Do Premium Bonds make sense?

Wheres_My_Cashback

ratechaser said:

I've been trying to persuade Mrs RC for a while now on PBs - all our unwrapped cash is in accounts in her name (because 40% tax is a bit better than 45%...), and she's getting no better than 0.6% net interest, whereas you'd realistically double that via PBs. 

But no. Because it's not a fixed/guaranteed rate. And "it's a bit like gambling isn't it". So on we plod... 

Is that a big red thumb print I can see on your forehead?
Get a grip man an educate her by putting it down on paper just how much you're losing each month by earning such a paltry rate.

eskbanker

zagfles said:

PBs look like a no-brainer at the moment. Best easy access account according to MSE is 1.16%. PBs pay 1.4% mean, and 1.2% mean even if you ignore all the prizes above £25. Someone with £10k+ should get a regular flow of £25 prizes.

At the risk of taking 'regular' too literally, the return on PBs is anything but regular, especially at lower holding values.  According to the MSE PB calculator, a £10K holding has a roughly 1 in 3 chance of winning a prize in any given month, but anyone literally expecting a prize every third month will be disappointed, even though it should gravitate to that as a long-term average eventually....

zagfles

Richmc said:

A couple of silly questions.
1). If the BOE interest rate goes negative, and premium bonds follow that, will that mean they run the draw and demand payment from the "winning" numbers, with two poor souls owing £1million?
2). Does anyone know the odds of an investor with £50,000 in bonds winning both £1million prizes in one month? I guess this will involve a lot of zeros!

1) Yes, it's the govt's plan to deal with the Coronavirus deficit

2) Approx 1 in 74092000000000000. You'd need to hold them for half a million times the age of the universe with average luck.

zagfles

eskbanker said:

zagfles said:

PBs look like a no-brainer at the moment. Best easy access account according to MSE is 1.16%. PBs pay 1.4% mean, and 1.2% mean even if you ignore all the prizes above £25. Someone with £10k+ should get a regular flow of £25 prizes.

At the risk of taking 'regular' too literally, the return on PBs is anything but regular, especially at lower holding values.  According to the MSE PB calculator, a £10K holding has a roughly 1 in 3 chance of winning a prize in any given month, but anyone literally expecting a prize every third month will be disappointed, even though it should gravitate to that as a long-term average eventually....

Well, there's only 0.75% chance of not winning anything in a year, and only about 3.6% chance of only winning once a year. Over 85% chance of winning at least 3 prizes a year. So I'd say that was pretty close to "regular"...

eskbanker

zagfles said:

eskbanker said:

zagfles said:

PBs look like a no-brainer at the moment. Best easy access account according to MSE is 1.16%. PBs pay 1.4% mean, and 1.2% mean even if you ignore all the prizes above £25. Someone with £10k+ should get a regular flow of £25 prizes.

At the risk of taking 'regular' too literally, the return on PBs is anything but regular, especially at lower holding values.  According to the MSE PB calculator, a £10K holding has a roughly 1 in 3 chance of winning a prize in any given month, but anyone literally expecting a prize every third month will be disappointed, even though it should gravitate to that as a long-term average eventually....

Well, there's less than a 0.2% chance of not winning anything in a year, and only about 1.5% chance of only winning once a year. Over 90% chance of winning at least 3 prizes a year. So I'd say that was pretty close to "regular"...

Sure, it was an essentially semantic point I was making, i.e. that regularity isn't the same as frequency:

regular

adjective

1. arranged in or constituting a constant or definite pattern, especially with the same space between individual instances.
   
   "plant the flags at regular intervals"

   
   
2. recurring at uniform intervals.
   
   "a regular monthly check"

AnotherJoe

Richmc said:

2). Does anyone know the odds of an investor with £50,000 in bonds winning both £1million prizes in one month? I guess this will involve a lot of zeros!

I make it 21.

lhsecons

A question for the premium bonds experts on here. Using the calculator on this site, it estimates that with average luck I would win £500 if I held £39000 worth of bonds. It also estimates that if I held £50000 worth I would also win £500. Does this mean that £39000 is the best amount to hold and the other £11000 should be put elsewhere?

eskbanker

lhsecons said:

A question for the premium bonds experts on here. Using the calculator on this site, it estimates that with average luck I would win £500 if I held £39000 worth of bonds. It also estimates that if I held £50000 worth I would also win £500. Does this mean that £39000 is the best amount to hold and the other £11000 should be put elsewhere?

No, it's a weakness in the selective data points used in the calculator, in that there are no options given between £500 and £750.

So, even if the expected return is £600, they state that the expected outcome is £500 but only on the flawed basis that this is more likely than £750.

If you look at the full odds, you'll see that £39K has a 51.6% chance of winning at least £500, whereas £50K has an 87% chance of winning at least £500, but only a 24.8% chance of the next arbitrary data point (£750), so they summarise it as £500 being the most likely outcome, even though the more accurate figure would be either £600 or £625.

zagfles

eskbanker said:

zagfles said:

eskbanker said:

zagfles said:

PBs look like a no-brainer at the moment. Best easy access account according to MSE is 1.16%. PBs pay 1.4% mean, and 1.2% mean even if you ignore all the prizes above £25. Someone with £10k+ should get a regular flow of £25 prizes.

At the risk of taking 'regular' too literally, the return on PBs is anything but regular, especially at lower holding values.  According to the MSE PB calculator, a £10K holding has a roughly 1 in 3 chance of winning a prize in any given month, but anyone literally expecting a prize every third month will be disappointed, even though it should gravitate to that as a long-term average eventually....

Well, there's less than a 0.2% chance of not winning anything in a year, and only about 1.5% chance of only winning once a year. Over 90% chance of winning at least 3 prizes a year. So I'd say that was pretty close to "regular"...

Sure, it was an essentially semantic point I was making, i.e. that regularity isn't the same as frequency:

regular

adjective

1. arranged in or constituting a constant or definite pattern, especially with the same space between individual instances.
   
   "plant the flags at regular intervals"

   
   
2. recurring at uniform intervals.
   
   "a regular monthly check"

I'd got that a bit wrong because I used the monthly probability rather than each bond's probability - obviously there's the chance of winning more than one prize a month. Having a bit of time to waste for an intellectual exercise - I've now done it properly, using each bond's probability.

For a £10k holding the probabilities of the amount of prizes you win per year are:

0 prizes: 0.75%

1 prize: 3.65%

2 prizes: 8.95%

3 prizes: 14.61%

4 prizes: 17.89%

5 prizes: 17.53%

6 prizes: 14.31%

7 prizes: 10.01%

8 prizes: 6.13%

9 prizes: 3.34%

10 prizes: 1.63%

11 prizes: 0.73%

12+ prizes: 0.47%

So pedantry aside, I think that shows that with a £10k holding you'll get quite a regular flow of prizes.

With a £50k holding it's even more regular - there's virtually no chance you won't win anything, and a 97% chance of getting at least 10 prizes a year.

eskbanker

zagfles said:

eskbanker said:

zagfles said:

eskbanker said:

zagfles said:

PBs look like a no-brainer at the moment. Best easy access account according to MSE is 1.16%. PBs pay 1.4% mean, and 1.2% mean even if you ignore all the prizes above £25. Someone with £10k+ should get a regular flow of £25 prizes.

At the risk of taking 'regular' too literally, the return on PBs is anything but regular, especially at lower holding values.  According to the MSE PB calculator, a £10K holding has a roughly 1 in 3 chance of winning a prize in any given month, but anyone literally expecting a prize every third month will be disappointed, even though it should gravitate to that as a long-term average eventually....

Well, there's less than a 0.2% chance of not winning anything in a year, and only about 1.5% chance of only winning once a year. Over 90% chance of winning at least 3 prizes a year. So I'd say that was pretty close to "regular"...

Sure, it was an essentially semantic point I was making, i.e. that regularity isn't the same as frequency:

regular

adjective

1. arranged in or constituting a constant or definite pattern, especially with the same space between individual instances.
   
   "plant the flags at regular intervals"

   
   
2. recurring at uniform intervals.
   
   "a regular monthly check"

I'd got that a bit wrong because I used the monthly probability rather than each bond's probability - obviously there's the chance of winning more than one prize a month. Having a bit of time to waste for an intellectual exercise - I've now done it properly, using each bond's probability.

For a £10k holding the probabilities of the amount of prizes you win per year are:

0 prizes: 0.75%

1 prize: 3.65%

2 prizes: 8.95%

3 prizes: 14.61%

4 prizes: 17.89%

5 prizes: 17.53%

6 prizes: 14.31%

7 prizes: 10.01%

8 prizes: 6.13%

9 prizes: 3.34%

10 prizes: 1.63%

11 prizes: 0.73%

12+ prizes: 0.47%

So pedantry aside, I think that shows that with a £10k holding you'll get quite a regular flow of prizes.

With a £50k holding it's even more regular - there's virtually no chance you won't win anything, and a 97% chance of getting at least 10 prizes a year. 

There's obviously limited mileage in continuing to debate the meaning of the word 'regular' but yes, the stats are what they are - I think your presentation is an excellent illustration of the variability of the return though, in that even though the most likely outcome for £10K would be four or five prizes, on average it's only going to be 35% of holders that would actually see those specific returns, i.e. you'd have a 65% chance of not achieving a return of between 1% and 1.25% inclusive (excluding higher returns)!