£40K sitting in non-interest bearing account

2

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  • kidmugsy
    kidmugsy Posts: 12,709
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    Premium Bonds may give you some small prizes, or some large ones, or even the top prize but, equally, you may get nothing

    Once you've got £40k-£50k invested you can expect a roughly steady stream of small monthly prizes, a tax-free 1.20 -1.25% p.a.

    The prize fund pays out 1.4% p.a. so the other 0.15% or so goes on the bigger prizes. The chance of the OP winning one is remote.
    Free the dunston one next time too.
  • Terry_Towelling
    Terry_Towelling Posts: 2,279
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    kidmugsy wrote: »
    Once you've got £40k-£50k invested you can expect a roughly steady stream of small monthly prizes, a tax-free 1.20 -1.25% p.a.

    The prize fund pays out 1.4% p.a. so the other 0.15% or so goes on the bigger prizes. The chance of the OP winning one is remote.

    There is that word again - 'Expect'. Long ago, when £20K was the max and then £30K and the prize fund rate was higher, I had the full quota of bonds. I got a reasonable number of small wins (£50 min in those days) and a couple of slightly bigger ones over the course of 12 months and then they just stopped coming over the second year. Eventually I got fed up and cashed them all in.

    Many people have reported this phenomenon of early wins and then nothing. If there is no 'fix' in the Bonds system (surely not) then this just goes to show that 'probability' (or 'expectation' if you prefer) and 'chance' are different animals and you just cannot rely on them unless you have above average luck - there's another one of those words, 'luck'; some people have it, some people don't: that's the nature of the beast.

    Another thing about averages is that it is sometimes rare for the average to ever occur. Often there is a considerable spread above and below but nothing on the average. Bonds will be no different and some people will get much more than expected and others will get less.

    Thinking about it, 1.25% (if you get it) isn't so bad but it isn't as good as a guaranteed 1.3% easy access account or a 1.66% notice account. Perhaps the only benefit then is if your interest will be taxable then a Bond win would be preferable because it attracts no taxation.
  • eskbanker
    eskbanker Posts: 30,400
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    Another thing about averages is that it is sometimes rare for the average to ever occur. Often there is a considerable spread above and below but nothing on the average.
    ....which gives me the chance to wheel out my favourite example of the quirks of averages, namely that the average human being has almost exactly one breast and one testicle (and most wouldn't be mad keen on meeting that in a club!)

    And of course the vast majority of the human race has an above-average number of legs, as very few have exactly 1.99999999999999 :)

    However, picking up on kidmugsy's point, a maximum holding for a significant period of time will naturally tend towards the (mean) average return, whereas smaller holdings, or smaller time periods, will intrinsically involve more volatile returns. If I could remember enough from my stats course from many moons ago, the answer will involve standard deviation....
  • Terry_Towelling
    Terry_Towelling Posts: 2,279
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    eskbanker wrote: »
    ....which gives me the chance to wheel out my favourite example of the quirks of averages, namely that the average human being has almost exactly one breast and one testicle (and most wouldn't be mad keen on meeting that in a club!)

    And of course the vast majority of the human race has an above-average number of legs, as very few have exactly 1.99999999999999 :)

    However, picking up on kidmugsy's point, a maximum holding for a significant period of time will naturally tend towards the (mean) average return, whereas smaller holdings, or smaller time periods, will intrinsically involve more volatile returns. If I could remember enough from my stats course from many moons ago, the answer will involve standard deviation....


    I think I met that person when I was at college!

    I can't remember (and haven't looked it up) but doesn't the premium bonds website suggest that people with average luck and the maximum holding should expect to win 12 or 13 prizes a year? (I think that applied in the days of the £30K max holding). Perhaps it should also say that such expectation is most likely to be observed in the longer term - i.e after several years (as you stated, Eskbanker). Is it perhaps a little improper of NS&I to suggest it is likely from the outset? (if it still does, that is).
  • DrEskimo
    DrEskimo Posts: 2,337
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    eskbanker wrote: »
    If I could remember enough from my stats course from many moons ago, the answer will involve standard deviation....

    As a statistician, I am more than happy to bore you with a deeper explanation of a standard deviation...

    But yes you are spot on. The standard deviation will give you a good idea of the spread of the data around the mean. Assuming the data follows a Gaussian distribution (so called 'normal' or 'bell-curve'), approximately 2 S.Ds above and below the mean will include approximately 95% of all your data points.
  • DrEskimo
    DrEskimo Posts: 2,337
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    edited 4 July 2018 at 11:23PM
    Premium Bonds may give you some small prizes, or some large ones, or even the top prize but, equally, you may get nothing and you don't get anything until they've been invested for a full month. Probability and chance are separate things. Statistical Probability says you may expect to get X% in return but chance says you could get something or nothing at all.

    Sorry to be pedantic, but it almost certainly is not equally likely...With any given holding over any given time frame the probability of getting a none, a small or a large prize is certainly not equal. On a large holding (say £50k), it's highly likely that any given month you will win a small amount, very unlikely you will win nothing, and extremely unlikely you will win any big prizes.
    Likewise, with a small holding, it's highly likely you will see no winnings, a small chance of a small prize, and again an extremely small chance of a big prize.

    Also I'm not entirely sure what you are trying to say at the end...? Probability and chance are absolutely the same thing. They are just synonyms of each other...? Unless you are alluding to the difference between expected winnings and observed winnings?
    Another thing about averages is that it is sometimes rare for the average to ever occur. Often there is a considerable spread above and below but nothing on the average. Bonds will be no different and some people will get much more than expected and others will get less.

    Without boring you too much and getting too technical, but this is not entirely accurate either, particularly with respect to premium bonds. The mean is a useful summary statistics at denoting the central tendency of any data. That is, it represents the data point that occurs at the highest frequency.

    The mean is only really suitable when the data follow a Gaussian distribution (otherwise known as 'normal' or 'the bell curve'). If the mean does not accurately represent the central tendency (i.e. the value that occurs most frequently), then other summary statistics should be used, such as the median. This is often seen with things like salaries (and indeed the number of legs :p), as this tends to be quite highly positively skewed, with large dispersion due to high value outliers. The mean will tend to overestimate the central tendency point, and the median can be more meaningful.
    Perhaps it should also say that such expectation is most likely to be observed in the longer term - i.e after several years (as you stated, Eskbanker). Is it perhaps a little improper of NS&I to suggest it is likely from the outset? (if it still does, that is).

    I agree, the quote of the rate could be misleading. It states 1.4% is the 'annual prize fund interest rate". Now I take this to mean that when the look at the entire holding over a year, and the entire amount paid out, it would equal a rate of 1.4%...? As you and Eskbanker say, the longer a person holds the bonds, the closer to this 1.4% rate they will be (in essence they have greater amounts of data, and the more data there is, the more likely it will represent the 'true' estimate). Of course knowing the spread of the data around this mean estimate would show you where you could lie in the extremes.

    The MSE premium bond calculator I believe just looks at the expected return at any given month, given the amount of bonds you hold. There is a saying in statistics, most models are wrong, but some are useful...that is to say that while the 'model' from the MSE premium bond checker can often be wrong in trying to predict the exact amount you will win (and in very rare cases, can be extraordinarily wrong..) it is helpful it gauging what you are likely to expect to get with a certain holding at any given month, and whether other savings may be more suitable.

    To go off on a bit of tangent, but the same applies in my field of medical statistics. We use large amounts of clinical data to model things, like risk of heart attack. We can look at things like age, cholesterol and diet to see what impact it has on the probability of having a heart attack. However, these models are generally pretty poor at predicting any one individuals risk of having a heart attack to a precise point in time..! Nevertheless, it's still useful in providing health advice and reducing the risk of heart attacks in the population in general.
  • eskbanker
    eskbanker Posts: 30,400
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    I can't remember (and haven't looked it up) but doesn't the premium bonds website suggest that people with average luck and the maximum holding should expect to win 12 or 13 prizes a year? (I think that applied in the days of the £30K max holding).
    It doesn't say that because it isn't true - it does say that each bond has 24,500 to 1 odds of winning a prize, or to put it another way (in my words rather than theirs) a £50K holding should win just over two prizes per month on average. Given the overwhelming likelihood that all such prizes will be £25s, this would give a (median) average annual return of £600, i.e. 1.2%, despite the mean average being the stated 1.4%.
    Perhaps it should also say that such expectation is most likely to be observed in the longer term - i.e after several years (as you stated, Eskbanker). Is it perhaps a little improper of NS&I to suggest it is likely from the outset? (if it still does, that is).
    The NS&I wording is careful, as you might expect, but is accurate in stating the odds of any bond winning in a given month, and also the mean return being 1.4%, in terms of this simply being the prize fund divided by the number of bonds.

    There are any number of ways of presenting the figures - one of the better ones IMHO is the MSE calculator, which allows modelling of different amounts over different time periods. However, its use of wide bandings distorts figures, so for £50K over one year (a popular choice for measuring annual return), it states that there's an 87% probability of winning at least £500 and a 24.7% probability of winning at least £750, with no intermediate results shown. Its high-level conclusion that "With £50,000 in Premium Bonds, if you have average luck you would expect to win roughly £500 over 1 year" is therefore flawed, as the true figure is more like £600 (£50 per month) - the difference between a (notional) 1% and a 1.2% return being quite significant....
  • "There are any number of ways of presenting the figures - one of the better ones IMHO is the MSE calculator, which allows modelling of different amounts over different time periods." eskbanker

    Funnily enough, I received an email from NS&I this morning and decided to check on the MSE calculator. I have a £30,000 holding and have received £350 "prizes" over the last 12 months. One side of the calculator said I was unlucky as 55% of bond holders received higher than this. :( The other side of the calculator said that, if I had average luck, I should receive £350. :o
    If I've calculated correctly, my interest looks to be 1.17% :o
    No longer trainee :o
    Retired in 2012 (54) :)
    State pension due 2024 (66) :(
  • Paul_DNAP
    Paul_DNAP Posts: 751
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    DrEskimo wrote: »
    I agree, the quote of the rate could be misleading. It states 1.4% is the 'annual prize fund interest rate". Now I take this to mean that when the look at the entire holding over a year, and the entire amount paid out, it would equal a rate of 1.4%...? As you and Eskbanker say, the longer a person holds the bonds, the closer to this 1.4% rate they will be (in essence they have greater amounts of data, and the more data there is, the more likely it will represent the 'true' estimate). Of course knowing the spread of the data around this mean estimate would show you where you could lie in the extremes.


    With the prize pot being so skewed, in particular the big jump up between the top prize and the second to top prize, then nobody will trend towards earning the 1.4% return rate. Nearly everybody will be earning below that, averaging about 1% return, who will be subsidising the millionaires who are getting a million percent uplift on a £100 bond.
    The only way to get 1.4% would be to own every single premium bond out there by yourself. Even if you let someone else have just one, they could win one of the £million prizes and make a serious dent in your returns (even if they won a £25 it would drop your return below 1.4%, but you'd have to go to a lot of decimal places to see it).
    (Although I could be wrong, I often am.)
  • eskbanker
    eskbanker Posts: 30,400
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    I have a £30,000 holding and have received £350 "prizes" over the last 12 months. One side of the calculator said I was unlucky as 55% of bond holders received higher than this. :( The other side of the calculator said that, if I had average luck, I should receive £350. :o
    Yes, that supports my point about the flaws in the calculator - the headline says that you should expect £350 with average luck, but it only says that because it's more likely than their next chosen data point of £400! As 64.9% should win at least £350 but 46% should win at least £400, this suggests to me that the median outcome is actually likely to be £375.

    However, to be fair, I haven't seen a better one out there....
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