade.

However, the exercise does demonstrate the importance of getting the optimal distribution frequency as one mechanism to enhance returns.

Its better for dividends to sit in your account ASAP rather than in the funds managers' account.

You might be better reading ‘The Story of a Number’ by Eli Moar The number is e. It is a constant which equals approximately 2.71828. Those who have done a maths degree will recognise this but I must say I have forgotten most of it and am not inclined to swot up on it now. Incidentally, the Swiss Bernoulli family were amazingly erudite in mathematics in the 17th and 18th centuries, almost to my mind as good as Euler. Some of them at least are I think buried at Basel.

Dod

[servodude]

As this board knows maths is not my strong point. So I do try and learn more.
Reading "The Art of More" by Michael Brooks I came across this vignette which I think is worth sharing.

In 1863 Jacob Bernoulli was working on the problem of how often a bank should add interest to your account.

Brooks uses the analogy of someone with a $1,000 earning interest at 100% a year.

If added yearly the investor would have $2,000 at the end of the year.

If added every six months he/she would have $2,2250 by year end.

If added quarterly the net result would be $2,414 at the year end.

If added monthly the result is $2,613 after 12 months.

But, strangely, moving to daily calculations only adds another $102 to take the the total to $2,715.

That's because the total heads towards a limit where there is virtually no change and into the realm of the Euler number which is above my pay grade.

However, the exercise does demonstrate the importance of getting the optimal distribution frequency as one mechanism to enhance returns.

Its better for dividends to sit in your account ASAP rather than in the funds managers' account.

You might be better reading ‘The Story of a Number’ by Eli Moar The number is e. It is a constant which equals approximately 2.71828. Those who have done a maths degree will recognise this but I must say I have forgotten most of it and am not inclined to swot up on it now. Incidentally, the Swiss Bernoulli family were amazingly erudite in mathematics in the 17th and 18th centuries, almost to my mind as good as Euler. Some of them at least are I think buried at Basel.

Dod

"Dr. Euler's Fabulous Formula" by Paul Nahin was a pretty good read (I've not tried the Moar)

Having spent a bit of time as an engineering student in Yorkshire I'll never forget it being put across as "Ee to the aye pie, plus one, equals nowt" (though I believe the lecturer was playing it up a bit - by not using j! )

[mike]

When you get to the point of considering earning interest on dividends received you are down to the smallest of differences to total income.

If you say have a div yield of 4% and instead of receiving the div once a year at year end you instead get it as 1% 4 times a year at quarter ends, that 1% will earn what ?

Say 1% at 9/12 at say 1.5%= 0.01125%
Say 1% at 6/12 at say 1.5%=0.0075%
Say 1% at 3/12 at say 1.5%=0.00375%

Total increase 0.0225% , applied to a dividend income of say £30,000 pa I think that is £6.75 to the good. (may have lost a few decimals but looks roughly right)

Looks like a bit more than a few decimals lost here methinks !

Taking the illustrative figures given

Four equal payments at quarter end of £30,000/4 = £7,500

£7,500 x 9/12 at 1.5% = £84.38
£7,500 x 6/12 at 1.5% = £56.25
£7,500 x 3/12 at 1.5% = £28.13

So total for the year would be just short of £170

And current rates are rather higher than 1.5% so the figure would be correspondingly larger.

[servodude]

When you get to the point of considering earning interest on dividends received you are down to the smallest of differences to total income.

If you say have a div yield of 4% and instead of receiving the div once a year at year end you instead get it as 1% 4 times a year at quarter ends, that 1% will earn what ?

Say 1% at 9/12 at say 1.5%= 0.01125%
Say 1% at 6/12 at say 1.5%=0.0075%
Say 1% at 3/12 at say 1.5%=0.00375%

Total increase 0.0225% , applied to a dividend income of say £30,000 pa I think that is £6.75 to the good. (may have lost a few decimals but looks roughly right)

Looks like a bit more than a few decimals lost here methinks !

Taking the illustrative figures given

Four equal payments at quarter end of £30,000/4 = £7,500

£7,500 x 9/12 at 1.5% = £84.38
£7,500 x 6/12 at 1.5% = £56.25
£7,500 x 3/12 at 1.5% = £28.13

So total for the year would be just short of £170

And current rates are rather higher than 1.5% so the figure would be correspondingly larger.

Haven't you both just agreed? (EDIT - just noticed Charlottesquare applied the correct percentage but to the income not the capital)

170 quid on the capital returning 30k at 4% would be pretty much 0.0225% ?

Whether you take it quarterly and put it in the bank rather than reinvesting it for any given year depends on whether you can get a return after tax greater than your 4% div

[Dod101]

As this board knows maths is not my strong point. So I do try and learn more.
Reading "The Art of More" by Michael Brooks I came across this vignette which I think is worth sharing.

In 1863 Jacob Bernoulli was working on the problem of how often a bank should add interest to your account.

Brooks uses the analogy of someone with a $1,000 earning interest at 100% a year.

If added yearly the investor would have $2,000 at the end of the year.

If added every six months he/she would have $2,2250 by year end.

If added quarterly the net result would be $2,414 at the year end.

If added monthly the result is $2,613 after 12 months.

But, strangely, moving to daily calculations only adds another $102 to take the the total to $2,715.

That's because the total heads towards a limit where there is virtually no change and into the realm of the Euler number which is above my pay grade.

However, the exercise does demonstrate the importance of getting the optimal distribution frequency as one mechanism to enhance returns.

Its better for dividends to sit in your account ASAP rather than in the funds managers' account.

You might be better reading ‘The Story of a Number’ by Eli Moar The number is e. It is a constant which equals approximately 2.71828. Those who have done a maths degree will recognise this but I must say I have forgotten most of it and am not inclined to swot up on it now. Incidentally, the Swiss Bernoulli family were amazingly erudite in mathematics in the 17th and 18th centuries, almost to my mind as good as Euler. Some of them at least are I think buried at Basel.

Dod

"Dr. Euler's Fabulous Formula" by Paul Nahin was a pretty good read (I've not tried the Moar)

Having spent a bit of time as an engineering student in Yorkshire I'll never forget it being put across as "Ee to the aye pie, plus one, equals nowt" (though I believe the lecturer was playing it up a bit - by not using j! )

Moar is an academic from Princeton and he is not that difficult to follow but it does take patience and some real attention.

Dod

[OhNoNotimAgain]

That's 3 pints in 'spoons.

And extra tax reporting each year,

I prefer 1 payment a year and a good sum I can do something with.

Or none.

There is no tax effect in Acc units and you only do one tax return a year so I don't see your point.

If you invest in companies that distribute quarterly the dividends can be reinvested during the course of the year for an additional gain.

I don't understand why everyone fixates on fees and not all the other stuff that can make small, incremental gains in returns.

[servodude]

That's 3 pints in 'spoons.

And extra tax reporting each year,

I prefer 1 payment a year and a good sum I can do something with.

Or none.

There is no tax effect in Acc units and you only do one tax return a year so I don't see your point.

If you invest in companies that distribute quarterly the dividends can be reinvested during the course of the year for an additional gain.

I don't understand why everyone fixates on fees and not all the other stuff that can make small, incremental gains in returns.

They were trained to look at what they pay in tax without understanding what they get for it

[scrumpyjack]

They were trained to look at what they pay in tax without understanding what they get for it

Yes, £30 billion on track & trace, £100 billion on a train line, paying for the PM to take a private jet etc etc.
Many people look at what they get for it and think they could spend it better themselves.

[servodude]

They were trained to look at what they pay in tax without understanding what they get for it

Yes, £30 billion on track & trace, £100 billion on a train line, paying for the PM to take a private jet etc etc.
Many people look at what they get for it and think they could spend it better themselves.

And therein lies the lesson!

Don't trust anyone that only shows you one side of the ledger

[Charlottesquare]

When you get to the point of considering earning interest on dividends received you are down to the smallest of differences to total income.

If you say have a div yield of 4% and instead of receiving the div once a year at year end you instead get it as 1% 4 times a year at quarter ends, that 1% will earn what ?

Say 1% at 9/12 at say 1.5%= 0.01125%
Say 1% at 6/12 at say 1.5%=0.0075%
Say 1% at 3/12 at say 1.5%=0.00375%

Total increase 0.0225% , applied to a dividend income of say £30,000 pa I think that is £6.75 to the good. (may have lost a few decimals but looks roughly right)

Looks like a bit more than a few decimals lost here methinks !

Taking the illustrative figures given

Four equal payments at quarter end of £30,000/4 = £7,500

£7,500 x 9/12 at 1.5% = £84.38
£7,500 x 6/12 at 1.5% = £56.25
£7,500 x 3/12 at 1.5% = £28.13

So total for the year would be just short of £170

And current rates are rather higher than 1.5% so the figure would be correspondingly larger.

Haven't you both just agreed? (EDIT - just noticed Charlottesquare applied the correct percentage but to the income not the capital)

170 quid on the capital returning 30k at 4% would be pretty much 0.0225% ?

Whether you take it quarterly and put it in the bank rather than reinvesting it for any given year depends on whether you can get a return after tax greater than your 4% div

Agreed, mea culpa.

Notwithstanding my mistake (at least the arithmetic was correct merely should have applied my percentage to the notional capital of £750,000 not to the £30,000 income) selecting shares with 4 divs a year in preference to say 2 is never going to be one of my selection screening tools, far more other criteria are used that imho are more important.

[OhNoNotimAgain]

When you get to the point of considering earning interest on dividends received you are down to the smallest of differences to total income.

If you say have a div yield of 4% and instead of receiving the div once a year at year end you instead get it as 1% 4 times a year at quarter ends, that 1% will earn what ?

Say 1% at 9/12 at say 1.5%= 0.01125%
Say 1% at 6/12 at say 1.5%=0.0075%
Say 1% at 3/12 at say 1.5%=0.00375%

Total increase 0.0225% , applied to a dividend income of say £30,000 pa I think that is £6.75 to the good. (may have lost a few decimals but looks roughly right)

Looks like a bit more than a few decimals lost here methinks !

Taking the illustrative figures given

Four equal payments at quarter end of £30,000/4 = £7,500

£7,500 x 9/12 at 1.5% = £84.38
£7,500 x 6/12 at 1.5% = £56.25
£7,500 x 3/12 at 1.5% = £28.13

So total for the year would be just short of £170

And current rates are rather higher than 1.5% so the figure would be correspondingly larger.

Haven't you both just agreed? (EDIT - just noticed Charlottesquare applied the correct percentage but to the income not the capital)

170 quid on the capital returning 30k at 4% would be pretty much 0.0225% ?

Whether you take it quarterly and put it in the bank rather than reinvesting it for any given year depends on whether you can get a return after tax greater than your 4% div

Agreed, mea culpa.

Notwithstanding my mistake (at least the arithmetic was correct merely should have applied my percentage to the notional capital of £750,000 not to the £30,000 income) selecting shares with 4 divs a year in preference to say 2 is never going to be one of my selection screening tools, far more other criteria are used that imho are more important.

Those that don't understand compounding returns are doomed to pay it.
Those that do earn it.

[pyad]

The effect of compounding more frequently is grossly exaggerated in the example by using the ridiculously high bank interest rate of 100%. Try it with the same sum but using actual rates available and the effect of increasingly frequent compounding, though still present, is of little consequence. Even with large sums the effect is pretty minimal in cash terms.

Also, banks have to quote the true Annual Equivalent Rate in addition to any headline rate used to promote the account. If there is a difference it will probably be due (apart from bonuses which some pay) to the compounding frequency offered.

EG. one bank I've just checked that pays monthly interest shows 2.25% AER/2.22% gross (variable), a tiny difference even on serious wad.