Is it still worth having any Premium Bonds?

badger09

gravel_2 said:

subjecttocontract said:

I'm only aware of the rate published by NS&I which is currently 4.4%.....where does your 'headline' rate come from ?

Worth looking here to see the average/expected return for your holding: https://premiumbondsprizes.com/#0

4.4% is the total amount paid out by NS&I on the aggregate amount held in PBs by all holders. But if consider a full holder winning £1m, that's a 2000% return in a month. £100k winning is 200%. These big pay outs erode the overall average annual pay out a normal punter with normal luck should hope to receive. If you make on average 4.4% from PBs you actually have quite good luck.

PBs have a place, especially for higher tax payers but saying "premium bonds pay an average 4.4%" is not helpful particularly to those reading about PBs without having any other understanding of them.

I wish I hadn’t followed that link. With my holding, my ‘Jackpot chance of winning £1000,000 over a year’ is 1 in 287,279,092. I’d be happy with a single £25 (in over 50 years). 

Do I feel lucky🤔

zagfles

nic_c said:

zagfles said:

nic_c said:

zagfles said:

arfster said:

subjecttocontract said:

Premium bonds pay an average 4.4% but it's tax free so a 20% basic rate tax payer would need 5.5% and a higher rate payer 7.3% before tax to get the same return. Those are the numbers that make them worthwhile once you have maxed out ISAs.

Those averages are highly skewed by the top prizes though. Median for 10k is 3.5%, for example.

I wouldn't say they're "highly" skewed, 80% of the prize fund is small prizes (£100 or less). The median will be higher the longer you hold them, the 3.5% is based on not winning anything other than small prizes, with £10k you should win a bigger prize every 13 years or so on average so if you hold them that long the median will be higher. 

Do you know what the definition of median is?
From Wikipedia

Err, yes, I know the definition of median. From my A level maths, not wikipedia. Actually it was probably O level. 

The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the "middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center.

The median is taking what everyone with that holding could expect to win (even £0) listing them in order and giving the middle value. So the 3.5% is not "based on not winning anything other than small prizes".

Yes it is. The median person with a £10k holding over a year would not win a medium or big prize. That's exactly what the 3.5% is based on.

From How we share out Premium Bonds prizes (nsandi.com) 

Based on June draw there are 5,864,452 prizes and 1 in 21,000 chance of winning a prize. Therefore there are 123,153 million total held in PBs, to the nearest million. 

There are 75,447 medium plus high value prizes. So the chance of someone with a £10k holding winning a medium or high prize in a year is 10000*12*75447/123,153,000,000 = 7.35%, ie about 1 in 13.5. So the median person with a £10k holding would not win a medium or big prize. Anyone who did win a medium or big prize would get a return of at least 5% and so be way above the median person. 

On average they'd win 2.1 £100 prizes, 2.1 £50s and 1.4 £25. That's £350, ie 3.5%. Obviously they aren't going to win fractions of a prize but with such a massive sample the median person would win some combination that added up to £350, eg 3 £100's and a £50, or 2 £100's, 2 £50's and 2 £25s etc. 

But that's over a year. The equation change over longer periods. Someone with a £10k holding for 10 years, assuming the same prize distribution, would have a >50% chance of winning a £500 prize in that period. So the median person will win a £500 prize. So that would bump up the return of the median person to about 4% pa. 

It's exactly the same equation as someone with a £50k holding for 2 years. The same number of entries into the prize draw, so the same median return. So it's meaningless saying "the median return for a x holding is y", without specifying the period of the holding. The median return for a £10k holding over 5 years is identical to the median return for a £50k holding over a year. Subject to prize rate changes obviously. 

The median "person" wouldn't win a medium or big prize over the year, so that's why it's 3.5%. Clearly whether you were taught about statistics at either O level or A level, you clearly did not understand it properly. The median does include all prizes, because it's based on what everyone who hold £10K in bonds wins and some possibly could win a big prize, just as there's a possibility of winning nothing. Most will win around 4 times in a year with £10K, but some will win more/less often.

Take the June 2024 draw, 35 people with a holding of exactly £10,000 won a prize of £5000 or more, including 2 who won £100,000. 

Yeah, but none of those 35 people will be the median person, will they? "The median is taking what everyone with that holding could expect to win (even £0) listing them in order and giving the middle value." You got that bit right. So, if if helps picture every £10k holder lined up in order of their winnings. Got that?

The 35 are going to be right at the front. They're not going to be the one in the middle. In fact everyone who won a big or medium prize will be near the front. The person in the middle won't have won a big prize. Geddit? 

Tell you what, I've shown my working to get the 3.5% result you quoted, let's see yours. If you think I'm wrong. 

Specifying the period, !!!!!!! When you talk about interest percentages it's always based on over a year otherwise how do you compare products. If you took out a 5 year fixed bond at 4.5% you'd earn just over £2460 in interest, but you don't start saying the median return is 24.6%

OMG. Do you know what pa means? I gave the annual return, not the total!

zagfles

badger09 said:

gravel_2 said:

subjecttocontract said:

I'm only aware of the rate published by NS&I which is currently 4.4%.....where does your 'headline' rate come from ?

Worth looking here to see the average/expected return for your holding: https://premiumbondsprizes.com/#0

4.4% is the total amount paid out by NS&I on the aggregate amount held in PBs by all holders. But if consider a full holder winning £1m, that's a 2000% return in a month. £100k winning is 200%. These big pay outs erode the overall average annual pay out a normal punter with normal luck should hope to receive. If you make on average 4.4% from PBs you actually have quite good luck.

PBs have a place, especially for higher tax payers but saying "premium bonds pay an average 4.4%" is not helpful particularly to those reading about PBs without having any other understanding of them.

I wish I hadn’t followed that link. With my holding, my ‘Jackpot chance of winning £1000,000 over a year’ is 1 in 287,279,092. I’d be happy with a single £25 (in over 50 years). 

Do I feel lucky🤔

Even on the full £50k the chance of winning the jackpot is miniscule, less than 1 in a million every draw. 

Albermarle

zagfles said:

badger09 said:

gravel_2 said:

subjecttocontract said:

I'm only aware of the rate published by NS&I which is currently 4.4%.....where does your 'headline' rate come from ?

Worth looking here to see the average/expected return for your holding: https://premiumbondsprizes.com/#0

4.4% is the total amount paid out by NS&I on the aggregate amount held in PBs by all holders. But if consider a full holder winning £1m, that's a 2000% return in a month. £100k winning is 200%. These big pay outs erode the overall average annual pay out a normal punter with normal luck should hope to receive. If you make on average 4.4% from PBs you actually have quite good luck.

PBs have a place, especially for higher tax payers but saying "premium bonds pay an average 4.4%" is not helpful particularly to those reading about PBs without having any other understanding of them.

I wish I hadn’t followed that link. With my holding, my ‘Jackpot chance of winning £1000,000 over a year’ is 1 in 287,279,092. I’d be happy with a single £25 (in over 50 years). 

Do I feel lucky🤔

Even on the full £50k the chance of winning the jackpot is miniscule, less than 1 in a million every draw. 

Or to put it another way. With the full £50K in bonds, you can expect on average to win a Million Pound prize every 43,000 years.

PixelPound

zagfles said:

nic_c said:

zagfles said:

nic_c said:

zagfles said:

arfster said:

subjecttocontract said:

Premium bonds pay an average 4.4% but it's tax free so a 20% basic rate tax payer would need 5.5% and a higher rate payer 7.3% before tax to get the same return. Those are the numbers that make them worthwhile once you have maxed out ISAs.

Those averages are highly skewed by the top prizes though. Median for 10k is 3.5%, for example.

I wouldn't say they're "highly" skewed, 80% of the prize fund is small prizes (£100 or less). The median will be higher the longer you hold them, the 3.5% is based on not winning anything other than small prizes, with £10k you should win a bigger prize every 13 years or so on average so if you hold them that long the median will be higher. 

Do you know what the definition of median is?
From Wikipedia

Err, yes, I know the definition of median. From my A level maths, not wikipedia. Actually it was probably O level. 

The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the "middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center.

The median is taking what everyone with that holding could expect to win (even £0) listing them in order and giving the middle value. So the 3.5% is not "based on not winning anything other than small prizes".

Yes it is. The median person with a £10k holding over a year would not win a medium or big prize. That's exactly what the 3.5% is based on.

From How we share out Premium Bonds prizes (nsandi.com) 

Based on June draw there are 5,864,452 prizes and 1 in 21,000 chance of winning a prize. Therefore there are 123,153 million total held in PBs, to the nearest million. 

There are 75,447 medium plus high value prizes. So the chance of someone with a £10k holding winning a medium or high prize in a year is 10000*12*75447/123,153,000,000 = 7.35%, ie about 1 in 13.5. So the median person with a £10k holding would not win a medium or big prize. Anyone who did win a medium or big prize would get a return of at least 5% and so be way above the median person. 

On average they'd win 2.1 £100 prizes, 2.1 £50s and 1.4 £25. That's £350, ie 3.5%. Obviously they aren't going to win fractions of a prize but with such a massive sample the median person would win some combination that added up to £350, eg 3 £100's and a £50, or 2 £100's, 2 £50's and 2 £25s etc. 

But that's over a year. The equation change over longer periods. Someone with a £10k holding for 10 years, assuming the same prize distribution, would have a >50% chance of winning a £500 prize in that period. So the median person will win a £500 prize. So that would bump up the return of the median person to about 4% pa. 

It's exactly the same equation as someone with a £50k holding for 2 years. The same number of entries into the prize draw, so the same median return. So it's meaningless saying "the median return for a x holding is y", without specifying the period of the holding. The median return for a £10k holding over 5 years is identical to the median return for a £50k holding over a year. Subject to prize rate changes obviously. 

The median "person" wouldn't win a medium or big prize over the year, so that's why it's 3.5%. Clearly whether you were taught about statistics at either O level or A level, you clearly did not understand it properly. The median does include all prizes, because it's based on what everyone who hold £10K in bonds wins and some possibly could win a big prize, just as there's a possibility of winning nothing. Most will win around 4 times in a year with £10K, but some will win more/less often.

Take the June 2024 draw, 35 people with a holding of exactly £10,000 won a prize of £5000 or more, including 2 who won £100,000. 

Yeah, but none of those 35 people will be the median person, will they? "The median is taking what everyone with that holding could expect to win (even £0) listing them in order and giving the middle value." You got that bit right. So, if if helps picture every £10k holder lined up in order of their winnings. Got that?

The 35 are going to be right at the front. They're not going to be the one in the middle. In fact everyone who won a big or medium prize will be near the front. The person in the middle won't have won a big prize. Geddit? 

Tell you what, I've shown my working to get the 3.5% result you quoted, let's see yours. If you think I'm wrong. 

Specifying the period, !!!!!!! When you talk about interest percentages it's always based on over a year otherwise how do you compare products. If you took out a 5 year fixed bond at 4.5% you'd earn just over £2460 in interest, but you don't start saying the median return is 24.6%

OMG. Do you know what pa means? I gave the annual return, not the total!

Someone who wins £350 on a £10k holding clearly does not win a big prize but you can't say that the median of 3.5% is the rate for small prizes only, because otherwise what's the rate for £10K including all prizes?

PixelPound

badger09 said:

gravel_2 said:

subjecttocontract said:

I'm only aware of the rate published by NS&I which is currently 4.4%.....where does your 'headline' rate come from ?

Worth looking here to see the average/expected return for your holding: https://premiumbondsprizes.com/#0

4.4% is the total amount paid out by NS&I on the aggregate amount held in PBs by all holders. But if consider a full holder winning £1m, that's a 2000% return in a month. £100k winning is 200%. These big pay outs erode the overall average annual pay out a normal punter with normal luck should hope to receive. If you make on average 4.4% from PBs you actually have quite good luck.

PBs have a place, especially for higher tax payers but saying "premium bonds pay an average 4.4%" is not helpful particularly to those reading about PBs without having any other understanding of them.

I wish I hadn’t followed that link. With my holding, my ‘Jackpot chance of winning £1000,000 over a year’ is 1 in 287,279,092. I’d be happy with a single £25 (in over 50 years). 

Do I feel lucky🤔

Does that mean your total holing is £18?

FlorayG

Gosh I've started a maths argument  
Anyway thank you all. I kind of like the chance element and if I buy £100 a month that's only missing out on a potential £60 a year I can take that. Plus it's a good savings account, even though it pays no interest, because your money is accessible but not instantly, which will make me more circumspect about withdrawing it and spending it. I think the decider is - are you wanting the best possible return or are you willing to take a risk? And at least the money isn't lost as it is on the lottery.

zagfles

nic_c said:

zagfles said:

nic_c said:

zagfles said:

nic_c said:

zagfles said:

arfster said:

subjecttocontract said:

Premium bonds pay an average 4.4% but it's tax free so a 20% basic rate tax payer would need 5.5% and a higher rate payer 7.3% before tax to get the same return. Those are the numbers that make them worthwhile once you have maxed out ISAs.

Those averages are highly skewed by the top prizes though. Median for 10k is 3.5%, for example.

I wouldn't say they're "highly" skewed, 80% of the prize fund is small prizes (£100 or less). The median will be higher the longer you hold them, the 3.5% is based on not winning anything other than small prizes, with £10k you should win a bigger prize every 13 years or so on average so if you hold them that long the median will be higher. 

Do you know what the definition of median is?
From Wikipedia

Err, yes, I know the definition of median. From my A level maths, not wikipedia. Actually it was probably O level. 

The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the "middle" value. The basic feature of the median in describing data compared to the mean is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center.

The median is taking what everyone with that holding could expect to win (even £0) listing them in order and giving the middle value. So the 3.5% is not "based on not winning anything other than small prizes".

Yes it is. The median person with a £10k holding over a year would not win a medium or big prize. That's exactly what the 3.5% is based on.

From How we share out Premium Bonds prizes (nsandi.com) 

Based on June draw there are 5,864,452 prizes and 1 in 21,000 chance of winning a prize. Therefore there are 123,153 million total held in PBs, to the nearest million. 

There are 75,447 medium plus high value prizes. So the chance of someone with a £10k holding winning a medium or high prize in a year is 10000*12*75447/123,153,000,000 = 7.35%, ie about 1 in 13.5. So the median person with a £10k holding would not win a medium or big prize. Anyone who did win a medium or big prize would get a return of at least 5% and so be way above the median person. 

On average they'd win 2.1 £100 prizes, 2.1 £50s and 1.4 £25. That's £350, ie 3.5%. Obviously they aren't going to win fractions of a prize but with such a massive sample the median person would win some combination that added up to £350, eg 3 £100's and a £50, or 2 £100's, 2 £50's and 2 £25s etc. 

But that's over a year. The equation change over longer periods. Someone with a £10k holding for 10 years, assuming the same prize distribution, would have a >50% chance of winning a £500 prize in that period. So the median person will win a £500 prize. So that would bump up the return of the median person to about 4% pa. 

It's exactly the same equation as someone with a £50k holding for 2 years. The same number of entries into the prize draw, so the same median return. So it's meaningless saying "the median return for a x holding is y", without specifying the period of the holding. The median return for a £10k holding over 5 years is identical to the median return for a £50k holding over a year. Subject to prize rate changes obviously. 

The median "person" wouldn't win a medium or big prize over the year, so that's why it's 3.5%. Clearly whether you were taught about statistics at either O level or A level, you clearly did not understand it properly. The median does include all prizes, because it's based on what everyone who hold £10K in bonds wins and some possibly could win a big prize, just as there's a possibility of winning nothing. Most will win around 4 times in a year with £10K, but some will win more/less often.

Take the June 2024 draw, 35 people with a holding of exactly £10,000 won a prize of £5000 or more, including 2 who won £100,000. 

Yeah, but none of those 35 people will be the median person, will they? "The median is taking what everyone with that holding could expect to win (even £0) listing them in order and giving the middle value." You got that bit right. So, if if helps picture every £10k holder lined up in order of their winnings. Got that?

The 35 are going to be right at the front. They're not going to be the one in the middle. In fact everyone who won a big or medium prize will be near the front. The person in the middle won't have won a big prize. Geddit? 

Tell you what, I've shown my working to get the 3.5% result you quoted, let's see yours. If you think I'm wrong. 

Specifying the period, !!!!!!! When you talk about interest percentages it's always based on over a year otherwise how do you compare products. If you took out a 5 year fixed bond at 4.5% you'd earn just over £2460 in interest, but you don't start saying the median return is 24.6%

OMG. Do you know what pa means? I gave the annual return, not the total!

Someone who wins £350 on a £10k holding clearly does not win a big prize but you can't say that the median of 3.5% is the rate for small prizes only, because otherwise what's the rate for £10K including all prizes?

It's not "the rate for small prizes", it just doesn't include any big prizes because the median person doesn't win any!! So the median person's wins just consist of small prizes. For £10k for one year anyway. Therefore the value of the big prizes does not affect the median.

The average (mean) return for everyone is 4.4%, that's the total prize pot divided by the total invested. But some people say that's misleading because it's skewed by a few high wins. So they think the median is a better guide to how much you're likely to win. The median will get closer to the mean the more prize draws you're in, which is your investment times the number of months you hold them for. You need about a million for the median to include big or medium prizes. £50k for 2 years or £10k for 10 years is 1.2 million prize draws. 

zagfles

FlorayG said:

Gosh I've started a maths argument  
Anyway thank you all. I kind of like the chance element and if I buy £100 a month that's only missing out on a potential £60 a year I can take that. Plus it's a good savings account, even though it pays no interest, because your money is accessible but not instantly, which will make me more circumspect about withdrawing it and spending it. I think the decider is - are you wanting the best possible return or are you willing to take a risk? And at least the money isn't lost as it is on the lottery.

it's similar to the lottery if you think of it as gambling the interest, eg putting £10k into a savings account and spending the interest on lottery tickets. IIRC the lottery is more skewed to bigger prizes, so you're more likely to win a million that way, but the median return will be less (and poss tax on the bank interest). 

subjecttocontract

Most people are loosing at best a few hundred quid in interest with premium bonds in exchange for a chance of winning more. I have a neighbour who spends hundreds of pounds on scratch cards and wins virtually nothing. It's whatever rocks your boat. It's called fun, remember that ?