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Post by bernythedolt on Jan 5, 2020 2:05:55 GMT
For ref, I use MSE. It's apparently actually surprisingly complicated to work out the median - MSE had to source an advanced mathematician apparently! For brevity I used 1.00%, but it varies by the amount invested. That figure comes from the bit which says "how much can i expect to win", and entering £50k. Or, for anyone interested, you can calculate this for yourself reasonably simply using the Poisson formula which provides a pretty accurate estimate of your win expectation. (A binomial expansion is the truly accurate way, but Poisson is a good approximation for this application and is easier to work with). With each premium bond having a win probability of 1 in 24500 (as currently set by NS&I), first set variable u to <no. of bonds>/24500. So in gravitykillz 's case u= 30000/24500 = 1.2245. At each monthly draw, your probability of x wins is very close to P(X=x) = e^(-u) * (u)^x / x! [where x! denotes x factorial] Time to plug in some values for x... Probability of zero wins, P(X=0) = e^-1.2245 * 1.2245^0 / 0! = 0.2939 [note that a^0 = 1; 0! = 1; e = 2.7182818] Probability of one win, P(X=1) = e^-1.2245 * 1.2245^1 / 1! = 0.3599 Probability of two wins, P(X=2) = e^-1.2245 * 1.2245^2 / 2! = 0.2203 ...and so on. Probability of three or more wins P(X>2) = 1 - 0.2939 - 0.3599 - 0.2203 = 0.1259 It's easy to build up a spreadsheet tabulating these figures for your own bond holding. So, with 30,000 bonds, the probability of winning something at each monthly draw is 71% (being 1 minus 0.2939). Now we can extend this to a year by setting u=12 x 30000/24500 = 14.6939, leading to the table below of number of wins for the year versus the probability of that event. The most likely number of wins for the year (i.e. where the probability is maximum) is seen to be 14 in the table. With the structure of today's prize distribution, these will consist almost entirely of £25 prizes. If you're lucky you might hit something bigger! With a holding of 30,000 bonds, I would anticipate prize money of approximately 14.69 x £25 = £367, so maybe £325 to £400 for the year. With NS&I paying out 1.4% in their prize fund, anyone claiming to have consistently received over that figure has been very lucky indeed! The vast majority are likely to achieve closer to 1.2% I would say, and this has held true for my wife and I since Dec 2017 (when NS&I's rate was increased to 1.4%). I haven't yet been brave enough to check my figures here tally with the MSE calculator - fingers crossed they match up! But this is calculated from first principles, so I'm fairly confident. Wins Prob 0 4.15461E-07 1 6.10473E-06 2 4.48511E-05 3 0.000219679 4 0.000806983 5 0.002371542 6 0.005807859 7 0.012191424 8 0.022392412 9 0.036559039 10 0.053719405 11 0.07175876 12 0.087867869 13 0.099316901 14 0.104239313 15 0.10211198 16 0.093776308 17 0.081055152 18 0.066167471 19 0.051171406 20 0.037595319 21 0.026305762 22 0.017569711 23 0.01122466 24 0.006872241 25 0.004039195 26 0.002282747 27 0.001242312 28 0.000651942
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Post by gravitykillz on Jan 5, 2020 8:20:36 GMT
I may pull out of premium bonds by summer. Just seeing how my luck is. Need to win £100 per month to justify the lost interest. Have increased my holdings to 36k now. Won nothing in January but 3x£25 in December. But hey it is exciting to think you have a possibility of winning a million no matter how small.
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agent69
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Post by agent69 on Jan 5, 2020 9:21:26 GMT
I was given some premium bonds as a christening present.
Many years later, having recently taken eary retirement, the cumulative total of my winnings is zero.
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Post by bernythedolt on Jan 5, 2020 10:57:29 GMT
I may pull out of premium bonds by summer. Just seeing how my luck is. Need to win £100 per month to justify the lost interest. Have increased my holdings to 36k now. Won nothing in January but 3x£25 in December. But hey it is exciting to think you have a possibility of winning a million no matter how small. You won't get anywhere near £100 per month, even with the maximum £50k holding. Not until NS&I increase their rate at least.
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Post by bernythedolt on Jan 5, 2020 11:05:36 GMT
I was given some premium bonds as a christening present.
Many years later, having recently taken eary retirement, the cumulative total of my winnings is zero.
You, and thousands like you. Exactly as the mathematics predict. You need to hold 2000 premium bonds to start collecting 1 regular prize per year. 20 bonds might just about see 1 prize per lifetime...and that will be almost certainly a £25.
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IFISAcava
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Post by IFISAcava on Jan 5, 2020 12:03:18 GMT
I was given £4 in premium bonds by my grandparents in 1966. I haven't ever won. Inflation would mean that £4 is the equivalent of ~£75 today (https://www.bankofengland.co.uk/monetary-policy/inflation/inflation-calculator) Had they invested it in the stock market (say S&P 500), it would on average have increased 3872% (https://dqydj.com/sp-500-return-calculator/) Add in the currency devaluation (£/USD 2.8 in 1966, 1.3 today) and it would be over £330 (yes, charges would obviously have eaten into that a bit, but the general point stands)
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scc
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Post by scc on Jan 5, 2020 14:05:45 GMT
A more reasonable comparison might be with lotto. Essentially, all of your grandparents bought you was a monthly lottery ticket(s) for the last 50 years. At least you still have your four quid.
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daveb
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Post by daveb on Jan 5, 2020 14:29:31 GMT
£750 on a £50k holding puts you at the junction of the top and 2nd quintile of luck. £600 pretty close to the median. Small holdings are just to fantasise about a prize, doesn't count as an investment.
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littleoldlady
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Post by littleoldlady on Jan 5, 2020 15:04:31 GMT
A more reasonable comparison might be with lotto. Essentially, all of your grandparents bought you was a monthly lottery ticket(s) for the last 50 years. At least you still have your four quid. Erm. No, no and no. Last time I checked, lotto tickets were not refundable. With NS&I Premium Bonds, if you put £50k in there, you can take your £50k out. With a large holding you are really buying 2 products with the interest you forgo. One is a cash account paying about 1%, the other is a lottery ticket. With a small holding only the second.
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IFISAcava
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Post by IFISAcava on Jan 5, 2020 17:13:00 GMT
And the other lesson is that you gift your grandchildren a stock market investment rather than a premium bond. Or indeed your children - invested my kids' child benefit (plus a bit extra) every month since they were born - XIRR 13%, £30k+ so far towards their first house, RTW trip, university, whatever. (Although of course we stopped actually getting the child benefit some time ago, which was fair enough as tax rises go)
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scc
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Post by scc on Jan 5, 2020 17:24:08 GMT
A more reasonable comparison might be with lotto. Essentially, all of your grandparents bought you was a monthly lottery ticket(s) for the last 50 years. At least you still have your four quid. Erm. No, no and no. Last time I checked, lotto tickets were not refundable. With NS&I Premium Bonds, if you put £50k in there, you can take your £50k out. Minus inflation. Plus any winnings you might make. Minus any interest you might have made in the first month. I agree the dynamic changes when you put more in, but if you've put a minimum or near minimum in (like this person's grandparents) - you are only buying the equivalent of a monthly lottery ticket with the interest/historical spending power you could have had. FWIW I do use Premium Bonds as a safe haven, but even for the ultra frugal £4/75 doesn't do that job. I reckon you need at least a couple of years worth of expenses in there. For many, that means putting the full £50K in there.
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Post by bernythedolt on Jan 5, 2020 19:22:17 GMT
With a large holding you are really buying 2 products with the interest you forgo. One is a cash account paying about 1%, the other is a lottery ticket. With a small holding only the second. Read my previous post. You know, the one where I said "Nor is the interest the point either". If you are yapping on about "interest you forgo" then its clear you don't understand the point of NS&I. You don't put money in NS&I for the interest. You do put money in NS&I for other perfectly valid reasons. End of story. Hint: Money management is not about "geez, I wonder how much interest I can make". This seems unnecessarily rude! Who died and made you forum investment monitor? Re your Hint, Wikipedia defines money management as "a strategic technique to make money yield the highest interest-output value...". Warren Buffet advocates, "favor expenditures on interest bearing items over all others". And re your "yapping on about" comment, MSE's Martin Lewis says of Premium Bonds, "it is only the 'interest' that is a gamble". So I confess I'm struggling with your insights above. Personally I'm prepared to forego the interest I could earn elsewhere by effectively gambling it instead on the PB prize mechanism. In the longer term, it is a very low risk investment returning a steady 1.2%, always with the outside chance of a life-changing win. You don't get that excitement with many other investments. The universe of utterly safe, instant-access investments is nowadays capped around 1.5% before tax. Why would you not put money into Premium Bonds for the interest? Given the realistic long-term expectation of 1.2% tax free, plus the outside chance of a decent win, what's not to like? I'm always ready to learn from those who know better, so comments and/or brickbats welcome!
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Greenwood2
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Post by Greenwood2 on Jan 5, 2020 20:45:10 GMT
And the other lesson is that you gift your grandchildren a stock market investment rather than a premium bond. Or indeed your children - invested my kids' child benefit (plus a bit extra) every month since they were born - XIRR 13%, £30k+ so far towards their first house, RTW trip, university, whatever. (Although of course we stopped actually getting the child benefit some time ago, which was fair enough as tax rises go) In the past you could also do NS&I Children's bonds, which were quite good, don't think they are around any more though.
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Post by bernythedolt on Jan 5, 2020 21:18:46 GMT
[…] for those who pay tax the winnings are also tax-free.
Depending on your tax rate, a return of 1.2-1.4% may be the same what you'd get in a 2.2-2.5% taxable account - so I think PBs only make sense for those paying a high tax rate, otherwise just put it in the best savings account and stop dreaming!
Except you're not comparing like-for-like. Unless you know of a 2.2-2.5% (taxable) account which is low risk and instant access? Some people want those two attributes, making PBs more suitable.
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Post by bernythedolt on Jan 7, 2020 14:51:02 GMT
Funnily enough, even if I were not a taxpayer I'd still take my PBs, with their 1.2% expectation, over your 1.35% account. In addition to the expected 1.2%, PBs do confer an advantage - the low probability of a high win. I'm happy to treat the meagre 0.15% difference as my little flutter each month (but I did once win £1000 many years ago, so I confess to a little bias ). Even a non-taxpayer can still feel comfortable with PBs (for some of their instant access cash) with rates so close as they currently stand.
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