ceejay
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Post by ceejay on Feb 23, 2020 16:02:56 GMT
Anyhoo, the point of my first post stands - the cut in rates has been hugely overstated by sensationalist reporting (in the Guardian of all places!). The overall payout at 1.3% is at the top end of current instant cash rates (tax free, risk free), and holders are choosing to get a bit less than that in exchange for said Licence To Dream. It's quite a lot less though. It's not just "90% of 1.3% = 1.17%" ... Why not? 90% of the fund is reserved for the small prizes. As long as you have enough bonds (£10k minimum, £30k better) for the averages to play out, you should get something approaching that over a small number of years.
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Post by carol167 on Feb 23, 2020 17:23:00 GMT
It's quite a lot less though. It's not just "90% of 1.3% = 1.17%" ... Why not? 90% of the fund is reserved for the small prizes. As long as you have enough bonds (£10k minimum, £30k better) for the averages to play out, you should get something approaching that over a small number of years. Well I've managed to average 1.52% in 13 years with the maximum amount. They've reduced the rates before, they even went back down to 1 million top prize not that long ago, then increased them and went back to 2. It ebbs and flows in line with general rates. My worst year scored 0.85% my best 4%. I'm hanging onto my premium bonds. They're great as long as they're just a part of an overall portfolio.
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r00lish67
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Post by r00lish67 on Feb 23, 2020 17:53:47 GMT
It's quite a lot less though. It's not just "90% of 1.3% = 1.17%" ... Why not? 90% of the fund is reserved for the small prizes. As long as you have enough bonds (£10k minimum, £30k better) for the averages to play out, you should get something approaching that over a small number of years. It's do with the magical wonder of multinomial probability ( which I totally didn't learn about from MSE 10 seconds ago), the impact of which basically boils down to the variations in prizes throwing up odd results. As well as punters having to 'pay' for the £1m prizes, they also have to fund the small prizes. Even in the lower prize pot, there are 27,000 odd £50 and £100 prizes which people will rarely see (bear in mind there are 3.4 million £25 prizes for context!). There are also then all sorts of combinations of prizes that could theoretically be won, which makes calculating the median very difficult Anyway, you really don't have to take my re-hashed version of it as truth, if you're interested you can read the full account on MSEI won't claim I'm able to comprehensively explain it all, but as per the article: "Eventually we tracked down a post-doctoral cosmology statistician (someone who calculates star movements) who had the requisite probability skills, and he wrote us an algorithm to build the Premium Bonds Calculator"
I think if there was any substantial doubt about the figures, some rivalling post-doctoral cosmology statistician would have piped up by now  carol167 , yep you've done well, but there also people who've piped up on here who say they've won the square root of bugger all. The variability of returns is another reason for most people to avoid them IMHO!
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Post by bracknellboy on Feb 23, 2020 18:25:45 GMT
Anyhoo, the point of my first post stands - the cut in rates has been hugely overstated by sensationalist reporting (in the Guardian of all places!). The overall payout at 1.3% is at the top end of current instant cash rates (tax free, risk free), and holders are choosing to get a bit less than that in exchange for said Licence To Dream. It's quite a lot less though. It's not just "90% of 1.3% = 1.17%" MSE's premium bonds calculator demonstrates that even with the old prize rate (it's yet to be updated), the median return for a £50k holding is £500 i.e. 1.00% . That will now be less, and given that the highest value prizes are maintained it also won't just be 0.90%, but even lower. At a guess, perhaps 0.8% p.a. Compare this to the leading 90d notice account at 1.65% (Investec (FSCS)) or 1 year fix (Atom 1.65%) , and you're lagging by about 0.85% or fully half of your possible return. Yes, admittedly, you're missing out on a "lottery ticket" by doing so, but it's an expensive one, and I'd much rather have a return on my savings that gets at least close to inflation personally. (I acknowledge that for higher rate taxpayers with £500+ annual interest already the maths is a little different). edit: I don't think Atom's 2-year fix at 1.8% will last much longer, that's what I'm goin' for.
My playing with the MSE prize calculator has led me to conclude its pretty badly flawed. Even a quick basic test demonstrates that. When they say they had some post doctoral astrophysict do the model behind it, I daren't contradict or that. However, I think the trouble is the way in which they "surface" the calculations, which starts to make a bit of a mockery of any highly complex calculations sitting behind it. I think the problem arises from granulairty, and that they are using (I think) a >50% outcome for what they display. Now of course PBs have discrete "returns" not continuous, and its important that is taken into account (which is where the "complex model" comes from). But the table below shows some of the problem.
27000 350 1.30%
30000 350 1.17%
31000 400 1.29%
32000 400 1.25%
33000 400 1.21%
34000 400 1.18%
Also, if you look at the 2 year on £30/31k/32k its £750. Umm.....
So a couple of quick observations. This illustrates they are using £50 "earnings" granularity / boundary conditions *. But the lowest prize quantum is £25, not £50, and the £25 is by far and away the highest probability. Many years ago it dropped from £50 to £25 (as I recall) as did the portion of prize money allocated to small prizes (upwards) - precisely to produce a more predictable/smoothed and in relative terms higher return for the average punter. So it seems nonsensical to use £50 boundary condition for the returns. But the problems look like they go further:
Another "insight" into potentially what is happening is if you click on the stuff below the calculations to get more detail. The table below comes from the "full breakdown" for £50k investment. The calculator gives an expected return of £500 - but that is 1%, which is lower than all of the numbers I've just shown above, despite the fact that the larger the investment (and longer period of time) the higher the likeliehood of hitting the "norm" (because discrete prize size doesn't change). Well if you look below, the "full odds" show you as having an 87% chance of getting £500. But that is also what they are giving as your likely return. What?? So with £25 minimum prize, over 12 months I don't still have a a > 50% chance of getting greater than £500 ? It drops off a cliff ? Statistically that simply is non-sensiscal. But wait, the next banding they show is £750 at 24.8%. Which presumably is why they are showing £500 and not say £550 or £575 or £600 or whatever the actual highest £25 incremental return still with a >50% likeliehood is. (Because they put the odds into a £500 band and a £750 band, the latter is < 50%, and they have no bands in between).
As I say, no matter how good the model/maths sitting at the back, the presentation / surfacing looks to be badly flawed. At least in terms of how it misleads people in their understanding of what they are seeing.
In the past I've kept a calculator that basically works on using the %age of the total winnings represented by either the lowest only (£25), or the £25/50/100.. I haven't done calcs for a while, but I think the £25 was maybe 88%, and the 25/50/100 was the 90%. Using the £25 only discounts skewing by large prizes.
The way bonds are structured now, if you hold a decent amount (say the max) and hold for decent duration, you'd expect to get a fairly smoothed return, bar being a lucky bugger.
Edit: *To clarify. They are using different granularity for different levels of return, which is illustrated by the table below for £50k/1 year.
This is the full table/details for the £50k "calculation". I couldn't find a simple way of screen shot'ing and pasting in.
Winnings
Probability
£0 Exactly 1 in 43,251,715,904
At least £25
Virtual certainty
At least £50
Virtual certainty
At least £75
Virtual certainty
At least £100
Virtual certainty
At least £150
Virtual certainty
At least £175
Virtual certainty
At least £200
Virtual certainty
At least £250
Virtual certainty
At least £350
99.3%
At least £400
97.7%
At least £450
93.9%
At least £500
87%
At least £750
24.8%
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Post by Ace on Feb 23, 2020 20:05:33 GMT
Great post bracknellboy, I'd played with the calculator before and also concluded that it was flawed, but didn't have the intellect to understand how/why. Would be interesting to send it to M Lewis or the originator for comment. |
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r00lish67
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Post by r00lish67 on Feb 23, 2020 20:40:47 GMT
Great post bracknellboy , I'd played with the calculator before and also concluded that it was flawed, but didn't have the intellect to understand how/why. Would be interesting to send it to M Lewis or the originator for comment. +1 ! They do have some sort of answer for the varying amounts, but it's not particularly convincing: "Why do you have a higher chance at £15,500 than at £31,000? Unless you're a stats nerd, avoid this answer, it's going to get tricky. Doing this table was actually incredibly hard. Even the Premium Bond Probability Calculator doesn't automatically show exact median winnings. So to be accurate I had to pick amounts where I had a high degree of confidence in the right answer. Hence picking £15,500 and £31,000, rather than more rounded amounts. In general, the more you have, the closer to the prize fund your median return is. But exactly at what amount the median hits is lumpy because it jumps at £25 a time, so vagaries of the statistics mean it doesn't rise in a purely linear way. (If you don't get this, use the calculator for different amounts and see where the 50% mark is likely to be.)"
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Post by bracknellboy on Feb 24, 2020 8:55:35 GMT
Great post bracknellboy , I'd played with the calculator before and also concluded that it was flawed, but didn't have the intellect to understand how/why. Would be interesting to send it to M Lewis or the originator for comment. But exactly at what amount the median hits is lumpy because it jumps at £25 a time, so vagaries of the statistics mean it doesn't rise in a purely linear way. (If you don't get this, use the calculator for different amounts and see where the 50% mark is likely to be.)" Quite, but as the numbers for £50k shows, that is precisely what the calculator fails to do.
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