Premium Bond Calculator Discussion

xnoxxnox

Temrael wrote: »

Hi MSE, will the Premium Bond tool need to be updated to account for the change in the odds from April? And will the "sweetspot" of £13k change, or will it remain at £13k but you'd just expect a smaller average return?.[/i]

There is no "sweetspot".

The probability curve is continious. The regular savings account curve is a straight line. Here too (the more bonds you hold, the more chances). The pay-off is not linear in premium bonds case, but is skewed.

Well not a continious line, but as a step ladder, in 1p increments for savings accounts, and a much "chunkier" 25GBP steps here.

The headline figure of "most likely" odds to win at least whatever amount simply shows whichever amount has 50% or more chance of winning. So, even half the people will not win that much, but less. (note the "average" luck in the title of the calculator). If you look at the table with full odd, you can see which amount has a bit more certainty of winning - e.g. 80% chance.

There is a lower probably of winning each additional at least 25 quid more. One can win almost any amount in 25GBP increments between nil, and 12 million with just one bond, over the course of a year and one month. (since a single bond could win a million each month, and first draw after purchase the bond is not eligible). Thus the full curve between 0 and 12 million would be nicer to see as a probability curve, but alas it is not graphed.

Next you need to know that not all levels have been calculated. If you look at the "full breakdown" table, you can see that there are jumps and probabilities are not calculated for every 25 gbp, e.g. 125 skipped, 225 skipped, 25 gbp increments between 5k and 10k skipped and so on.

Thus one needs to itrapolate between available odds. E.g. currently calculator at 8k shows good odds, at 25 quid increments between 0 and 100 quid. 100 quid is at 56%, so still a head or tails type of thing kind of thing, 75 gbp has a much better probability 75%, aka odd of three/quarters.

These probabilities do scale and add up. Meaning 10k of bonds should have the same probability of winnings as 10 accounts of 1k bonds. More or less, note this is not quite true due to same bond in-eligible of winning multiple times in a draw. Thus it is more useful to say, there is between 50% and 75% chance to generate between 1.25% and 0.94% yield respectivily (taken by using 8000 figure, as that lists good probability threshold at 25gbp increments at the low end).

Thus 13k may generate between 162.50 and 121.875, but these levels are not winable, hence something like either 150 or 125 over the course of a year. If one errors on the lucky side, either 150 or 175 gbp.

And 13,001 bonds, have that one extra chance, and thus a few decimal points higher chances to error on the 175 side, versus the 150 side.

There are no sweetspots, but 25GBP prize jumps mean that one needs quite a few bonds to have a desired probability (e.g. 50%+) of winning at least something over the course of the year.

It's much easier to throw away all the math. 98% of the prizes in the last draw were 25 quid ones. For the purpose of comparison with a savings rate, one can ignore that the prizes have higher values than 25 quid -> meaning ignore the 2% of the prizes, or better approximate them as "at least 25 quid" prizes.

Odds of winning of any bond is 24,500 to one due to prize fund skew, and since we approximate the payout as "at least 25 quid", it means ove the year N amount of bonds has a payout of N * 12 * 25 / 24500 or a rate of 1.224489795%.

So what can we take away from this?

If held for one eligible draw (one month and one day, purchased on the last day of the month), to get the minimum 25GBP payout one should have about 25,000 of bonds, anything less is a bit pointless.

If held for a full year (purchased on 30th of November, and held all of subsequent year), to get the minimum 25GBP payout one should have about 2,050 of bonds, anything less is a bit pointless.

The more you buy, the better it gets, and one can approximately get the 1.22% return which jumps a bit (as in buying in 2k+ increments makes more sense). The difference between 1.4% headline figure and the 1.22%, pays for the lucky 2% of the prize fund with higher values.

ps. you can joke that this is an 1.4% yield bond ETF, with an 0.18% OCF, and a minimum investment requirement of 2k, on average, across the year.

Doggit

The calculator is not working. You can enter all the values, but nothing happens when you hit the 'calculate' button.

WaywardDriver

Doggit said:

The calculator is not working. You can enter all the values, but nothing happens when you hit the 'calculate' button.

Works OK for me on both IE and Edge. What browser are you using?

Temrael

The calculator is currently throwing an error...
Cross-Origin Request Blocked: The Same Origin Policy disallows reading the remote resource at https://prod-api.moneysavingexpert.com/legacy-premium-bonds/results?months=12&bonds=1000&period=this_months. (Reason: CORS header 'Access-Control-Allow-Origin' missing).
Looks like the page needs to be given access to the API that runs it.
Thanks,
Tem

Temrael

This is now working again. Thanks whoever fixed it.

Nick_S

I think it's broken.

I've just been playing with the same investment over different lengths of time; 1 yr, 2yrs, 4 yrs

With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £175 over 1 year
With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £350 over 2 year(s)

With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £500 over 4 year(s)

The probability should be the same in any given year, so scaling from 1 yr to 2 years should double - and it does. Over 4 years it should be double the 2 years - and it isn't. Suddenly your return drops from 0.875% to 0.625%.

And also with different amounts:

With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £500 over 4 year(s)

With £40,000 in Premium Bonds, if you have average luck you would expect to win roughly £1000 over 4 year(s)

With £50,000 in Premium Bonds, if you have average luck you would expect to win roughly £1500 over 4 year(s)

For the £20,000 and £40,000 calculations it's still at that 0.625%. For £50,000 it shoots up to (a still poor) 0.75%

Does not compute...

eskbanker

Nick_S said:

I think it's broken.

I've just been playing with the same investment over different lengths of time; 1 yr, 2yrs, 4 yrs

With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £175 over 1 year
With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £350 over 2 year(s)

With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £500 over 4 year(s)

The probability should be the same in any given year, so scaling from 1 yr to 2 years should double - and it does. Over 4 years it should be double the 2 years - and it isn't. Suddenly your return drops from 0.875% to 0.625%.

And also with different amounts:

With £20,000 in Premium Bonds, if you have average luck you would expect to win roughly £500 over 4 year(s)

With £40,000 in Premium Bonds, if you have average luck you would expect to win roughly £1000 over 4 year(s)

With £50,000 in Premium Bonds, if you have average luck you would expect to win roughly £1500 over 4 year(s)

For the £20,000 and £40,000 calculations it's still at that 0.625%. For £50,000 it shoots up to (a still poor) 0.75%

Does not compute...

It's not broken as such but chooses inconsistent* data points for presenting the results, which can lead to some odd effects if you only read the headline summaries that you're quoting.  If you look at the 'full odds' tab you'll see what's going on....

£20K for one year - 57.4% chance of at least £175 and 43.5% chance of at least £200, so £175 is a reasonable estimate of the expected average.

£20K for two years - 58.1% chance of at least £350 and 39.2% chance of at least £400, so again £350 is a reasonable estimate, being the last outcome above 50%.  Note that they choose not to show the chance of £375.

£20K for four years - 96% chance of at least £500 and 47.1% chance of at least £750, with no intermediate data points presented!  Of these two options, the first is the only one above 50%, so that's why they use that as the headline expected return, but (without access to the full model) you'd expect the chances of at least £725 to be slightly above 50% and so that would be a more realistic expected outcome.

Stick to an 'average luck' expectation in 0.9% territory but understand that you're more likely to be closer to this for larger holdings over longer periods, and for smaller holdings or shorter durations, the returns will be more volatile.

* actually, 'inconsistent' is the wrong word here!  In fact the chances are shown for an identical set of outcomes each time, regardless of whether it's analysing £1000 for a month or £50K for five years, but their applicability is inconsistent when there are such wide gaps left uncovered further up the scale....

supersteamer

I'm moving this discussion here as I started it in the wrong place... 

Just for fun, I've run the calculator 5 times (1 year --> 5 years) for 50k of bonds, and am just looking at the last row of the output in each case (At least £1,000,000):

For "Over What time?" 1 Year

At least £1,000,000

1 in 5,747

For "Over What time?" 2 Years

At least £1,000,000

1 in 46,994

For "Over What time?" 3 Years

At least £1,000,000

1 in 1,290

For "Over What time?" 4 Years

At least £1,000,000

36.8%

For "Over What time?" 5 Years

At least £1,000,000

45.6%

This is obviously incorrect - odds that go up and down again over time?!   Nearly 50% chance of winning a million after 5 years?!

This has been reported but just re-posting here for visibility in case anybody is making actual decisions based on the output of the calculator!    Doesn't seem to be trustable at the moment.  For > £1m it's obviously wrong, but may not be so for smaller numbers where it might look more reasonable.

RedImp_2

I’ve got £49,500 worth (for some time), I’ve never topped up to the maximum for no particular reason.  I’ve never seen or used the calculator but I assume will tell me the difference the extra £500 might make.  I guess one extra £25 win will be better than anything I would get for £500 in a savings account.

eskbanker

RedImp_2 said:

I’ve got £49,500 worth (for some time), I’ve never topped up to the maximum for no particular reason.  I’ve never seen or used the calculator but I assume will tell me the difference the extra £500 might make.  I guess one extra £25 win will be better than anything I would get for £500 in a savings account.

The calculator rounds to the nearest full thousand so won't allow you to model the difference that the extra £500 would make but it's negligible anyway - with odds of any bond winning in any month being 24,000 to one, a block of 500 would be expected to win one prize every four years on average.

Or to put it another way, going from exactly 99% of the maximum holding to 100% is only going to increase expected returns by about 1%, subject to rounding and so on....