NS&I raises interest rates

Eirambler

eskbanker said:

Albermarle said:

eskbanker said:

Albermarle said:

As discussed many times before, the Million Pound prizes distort what you can expect to get in reality, which is about 4.3/4.4 % ? Non taxable of course.
Best paying easy access ISA is 4.4%, so the PB's are now pretty much on the money for tax free easy access savings.

Based on the prize distribution, under which the top 20% of the prize fund is delivered by just 1.36% of the prizes, the median outcome is still likely to be closer to 80% of the headline rate, so the 'average luck' return should be expected to be more like about 3.7% than the figures you suggest - obviously better than before, but not as competitive against similar products as you've implied.

OK I was hoping someone with a better grasp of maths/probabilities would come along 

So 3.7% and a slightly better chance of winning a bigger prize than before ( as there are more of them apart from the two Million prizes) . Would that be a fair comment? 

Effectively, yes - the chances of winning any prize have improved by virtue of the move from 22K:1 to 21K:1, and the >£100 ones now make up 1.36% instead of 1.225% of the prizes by volume, but they still represent 20% of the prize fund by value, as before.

That 3.7% would also rise somewhat based on how much someone actually held in bonds. That 1.36% volume of big prizes means that on average one in every 73 or so prizes someone wins would be greater than £100 (almost certainly a £500 or £1000 win).

Someone with a max holding would expect to win roughly 30 prizes a year, so that one bigger win should come about on average every 2.5 years or thereabouts for them.

A couple both on max holding would expect to win roughly 60 prizes a year so they could reasonably expect one big win every 15 months or so i.e. they would get a big win more years than they wouldn't. So, factoring this in, the prize rate would be notably higher for someone or a couple with significant investment in the bonds.

The odds of winning more than £1000 in a single prize remains remote unfortunately.

Albermarle

Eirambler said:

eskbanker said:

Albermarle said:

eskbanker said:

Albermarle said:

As discussed many times before, the Million Pound prizes distort what you can expect to get in reality, which is about 4.3/4.4 % ? Non taxable of course.
Best paying easy access ISA is 4.4%, so the PB's are now pretty much on the money for tax free easy access savings.

Based on the prize distribution, under which the top 20% of the prize fund is delivered by just 1.36% of the prizes, the median outcome is still likely to be closer to 80% of the headline rate, so the 'average luck' return should be expected to be more like about 3.7% than the figures you suggest - obviously better than before, but not as competitive against similar products as you've implied.

OK I was hoping someone with a better grasp of maths/probabilities would come along 

So 3.7% and a slightly better chance of winning a bigger prize than before ( as there are more of them apart from the two Million prizes) . Would that be a fair comment? 

Effectively, yes - the chances of winning any prize have improved by virtue of the move from 22K:1 to 21K:1, and the >£100 ones now make up 1.36% instead of 1.225% of the prizes by volume, but they still represent 20% of the prize fund by value, as before.

That 3.7% would also rise somewhat based on how much someone actually held in bonds. That 1.36% volume of big prizes means that on average one in every 73 or so prizes someone wins would be greater than £100 (almost certainly a £500 or £1000 win).

Someone with a max holding would expect to win roughly 30 prizes a year, so that one bigger win should come about on average every 2.5 years or thereabouts for them.

A couple both on max holding would expect to win roughly 60 prizes a year so they could reasonably expect one big win every 15 months or so i.e. they would get a big win more years than they wouldn't. So, factoring this in, the prize rate would be notably higher for someone or a couple with significant investment in the bonds.

The odds of winning more than £1000 in a single prize remains remote unfortunately.

The average prize rate should stay the same, however many bonds you have. What changes is the likely spread of the prize rate. For example ( just using guesswork figures) 
The large majority of people with the full £50K for 12 months will get between 3.5% and 4% ( there will be some unlucky and lucky outliers as well)
The majority  with £25K should be in the range 3% to 4.5% ( as a guess) 
The majority with £10K should be in a range of 2% to 6%
Somebody with only £1K will be in range for 0 to 10% 

The more binds you have the closer to the average rate you should achieve . The possibility of winning say a £1000 every 2.5 years is already taken account of in the average rate.

Eirambler

No, the average rate across all the prizes is 4.65%, the overall average doesn't change in that regard.

However, unless the poster (eskbanker) wishes to clarify otherwise, my understanding is that the 3.7% rate was calculated by taking out the 20% of winnings that is shared out between relatively few bondholders who win high prizes. However, this 20% includes all prizes down to £500 (£94m worth in total). So that excludes the £1,000 and £500 prizes, which are far more winnable than those from £1000 up, especially for those with max holdings, from the calculated rate.

So, for someone with £50,000, there's an argument that you should include these in the calculation also, which would increase the likely win rate from 3.7%. For a couple who both have max holding, it's probably more accurate if you do include the £500 and £1000 prizes in the calculation. Prizes above £1k should still be left out as it is a statistical improbability that any one individual would win one of those.

EthicsGradient

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%.

Eirambler

Yes, that's my calculation also.

Albermarle

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 

eskbanker

Eirambler said:

No, the average rate across all the prizes is 4.65%, the overall average doesn't change in that regard.

However, unless the poster (eskbanker) wishes to clarify otherwise, my understanding is that the 3.7% rate was calculated by taking out the 20% of winnings that is shared out between relatively few bondholders who win high prizes. However, this 20% includes all prizes down to £500 (£94m worth in total). So that excludes the £1,000 and £500 prizes, which are far more winnable than those from £1000 up, especially for those with max holdings, from the calculated rate.

So, for someone with £50,000, there's an argument that you should include these in the calculation also, which would increase the likely win rate from 3.7%. For a couple who both have max holding, it's probably more accurate if you do include the £500 and £1000 prizes in the calculation. Prizes above £1k should still be left out as it is a statistical improbability that any one individual would win one of those.

Yes, the 3.7% was indeed based on the simplistic calculation as described - it is undoubtedly true that the higher the numbers of draws and/or bonds are involved then the median return gradually converges towards the mean, so yes, for maximum holdings over multiple years then the medium tier of prizes does start to come into play, more so than before.

eskbanker

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.

Albermarle

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 ?

eskbanker

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?