Premium bonds

mrsyardbroom

Now that the interest rate on our savings accounts has dropped I'm thinking about buying £1000 worth of premium bonds. I've been to the National Savings website but I can't find out how many bonds there are and how many monthly prizes are generated. I know the figures must vary from month to month but I want to get some idea of the probability of winning a prize over the period of a one year. If there's a high probability of winning even one prize of £50 then we'll get a better return on our money than we're getting at present.

Lokolo

1.8% average return.

Milarky

Minimum prize £50 - so average time to wait... 3 years...

[Equivalently; odds @ 1:36000 require 3 years or 36 months x 1000 entries per draw to achieve]

mrsyardbroom

I pay 20% tax on my savings so it might be worth investing just £1000.

Lokolo

1.8% * 1.25 = 2.25%

Thats the rate you need to beat (before tax) to get an average better return.

mrsyardbroom

..and I've just found this calculator on this site http://www.moneysavingexpert.com/savings/premium-bonds-calculator/

Aegis

Lokolo wrote: »

1.8% average return.

Remember, that's the mean rather than the median return. In the case where you have extremely unlikely events, the median is arguably a better way to predict the return.

For example, if 1000 people are in a competition to win £1000, the mean return would be £1 if you assume a pure random selection. However, the median win will be £0, and that would be a much better estimate of winnings than the mean (after all, the median will only be wrong for one person, the mean will be wrong for all of them).

john_s_2

Aegis wrote: »

Remember, that's the mean rather than the median return. In the case where you have extremely unlikely events, the median is arguably a better way to predict the return.

For example, if 1000 people are in a competition to win £1000, the mean return would be £1 if you assume a pure random selection. However, the median win will be £0, and that would be a much better estimate of winnings than the mean (after all, the median will only be wrong for one person, the mean will be wrong for all of them).

Hmmm... I dig where you're coming from, but the two competitions aren't comparable. Your competition is a one-off lottery. While premium bonds are continuous (or until you withdraw your 'stake').

Given a long enough timescale, an individual's winnings would tend towards the mean. The more they hold, the shorter this timescale would be.

On the flipside... I've had £1 premium bond for nearly 40 years, and another £100 for about five. I've never won a penny!

Aegis

john_s wrote: »

Hmmm... I dig where you're coming from, but the two competitions aren't comparable. Your competition is a one-off lottery. While premium bonds are continuous (or until you withdraw your 'stake').

It wasn't a direct analogy to Premium Bonds themselves, but rather a demonstration of when the median can be more appropriate than the mean. It's a simplistic problem, but it works well on a month-by-month basis.

Given a long enough timescale, an individual's winnings would tend towards the mean. The more they hold, the shorter this timescale would be.

True enough, but even in the long run the winnings would only tend to the mean if the top prize was won at least once. Most people can safely rule this chance out as statistically unlikely over the course of their life, so the expected value over a whole lifetime will in most cases be lower than the mean.

On the flipside... I've had £1 premium bond for nearly 40 years, and another £100 for about five. I've never won a penny!

Not too surprising given the odds

john_s_2

True enough, but even in the long run the winnings would only tend to the mean if the top prize was won at least once. Most people can safely rule this chance out as statistically unlikely over the course of their life, so the expected value over a whole lifetime will in most cases be lower than the mean.

I came back to edit my post to this effect. You've done it for me!

I don't know the probability off the top of my head but I'd imagine that it would take many lifetimes with £30K holdings before you would have a better than evens chance of winning the big one M. So I accept that it (and I daresay the 500Ks) should be taken out of the equation :-)