NS&I raises interest rates

Eirambler

Albermarle said:

eskbanker said:

Albermarle said:

EthicsGradient said:

I make the effective rate you get from just the £100, £50 and £25 prizes 3.72%. This goes up to 4.00% if you include the £500 prizes; you would have to hold the £50,000 about 2.5 years to stand a 1 in 2 chance of getting one of those wins (or 1 year 3 months for a couple each with the max). You'd have to hold the max for 7 years to have a 1 in 2 chance of a £1,000 win; taking that into the calculation, the rate goes up to 4.18%.

However the people holding less than £50K, also have a chance of winning £500 or a £1000. Obviously a smaller chance but as they hold less bonds, their average prize rate will be the same.
Although clearly someone with £50K will normally win more than someone with £25K , the average prize rate, averaged over many customers and many years has got to be the same as far as I can see.

@eskbanker Your opinion please 

It all comes down to the definition of 'average', which generally refers to the arithmetic mean, so aggregating all prizes across all bonds for a year will indeed calculate the return as 4.65% each.

However, the median average is often seen as a more realistic measure for premium bonds, i.e. the middle outcome if all are lined up in order of return, sometimes referred to as the 'average luck' expected return.  For low holdings, especially over short durations, this will simply be zero, and conversely if looking at the entire population of bonds it'll be the same as the mean, so it is indeed true that the median return (as a percentage) for larger holdings over longer periods will be higher than for smaller holdings over shorter periods, even though the mean would be constant.

As above, the medium tier of prizes (£500/£1000) has been enhanced substantially in recent changes - a year and a half ago it only constituted 0.23% of prizes but is now 1.3%, so is now far more significant when assessing likely outcomes, especially for larger holdings/durations, rather than being a factor that could largely be ignored.

Thanks for the explanation, I should have known when talking about averages, that there three different ones !
 So if I hold £50K what is my median prize rate going to be?
Is it 4.18% as suggested by @Eirambler and @EthicsGradient ?

It depends on the period. If you mean over the next 12 months it will be more than the 3.7%, but it won't be as much as 4.18%. I'll let someone with better maths skills than me calculate the exact number, I'd say maybe somewhere around the 3.9% mark as an estimate...

EthicsGradient

Albermarle said:

eskbanker said:

Albermarle said:

EthicsGradient said:

I make the effective rate you get from just the £100, £50 and £25 prizes 3.72%. This goes up to 4.00% if you include the £500 prizes; you would have to hold the £50,000 about 2.5 years to stand a 1 in 2 chance of getting one of those wins (or 1 year 3 months for a couple each with the max). You'd have to hold the max for 7 years to have a 1 in 2 chance of a £1,000 win; taking that into the calculation, the rate goes up to 4.18%.

However the people holding less than £50K, also have a chance of winning £500 or a £1000. Obviously a smaller chance but as they hold less bonds, their average prize rate will be the same.
Although clearly someone with £50K will normally win more than someone with £25K , the average prize rate, averaged over many customers and many years has got to be the same as far as I can see.

@eskbanker Your opinion please 

It all comes down to the definition of 'average', which generally refers to the arithmetic mean, so aggregating all prizes across all bonds for a year will indeed calculate the return as 4.65% each.

However, the median average is often seen as a more realistic measure for premium bonds, i.e. the middle outcome if all are lined up in order of return, sometimes referred to as the 'average luck' expected return.  For low holdings, especially over short durations, this will simply be zero, and conversely if looking at the entire population of bonds it'll be the same as the mean, so it is indeed true that the median return (as a percentage) for larger holdings over longer periods will be higher than for smaller holdings over shorter periods, even though the mean would be constant.

As above, the medium tier of prizes (£500/£1000) has been enhanced substantially in recent changes - a year and a half ago it only constituted 0.23% of prizes but is now 1.3%, so is now far more significant when assessing likely outcomes, especially for larger holdings/durations, rather than being a factor that could largely be ignored.

Thanks for the explanation, I should have known when talking about averages, that there three different ones !
 So if I hold £50K what is my median prize rate going to be?
Is it 4.18% as suggested by @Eirambler and @EthicsGradient ?

4.18% is the amount given out in prizes of £25 to £1,000 over a year divided by the total number of bonds they assume for the calculation in the link given earlier of their estimate of prizes. You personally do not have a "median" prize rate; the collective holders of Premium Bonds can have a median (ie you can say half of them win more, half win less). To find it, you have to do the calculation that the MSE Premium Bonds calculator attempted (but it seemed to have been unreliable recently; I'm not sure if it was fixed (on edit: there's still a warning on it saying it's not accurate for large amounts), and anyway almost certainly has not been updated with the latest changes to the prize odds).

I gave the time you'd have to hold the maximum to be more likely than not to get a £500, or £1,000, prize to give an idea of how likely it is to get that.

Keith80

ColdIron said:

From Paul Lewis (MoneyBox)

Premium Bonds: new odds and interest rate and changed prize structure from Sept draw mean someone with max £50,000 holding can expect 1x£50 plus 1x£100 prize each month and five £25 prizes per year = 3.72% tax free = 4.65% (basic) or 6.2% (higher). 1.16m people have the max.

This is a helpful way of considering the issue because it appears to be based on the odds, which at 21k:1 imply, with a £50k holding, a win rate of 2.38 prizes per draw. So more likely two than three prizes, and as there are so many more £50 and £100 prizes in the draw, followed by £25 prizes, you are most likely to get something in the £50 to £200 range, unlucky if you get less than £50, lucky if you get more than £200.

Albermarle

eskbanker said:

Albermarle said:

So if I hold £50K what is my median prize rate going to be?
Is it 4.18% as suggested by @Eirambler and @EthicsGradient ?

Over what period?

Lets say 3 years.

eskbanker

Albermarle said:

eskbanker said:

Albermarle said:

So if I hold £50K what is my median prize rate going to be?
Is it 4.18% as suggested by @Eirambler and @EthicsGradient ?

Over what period?

Lets say 3 years.

Based on @EthicsGradient's calculation, you'd expect one £500 prize over a three year period with average luck (but not a £1K one) so that would bump up the median return to about 4%.

Albermarle

eskbanker said:

Albermarle said:

eskbanker said:

Albermarle said:

So if I hold £50K what is my median prize rate going to be?
Is it 4.18% as suggested by @Eirambler and @EthicsGradient ?

Over what period?

Lets say 3 years.

Based on @EthicsGradient's calculation, you'd expect one £500 prize over a three year period with average luck (but not a £1K one) so that would bump up the median return to about 4%.

Thanks, I shall wait patiently for my £500 !

PixelPound

It was mentioned that the number of £25 prizes is going down. So taking the info from the NS&I news section we have the below figures for each draw.



There does seem to be a downward trend in £25 prizes (when the rate changes), which I suppose is to make winning a prize still "special". Winning a £100 is probably psychologically better than winning the equivalent in smaller prizes.

Though maybe they've missed a trick? If the £100 and £50 were closer to 2 million, they could have had closer to 3 million £25 prizes and the odds of winning a prize down to 17000:1.

Though I suppose as the vast bulk of PB are held by those with Max holdings it makes sense to reduce the smaller prizes.