Premium Bonds: Are they worth it? Discussion Area

Dan29

casca wrote:

Can someone please explain how the calculation of winning the lottery is 1 in 14 million? By my calculation, 49^6 = +- 13.8 billion.

Also, if the odds were 1 in 14 million, all I'd need to do is wait for the prize to go above £14m and I'd be a guaranteed winner.

See page 2 of this document.

Rustylino

All I know is that I have doen the lottery since inception and have the same numbers each week and have won no more that 30pounds - Investing in Premium Bonds I have won over a thousand pounds on an initial investment of approx 600pounds. Of course you don't have premium bonds to make a quick buck but I think despite all the nerdy stuff they are a good bet.

:whistle:

whambamboo

Martin really should be ashamed of his article - the stuff at the end is statistically illiterate, by excluding some of the prizes to make some meaningless partial return %. Premium bonds are just fine: they are not supposed to be as dull as dishwater - you get your £50 'winnings' in lieu of interest, and it's more interesting than a bank statement, and there's nothing wrong with that as a bit of fun for people. No, it's not better than the best savings account unless you're a higher rate tax payer, but it's an instant access way to hold cash, and if people want to gamble, they'd better off with this than the lottery: £100 of premium bonds returns on average £103. The lottery returns £50.

Enough said.

The lottery is an awful awful gamble with a 50% return.

whambamboo

As I said, the article is mathematically illiterate.

Here is a better way of looking at it:

If you have £1000 of premium bonds, and already have a cash ISA, then you could earn with Icebank's 5.2% (which is the best on the market: in practice most people are earning less than this, making premium bonds relatively more attractive):

non-tax payer: £52/year
basic-rate tax payer: £41.60/year
higher-rate tax payer: £31.20/year

You are gambling with this lost interest in effect, as you keep the £1,000, but don't get any interest.

The expected return on premium bonds is 3.15% tax-free, for all tax payers, so you expect to make £31.50/year.

Effectively you are then buying

£52,
£41.60, or
£31.20
of Premium Bond 'lottery' tickets,

with an expected return of £31.50.

Therefore your conceptual lottery tickets are returning:

60.6% for non-tax payers (cf. the lottery, paying 50%)
75.7% for basic-rate tax payers
100.96% for higher-rate tax payers

So overall premium bonds represent a gamble
holding £100 of
£5.20/£4.60/£3.12
holding £1000 of
£52/£41.60/£31.20
holding £10000 of
£520/£416/£312
holding £30000 of
£1160/£1248/£936

in each case returning
60.6%/75.7%/100.96%

Now if this was Las Vegas the first two numbers would be very poor (although the key with Vegas is the re-betting of money: a slot machine might return 90%, but typically a player will bet the same $10 over and over again, so the return actually works out a lot lower than the 90%, because you have actually wagered say $50, by re-betting the pay-offs, and the return is then 90% of $50, i.e. $45, which means you lost half your initial $10 - so a better comparison is the 50% paying lottery, where you lose your stake and don't rebet it), but the 100.96% would have people queueing up to play.

So the question really is, 'do you want to gamble with your interest?', and 'are you happy with the return that gamble is providing?'.

Don't think of it as an investment, it's a GAMBLE, and for the specific value of your interest. Just like the lottery, but with better payout rates (and for higher rate tax payers it's a rare gamble biased in favour of the player). If you like gambling, good, but don't put out intellectually diminished articles like the one that started this thread: it's not an investment, it's a means of gambling with interest. You could achieve a similar effect by depositing money into an online casino..

By its very nature gambling has variance: some people win less than the mean, some more.

panlane

Good post but I'm not sure about the upped hostility. Took a few readings to follow you through, but I agree with the thrust of it. I think what Martin was trying to do was express the aggregated quality of the winnings and their consequent effect on winnings in such a way as those unfamiliar with statistics could comprehend. The problem was he fell into the dumbing-down trap. You can't shave off the probabilities when the potential gains hinge on fractions of a percent.

Perhaps it would be best illustrated with four pretend case studies where people had large sums over short times, large sums over long times, small sums over short times and small sums over long times. These would then show how their winnings homed in on the predicted mean return. Alternately, it wouldn't be too hard to create a macro that ran a random winning walk of a specified sum over time. A simple line graph of your future winnings (whilst all hypothetical) would no doubt intrigue and educate many.

MSE_Martin

Whambamboo

I've read your points - and ignoring the unnecessary insults and slightly struggling to see where you disagree with what was written.

You say

1. Premium bonds are a good bet for higher rate taxpayer, I agree, so does the article
2. Premium bonds are a better gamble with your interest than the lottery, I agree so does the article.

So what exactly are you objecting to?

Martin

dealsearcher

I have had £40,000 invested for my wife and I over the last 12 years. I keep a record of all of my winnings and the average rate of return has been 3.33%. That is about 1.5% down on what I would have got in a savings account over those 12 years. This would be my maximum loss, without considering high risk investments. However there has been a statistical chance that I could have gained considerably more money. Futhermore the winnings every month are a certainty for someone out there, wheras the lottery may not be won by anyone if no one picks the correct numbers.

Premium bonds are also good for people with a large amount of savings where their total interest for the year may exceed their annual tax allowance. If that were the case for me then 3.33% after tax is actually quite good, as that is all I could have expected with a savings account for interest that exceeded my annual tax allowance.

whambamboo

MSE_Martin wrote:

Whambamboo

I've read your points - and ignoring the unnecessary insults and slightly struggling to see where you disagree with what was written.

You say

1. Premium bonds are a good bet for higher rate taxpayer, I agree, so does the article
2. Premium bonds are a better gamble with your interest than the lottery, I agree so does the article.

So what exactly are you objecting to?

Martin

I am sorry for the insults.

However, I don't think it's fair to write off premium bonds as much as you do.

They have an average rate of return for non-higher rate tax payers, but are still better than the lottery. If people want to gamble it is normal to pay a premium for this. As a gamble premium bonds are perfectly reasonable fun thing to do, and a non-tax payer with £1000 would still be better off buying £1000 of premium bonds than buying a lottery ticket every week, and would have a higher return than the lottery ticket buyer.

You might as well tell people they shouldn't play bingo.

And regarding the second section of the article, the compounding argument is misleading, as is the concept of a mean that excludes part of the return.

It can be easily seen to be so by simplifying the maths. Imagine a conceptual £10,000 bond that pays out 3%. This would return £300/year on average.
,
Again imagine this is made up of one £3,000,000 prize, once per year and no smaller prizes.

This is similar to premium bonds.

The odds are then 10,000 - 1.

Your £3m prize is withdrawn and invested in a 3% net savings account.

So after 1 year:

9,999 people have £10,000
1 person has £3,010,000

After 2 years, the winner sells his stake, and a new player buys in:

9,999 people have £10,000
1 person has £3,010,000 + 3% interest = £3,100,300
1 person has £3,010,000
+ £300 interest on the new player's £10,000 from a previous year in a normal savings account

After 3 years, the second winner sells up, a new player buys in:

9,999 people have £10,000
1 person has £3,010,000 * 1.03 * 1.03 = £3,193,309
1 person has £3,010,000 + 3% interest = £3,100,300
1 person has £3,010,000
+ £300 interest on the player who joined in year 2, + £609 for the player joining this year.

So after 3 years there are 10,002 people involved and the total sum in circulation is:

9999 * £10,000 + £300 + £609 + £3,193,309 + £3,100,300 + £3,010,000

=
£109,294,518

The average wealth of the initial players is then £10,927.27

If they had invested in a savings account at 3%, then it would be £10,000 * 1.03^3 = £10,927.27

So the result is EXACTLY THE SAME.

So this statement is misleading:

"Yet as you're very unlikely to earn the true interest rate, each year you fall behind, as the smaller growth means and the fact that with the prize distribution this is likely to continue over time, means overtime it's likely he would fall further and further behind."

in fact on *average* the compound return is absolutely identical (or in fact a little higher for a higher rate tax payer, and if you do win, it exactly makes up for any previous loss of return: the implication that by holding premium bonds longer you are falling further and further behind is incorrect - on AVERAGE holding £100 of premium bonds for 10 years will return EXACTLY the same as £100 in an equal paying investment account.

And I assume the reason people buy premium bonds is because they want a chance to win, not because they want to discount the biggest prizes on the basiss that they are unlikely to win.

It is a zero sum game, and premium bonds work out just the same as anything else in terms of compound return.

I think the article should concentrate more on premium bonds as a gamble with your interest and emphasise the amount that you are gambling (viz. your interest), and the effective return on that gamble, rather than trying to make it out as a dull 'investment' by excluding the big wins.

MSE_Martin

Thanks for your kind reply WBB

I'm afraid I disagree with your on a number of basis.

Firstly the article is about not using Premium Bonds (excluding high rate taxpayers) as a main stay place of your savings - however I do say 'if you're looking for a place to put non-significant cash for a bit of a flutter it's fine'.

Also one of the explicit points you make is comparing the returns to normal rather than best buy savings accounts. Well I don't do that - people simply shouldn't have money in poor accounts - that goes against the entire philosophy of MoneySaving and what I do. Thus comparing it against the markets best is the only way I can do it.

As for your point about the final analysis. I did consider going through the median and modal averages to express the realistic outcomes that way - but in the end decided it was simpler to explain by simply excluding the most unlikely (and in fact in many ways negligible) outcomes and coming up with a rate that way.

We live in a society where 100,000 people apply for X-Factor all of them knowing "I'm going to win" - sometimes you have to moderate expectations if you want people to plan sensibly.

Martin

roswell

MSE_Martin wrote:

Also one of the explicit points you make is comparing the returns to normal rather than best buy savings accounts. Well I don't do that - people simply shouldn't have money in poor accounts - that goes against the entire philosophy of MoneySaving and what I do. Thus comparing it against the markets best is the only way I can do it.

Sorry But i must take exception to that comment, yes best buy is best but not everyone will have best buy, if your talking average luck then its average everything... Its like saying a disposable camera takes a average photo and a top DSLR take an exceptional photo. you are not talking of the top 1 % of the population but an average proporttion with average income and average knowledge of financial products. There for average everthing.