Introducing the LemonFools Personal Finance Calculators

Stocks and Shares ISA , Choosing funds for ISA's, risk factors for funds etc
Investment strategy discussions not dealt with elsewhere.
XFool
Lemon Quarter
Posts: 3597
Joined: November 8th, 2016, 7:21 pm
Been thanked: 216 times

Eboli wrote:XFool wrote:

That indeed is the only explanation I have been able to come up with for pyad's exuberant pedanticism. It sounds as if he is unlikely to explain any further. The trouble with this, AFAICS, is what then is left that can be called "interest", apart from fixed interest bonds? A normal "variable interest rate savings account" does not typically have a guaranteed for a year fixed rate - so that's not "interest"!

It's not that simple. The trouble is pyad (correctly) calling the interest forgone on the cost of purchase of a PB as being a "stake". In normal betting parlance it would be unusual for this to be referred to as a stake. Rather it is a bundle of stakes (and pyad, because of his tax history, will know that the question that then follows is how many stakes makes it a bundle). In a typical bet if you win you win your stake plus a return and if you lose you lose your stake. With PBs the more likely outcome is a partial loss of the interest forgone.

Consider paying someone £37 to place £1 on a given number on a roulette wheel for 37 spins. Of course the number of times you pay over £37 the more likely your average return will be £36 per bundle. But a stochastic distribution will produce in very large number of bundles many cases where no return whatsoever is paid. And indeed, like fund managers, there will always be the possibility of 37 wins in a row. And indeed when the numbers get large there may be more than one bundle that has this highly unlikely outcome.

You cannot draw a comparison with a variable interest account not having a guaranteed return. Because it is always possible to hold PBs and have no winnings at all perhaps for the rest of your life.

You can draw such a comparison. I do, as do others, it is simple and obvious. Nobody - apart from those who want to start a scrap - is saying it IS INTEREST. That is irrelevant. Income is income (after tax etc).

If I get £1000 in a year for working as a painter and decorator, you get £1000 in a year for working in a restaurant, who would claim: "I get an income from work - you do not get an income from work"? Well, there's always one...

IMO for a return on a lump sum you can choose to make the comparison with PBs, unless the recipient does have some specific requirement that definitely rules out PBs, such as a need for a definite monthly cash payment. Which, if they did, they would presumably know about and have already ruled out PBs for just that reason. But the context of this discussion, arising from the OP, is somebody who has heretofore been happily holding £40,000 in PBs.

Because it is always possible to hold PBs and have no winnings at all perhaps for the rest of your life.

"always possible", but how probable is that? It is not impossible that all the oxygen molecules in a room leave simultaneously for the other side of the room. I'm not worried. Should I be?

The variability of the annual return on a given (large) number of PBs is one of the "interesting" things that could be addressed by doing more maths than the easy back-of-the envelope annual return calculation referred to earlier. I haven't done so - I am far from sure I would know how to. Have you done this? This might be of more interest(!) than quibbles over "interest", IMO.

XFool
Lemon Quarter
Posts: 3597
Joined: November 8th, 2016, 7:21 pm
Been thanked: 216 times

One example, using the Money Saving Expert Premium Bond Calculator (But see previous posts - I'd prefer to see the maths)
https://www.moneysavingexpert.com/savin ... calculator

50,000 Bonds; over 1 Year;

Winnings

£25:
Sorry you are unlucky! Almost 100% of people who have put £50,000 in premium bonds over 1 year win more than £25.

£50:
Sorry you are unlucky! Almost 100% of people who have put £50,000 in premium bonds over 1 year win more than £50.

£100:
Sorry you are unlucky! Almost 100% of people who have put £50,000 in premium bonds over 1 year win more than £100.

£250:
Sorry you are unlucky! 99.9% of people who have put £50,000 in premium bonds over 1 year win more than £250.

£500:
Sorry you are unlucky! 82.2% of people who have put £50,000 in premium bonds over 1 year win more than £500.

£625:
You have average luck! Only 49% of people who have put £50,000 in premium bonds over 1 year years win more than £625, meaning you're about spot on.

Of course, averaged over say three years, results would be expected to even out.

Eboli
Lemon Pip
Posts: 75
Joined: November 7th, 2016, 9:05 pm
Been thanked: 16 times

XFool wrote:

...it is simple and obvious. Nobody - apart from those who want to start a scrap - is saying it IS INTEREST. That is irrelevant. Income is income (after tax etc).

I wasn't suggesting saying it is interest is a problem. But I DO have a problem in calling it income! Income - as one tax judge put it - is like the fruit from a tree. Income has the nature of regular recurrence. And that's where stochastic distributions come in because, as I said, it is possible (however unlikely) that you could hold your PBs for the rest of your life without ever getting a - let's call it neutrally - a "prize".

Prizes from PBs just do not feel like they are in the nature of income to me. Indeed, if the prizes were not specifically made exempt from tax, do they feel to you as if they should be taxable as income? They don't to me. And if they don't then surely something suggests they are distinguishable from being income.

But like the nature of art perhaps this is simply subjective and a quality determined by the observer. In which case call the prizes what you like. But I do think pyad is right here.

Eb.

GoSeigen
Lemon Quarter
Posts: 1616
Joined: November 8th, 2016, 11:14 pm
Has thanked: 378 times
Been thanked: 379 times

XFool, I also think you are barking up the wrong tree here, unfortunately. Perhaps you can think about it this way:

Imagine you take your most positive scenario: everyone who plays PBs buys the maximum they are allowed to hold and keeps them for ten years ; a similar size control group each buy the same amount of ten-year gilts. What is the difference? Well I identify two key differences, one of which you have acknowledged, the other which you have not:
1. The gilt investors get the same income each year for each of the ten years; practically all the premium bond holders get a different income each year. So far, common ground I think.
2. The gilt investors ALL get the same total income over the ten years. However the premium bond investors get varying amounts of total income over the ten years. Crucially, unless I am mistaken, the distribution of their incomes approximates a normal distribution (with a very strange tail for the big winners, but let's ignore that). I'm sure you're familiar with the normal and similar distributions. The bulk of people lie near the middle of this distribution and I think that is what is central in your mind. However, a significant number of people have winnings fairly far from the mean. [And remember the gilt investors ALL hit the mean exactly.] Many earn double the mean. Many earn half the mean. Many do even better or worse than this. As some have pointed out there are even people who win nothing over the entire ten years and others who earn a huge windfall.

So the point is this: how do you know where in that distribution you will be? The answer is you don't! Yes, you may be lucky and end up somewhere near the middle of the distribution, but many many people will be unlucky and earn far less, and some will earn rather more. This makes a nonsense of the concept of yield. If you know the yield of a gilt at purchase you know how much you will earn to maturity. You simply cannot make the same forecast with PBs, even if you own the maximum over a significant period.

HTH

GS

XFool
Lemon Quarter
Posts: 3597
Joined: November 8th, 2016, 7:21 pm
Been thanked: 216 times

Eboli wrote:XFool wrote:
...it is simple and obvious. Nobody - apart from those who want to start a scrap - is saying it IS INTEREST. That is irrelevant. Income is income (after tax etc).

I wasn't suggesting saying it is interest is a problem. But I DO have a problem in calling it income! Income - as one tax judge put it - is like the fruit from a tree. Income has the nature of regular recurrence.

It is "income" as far as I am concerned! Money is money. You may have your own private definition, but that is up to you. The normally accepted definition of income does not seem to require any mention of regularity: https://www.collinsdictionary.com/dicti ... ish/income

A person's or organization's income is the money that they earn or receive, as opposed to the money that they have to spend or pay out.

income in British
(ˈɪnkʌm , ˈɪnkəm )
noun
1. the amount of monetary or other returns, either earned or unearned, accruing over a given period of time

"or other returns"...

Eboli wrote: And that's where stochastic distributions come in because, as I said, it is possible (however unlikely) that you could hold your PBs for the rest of your life without ever getting a - let's call it neutrally - a "prize".

Again, how probable is that? I could be killed through being hit on the head by a falling meteor. Being hit by a car seems a lot more likely to me. Other opinions are (doubtless) available.

Eboli wrote:Prizes from PBs just do not feel like they are in the nature of income to me. Indeed, if the prizes were not specifically made exempt from tax, do they feel to you as if they should be taxable as income? They don't to me. And if they don't then surely something suggests they are distinguishable from being income.

Yes, as income(!) or winnings from a lottery they are presumably taxed as receipts from gambling which, in the UK are not subject to income tax. Why not?

Forbes

I feel you, and others, are still overlooking the distinction between the PB form of lottery and a normal straight lottery. Put up the refundable money one time to enter a monthly rolling lottery against pay once to enter once and either win a prize or lose your money forever. Which was always the point of PBs, from the start.

XFool
Lemon Quarter
Posts: 3597
Joined: November 8th, 2016, 7:21 pm
Been thanked: 216 times

GoSeigen wrote:XFool, I also think you are barking up the wrong tree here, unfortunately. Perhaps you can think about it this way:

Imagine you take your most positive scenario: everyone who plays PBs buys the maximum they are allowed to hold and keeps them for ten years ; a similar size control group each buy the same amount of ten-year gilts. What is the difference? Well I identify two key differences, one of which you have acknowledged, the other which you have not:
1. The gilt investors get the same income each year for each of the ten years; practically all the premium bond holders get a different income each year. So far, common ground I think.
2. The gilt investors ALL get the same total income over the ten years. However the premium bond investors get varying amounts of total income over the ten years. Crucially, unless I am mistaken, the distribution of their incomes approximates a normal distribution (with a very strange tail for the big winners, but let's ignore that). I'm sure you're familiar with the normal and similar distributions. The bulk of people lie near the middle of this distribution and I think that is what is central in your mind. However, a significant number of people have winnings fairly far from the mean. [And remember the gilt investors ALL hit the mean exactly.] Many earn double the mean. Many earn half the mean. Many do even better or worse than this. As some have pointed out there are even people who win nothing over the entire ten years and others who earn a huge windfall.

There are some who have claimed such, I just wonder what the actual figures are.*

GoSeigen wrote:So the point is this: how do you know where in that distribution you will be? The answer is you don't! Yes, you may be lucky and end up somewhere near the middle of the distribution, but many many people will be unlucky and earn far less, and some will earn rather more.

I don't think you are "lucky" if you are somewhere near the middle of the distribution, surely you are simply average? You are, IMO, "lucky" if you are at the high end of the distribution and unlucky to be at the low end.

So the interesting question is what is the variability and how do you calculate it? It isn't immediately easy to find out - apart from slogging with that Money Saving Expert calculator. About the time I was originally interested in PBs I bought John Haigh's 'Taking Chances' © First Addition 1999, precisely because he had a chapter on 'Football Pools, Premium Bonds'. It had some interesting detail but was a disappointment to me as he didn't address my question at the time: "What return can I expect?". I later realised this was trivially easy to work out if you knew the current odds and assumed any prize was going to be of the lowest value. The more complex matter of variability I left unanswered.

Haigh, in his book, discusses 'Averages and variability' in Appendix III and wrt Premium Bonds:

But on the Lottery, Pools or Premium Bonds, the reward variance is so large that these benchmarks will apply only to an enormous number of plays, more than one person will be exposed to in a lifetime. Here the benchmarks for the normal distribution cannot be used with any confidence, and you have to rely on exact calculation.

But I am unsure exactly what he means there.

More interesting stuff, but still doesn't answer the question:

From the above, Aaron Brown discusses Premium Bonds here:

I remember Gengulphus, on the old TMF Premium Bond forum, went into great detail on the probability of various returns (I think), possibly using a Poisson Distribution(?) but I cannot now find it on The Wayback Machine.

GoSeigen wrote:This makes a nonsense of the concept of yield.

Why? This is, if you will, trailing yield. It can fluctuate. Isn't this a criticism you could make on dividends from shares? OK, over more than one year, as presumably the yield for one year is known in advance. But then, with shares, there is more risk - what if your company goes bust and you lose both the income and the capital?

Anyway, with PBs, looking forward I usual describe this as 'expected yield', seems fair enough to me.

GoSeigen wrote:If you know the yield of a gilt at purchase you know how much you will earn to maturity. You simply cannot make the same forecast with PBs, even if you own the maximum over a significant period.

So, if you require a fixed, known in advance, regular income, buy a gilt or other fixed rate bond (risks?) not PBs, or shares. Horses for courses.

* Quoting from John Haigh's book again - albeit with a different prize structure and odds to today:

Suppose 100,000 people who held the maximum in July 1997 retained their bonds for a year. Each can expect to win 12.6 prizes, on average, and the single most likely outcome is 12 prizes. But about four or five of them would win no more than one prize over the whole twelvemonth, and about the same number would find at least 29 cheques dropping on the doormat.

GoSeigen
Lemon Quarter
Posts: 1616
Joined: November 8th, 2016, 11:14 pm
Has thanked: 378 times
Been thanked: 379 times

XFool wrote:
GoSeigen wrote:Many earn double the mean. Many earn half the mean. Many do even better or worse than this. As some have pointed out there are even people who win nothing over the entire ten years and others who earn a huge windfall.

There are some who have claimed such, I just wonder what the actual figures are.*

Anyone can work it out with some reasonable assumptions and GCSE maths. Read about the Normal approximation of the Binomial Distribution. Plug in some figures and you should get an answer. Sorry, don't have enough time or interest to do it myself.

GoSeigen wrote:So the point is this: how do you know where in that distribution you will be? The answer is you don't! Yes, you may be lucky and end up somewhere near the middle of the distribution, but many many people will be unlucky and earn far less, and some will earn rather more.

I don't think you are "lucky" if you are somewhere near the middle of the distribution, surely you are simply average? You are, IMO, "lucky" if you are at the high end of the distribution and unlucky to be at the low end.

Don't want to argue semantics, but I was using "lucky" in a more neutral sense of income received "not as of right but through chance". If I were to do premium bonds I'd start with the assumption that I'd get nothing, and any much better outcome would be "lucky" -- but I don't mind if others think about it differently.

So the interesting question is what is the variability and how do you calculate it?

[...]

I remember Gengulphus, on the old TMF Premium Bond forum, went into great detail on the probability of various returns (I think), possibly using a Poisson Distribution(?) but I cannot now find it on The Wayback Machine.

See above. If you want to get Gengulphus to repeat his explanation, try cunningly disguising it as a puzzle and post on the "Games, Puzzles and Riddles" board.

GoSeigen wrote:This makes a nonsense of the concept of yield.

Why? This is, if you will, trailing yield.

Of course, trailing yield is always easy, but not interesting! It is yield to maturity that gets the bond investor's juices going. If you're not sure why, it might help to have a look at the maths of bond pricing.

It can fluctuate. Isn't this a criticism you could make on dividends from shares?

[...]

Anyway, with PBs, looking forward I usual describe this as 'expected yield', seems fair enough to me.

Agree with the last point. Re. the question: yes and no. Shares are a bit different. The income from them (i.e. dividend) is far more steady then PB prizes. Quite apart from anything, the shareholders control the directors so theoretically can dictate the dividend policy. PB holders can't do the same with the prizes! With shares it is the market price that varies hugely. So completely different beasts to premium bonds. [Aside: per my point 2, all shareholders have equal income; PB buyers don't.]

GoSeigen wrote:If you know the yield of a gilt at purchase you know how much you will earn to maturity. You simply cannot make the same forecast with PBs, even if you own the maximum over a significant period.

So, if you require a fixed, known in advance, regular income, buy a gilt or other fixed rate bond (risks?) not PBs, or shares. Horses for courses.

Absolutely, but if you are looking for ways to earn an income recognise the unpredictability (chance/luck) of PB income. Also, recognise that you are receiving close to instant-access rates but committing to a long holding period with the aim of "smoothing out returns". I'm sure there are people for whom these are suitable, but I'd bet that the vast majority are short-changing themselves in purely financial terms (i.e. ignoring entertainment value).

* Quoting from John Haigh's book again - albeit with a different prize structure and odds to today:

Suppose 100,000 people who held the maximum in July 1997 retained their bonds for a year. Each can expect to win 12.6 prizes, on average, and the single most likely outcome is 12 prizes. But about four or five of them would win no more than one prize over the whole twelvemonth, and about the same number would find at least 29 cheques dropping on the doormat.

Those are good figures; note though that they refer to a time when payout rates were significantly higher; to account for the entire £60bn invested in 2016 you need to scale the number of holders to 1.2m; and the author's chosen "poor" outcome of winning one prize is 8% of the mean where my "many many" guess referred to half the mean. I think many are disappointed at poor returns (and yes a smaller "many" pleased at better-than-expected returns).

Sorry, post may be rough as hurrying out...

GS