#### Raging Bull

##### Frequent Poster

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- Thread starter Raging Bull
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The interest rate currently being used to determine the prizes is 1.75% tax free. www.prizebonds.ie

This is a comparably attractive rate.

You can access the money at any time - no penalties

Compared to the 1.375% (2.5% gross) you can get on the best instant access deposits, this is indeed attractive.

Even if you win nothing, you are giving up only 1.375%.

It was different when rates were 5%.

In my experience, you'd need to be very lucky to win anything substantial on a 4k investment in prize bonds, as there are currently approximately 280 million of them held.

I suppose if you won even the smallest prize of 50 euro just once a year, you'd be no worse off than if you'd placed it on deposit (with an outside outside chance of winning something bigger). If...

You need to factor in odds as a comparable factor to deposit interest. Odds are not specially driven by the 'average' rate of return that the NTMA pay on State Savings Prize Bond prizes because very few people get the 'average'.

€1,000,000 is given to 1 person 6 times a year. With 6 million (the last figure I can find) of Prize Bonds in circulation, the changes of you winning this in per year are approx. 1 in 1 million. Hence, you have a 0.00001% chance of winning this per year.

€20,000 is given to 1 person 52 times a year. With 6 million (the last figure I can find) of Prize Bonds in circulation, the changes of you winning this in one year are approx. 1 in 115,384.

There are small prizes of 50 EUR to 1,000 EUR. You would need to use countless variables to work out the real probability, suffice to say that it is low, very low, of getting any meaningful return.

The 'average' person gets far less than 1.75%.

Marc did a great post on this a while ago, the post is very dated, with old rates of return, but the principle remains the same.

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Hi CiaránYou would need to use countless variables to work out the real probability, suffice to say that it is low, very low, of getting any meaningful return.

But there is no meaningful net return on ordinary deposits either.

If the choice is between

a) A deposit paying 5%

and

b) A Prize Bond with an average return of 5%, but a 99% chance of 0 and a 1% chance of 500%

I would choose a)

But if it's between

a) a net reurn of 1.5%

and

b) An average of 1.75% with a 99% chance of 0

I just might go for b)

Brendan

I have worked out some rough numbers based on the latest data on the website.

At the end of April this year according to prizebonds.ie the total amount in prize bonds was 1.7 Billion and the "interest rate" is 1.75%

1.7 billion times 1.75% = 29,750,000 in prizes.

Remove the 1m jackpots (every 6 months) that you probably won't win from the prize fund

= 29,750,000 - 6,000,000 = 23,750,000 realistic prize fund

Divide that back into the bond pool of 1.7 billion and you get 1.397%

So a more meaningful "interest rate" for prize bonds is 1.4%

Now build in a risk factor which is that some months you will "win" less than this "average" in fact for some people they may win nothing at all. Of course someone has to win the jackpot.

So just how likely is this? There are 280 million bonds in issue so every other month each bond you own has a 1 in 280 million chance of winning a million.

The problem with grasping the smallness of "1 in 280 million" is that we never see 280 million objects. I am one of 4 children in my family - easy. But one in 280 million cannot be readily visualized.

Have a guess how many years 280 million seconds is..........answer at the bottom

We therefore tend to overestimate the likelihood that we could win the jackpot and this is compounded by the fact that every other month someone actually does win.

We also know that people prefer impossibly small chances of winning but hate any chance of losing. Hey, your original stake is safe and you can have it back anytime ( less inflation and the opportunity cost of the lost interest you could have made if you had done something sensible)

If you buy more than one bond in the hope of improving your chances of winning the jackpot , you really just expose more of your savings to the risk of earning less than the average 1.4%pa. Until you are able to hold every single bond in existence for an infinite period at which point your prize is exactly the 1.75% interest rate.

The only body capable of pulling off that feat is NTMA who win the prize of borrowing your savings at an interest rate of just 1.75% rather than much higher rate in the bond market.

280 million seconds is 8.872 years. Just say tick tock to yourself, now imagine that for nearly 9 years .

You have to randomly select just one of those seconds over that whole period.

Pick any date in the future: On wednesday 20th December 2017 at 10.45 in the morning and 26 seconds or is it 27 seconds?

A 1 in 280 million chance of getting the top prize (and there are not many small prizes anymore) needs to be factored into anyones decision when choosing between deposit products and Prize Bonds.

Brendan, whilst I see where you are coming from, I think the probability of a zero return via Prize Bonds is far too high to justify choosing Prize Bonds over deposit products or other investment products.

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You are working out the chances for someone with €1 invested for exactly one year.

I think you should work out what the Expected Return is for someone who has €100,000 invested.

And most people don't invest for one year. They leave their deposits there for the long term. So I would imagine that their return would average out at the 1.397% return you have calculated.

For someone who is putting there money away in three year NTMA Bonds at 1.3%, it's roughly the same return, but with access to their money.borrowing your savings at an interest rate of just 1.75% rather than much higher rate in the bond market.

Just to be clear - I think that people should hold a diversified portfolio of shares and not be bothering with deposits of any sort. But for people who are invested in deposits, Prize Bonds are now relatively attractive.

Hi Brendan, with the changes in interest rates and hikes in DIRT and PRSI, I'm considering putting a considerable chunk in prize bonds. I did some calculations on likely returns and thought I would share them here. Although, as Marc has said, an exact calculation of the odds of a given return is complex, it is easy to simplify roughly to within any given confidence level. (The likely returns are a little less than what Marc calculated). The main thing for people to bear in mind is that for a small investment, your chances of an average return are negligible, and Prize Bonds areI think you should work out what the Expected Return is for someone who has €100,000 invested.

The prize fund is split between a small number of large prizes which you have essentially no chance of winning, and a large number of small prizes which -- if you invest enough -- you can reasonably rely on an average return from.

Your chances of achieving an average return increase with the amount of money you invest. Note that your return may be more or less than the average no matter how much you invest, but the chance of getting near the average are better for higher amounts and longer periods of investment.

For an investment of €10k to 100k you will probably achieve about 1.18% (equivalent to 2.1% from a bank account assuming 41% DIRT + 4% PRSI). For an investment of 100k+ you may achieve 1.33% (equivalent to 2.4% assuming DIRT and PRSI). Note that these are all probabilistic values with reasonable confidence levels. If you want the excruciating detail, read on.

The total prize fund is currently calculated at 1.75% of the value of total Prize Bonds held. Latest figures are as of April 2013 and can be viewed on the State Savings web page. Since the total value is currently €1.7b (made up of 280m individual Prize Bonds), this gives a total annual prize fund of €29.75m, structured as follows:

€1,000,000 x 6 times annually = €6,000,000

€20,000 x 46 times annually = €920,000

€1,000 x 5 times weekly = €260,000

€100 x 500 weekly = €2,600,000

Now, ironically, the above details can be almost ignored, since you won't be winning any of that. Almost all of your returns will come from the €50 prizes which make up the remainder of the prize fund. The only reason for the above calculation is to subtract the money you won't win (€9.78m) from the total prize fund (€29.75m) to give the total value of €50 prizes: €19.97m. This works out at 399,400 x €50 prizes per year.

It would be messy to calculate odds based on number of prize bonds held. It's easier to calculate your fraction of the total prize bonds by dividing your investment into the total monetary value of all bonds. For a holding of €100,000 you have €100k/€1.7b = 1/17,000 of all bonds. This is very important!

Unfortunately, few people have an intuitive feel for odds and risk. Think about those €1,000 prizes, 5 times weekly. There are 260 per year. With your investment of €100k you will win one on average every 17,000 / 260 = 65 years. Do you want to bet on a return that might come in every 65 years (or might not)? Clearly not. There's a good chance you won't collect on it in your lifetime. Still, it's worth thinking about this in terms of confidence levels. These are a little complicated to work out so I won't go into details, but will just state that: you have a 50% chance of winning that €1,000 prize within 45 years. If you want a 90% level of confidence, you will have to wait 150 years. And to have a 99% chance of winning, you will wait 300 years!

Now, I'd be prepared to treat a 99% chance of winning as a fairly sure bet, although I'd still want to think about the consequences of the 1% chance that I

Hopefully it's obvious that there's no point even thinking of winning any of the big Prize Bond prizes, unless you are a gambler rather than an investor. On the other hand, look at the number of €50 prizes annually -- 399,400. With your €100k investment you stand to win 399,400 / 17,000 = 23.5 per year on average, or nearly one per fortnight. Just as importantly, we want to know what the confidence level is that you will achieve this average or close to it. Here we have to use some horrible statistical methods again (the binomial distribution, for anyone who wants to check it out), so I will just state the result: there is about a two thirds chance that you will win the €50 prize between 20 and 28 times annually, and a 92% chance you will win it between 16 and 32 times. The long and short of this is that "your mileage may vary" but there is a good chance you will get close enough to the average.

So what is the

The difference in lumpiness should be obvious. For €10k you will win 2.35 times on average, but there's a hefty 9% chance you'll win nothing at all in a given year, and only a 70% total chance that you'll win 1 to 3 times. Things are much smoother with the €100k -- you could still win nothing but the chances are tiny: much less than one in a billion! The chances are less than one in a hundred that you will win less than 14 times (or more than 35 times).

So, an average return of 1.175% would be the final answer except that between the €1000 (and upward) prizes that you will

Remember, this is all statistical.

The numbers I used here are based on the Prize Bond FAQ which gives a total value of outstanding Prize Bonds of €1.7b as of April, and an implied number of €50 prizes of 399,400 per year, or 7,680 per week. However, the front page of the Prize Bonds website states that there are now over 8,000 €50 prizes per week. And the results for the latest draw (currently 15-Nov-2013) show 9,346 prizes in that week. Subtracting the 506 prizes greater than €50, that leaves 8,840 €50 prizes. Now,

EDIT: add graphs

EDIT2: update with finer grained graphs.

EDIT3: add caveat about increase in outstanding bonds.

EDIT4: update with more accurate graph and numbers based on using Stirling's formula

My wins so far are

Week 1: 1 x 50

Week 2: nothing

Week 3: nothing

Week 4: 2 x 50

Week 5: 1 x 50

Week 6: 1 x 50

Pleased with that so far and if it continues for a year the return will be just over 2% net, higher than I'd get with a one year fixed term deposit.

I confess to getting quite excited at 12:30 every Friday logging onto prizebonds.ie and knowing that there is a good chance that I'll win 50 quid.

Also, I put my winning cheques into ten year Solidarity Bonds so I'm compounding my returns. Handy that the minimum amount for SBs is 50 euro.

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Great post also.... it gives actual returns and i can identify with the feeling of excitement on a Friday checking your numbers,,, to steal a quote from an advert ... PRICELESS

My wins so far are

Week 1: 1 x 50

Week 2: nothing

Week 3: nothing

Week 4: 2 x 50

Week 5: 1 x 50

Week 6: 1 x 50

Pleased with that so far and if it continues for a year the return will be just over 2% net, higher than I'd get with a one year fixed term deposit.

I confess to getting quite excited at 12:30 every Friday logging onto prizebonds.ie and knowing that there is a good chance that I'll win 50 quid.

Also, I put my winning cheques into ten year Solidarity Bonds so I'm compounding my returns. Handy that the minimum amount for SBs is 50 euro.

anyway i invested last week, a tidy sum also, will let u know how i get on.

Pat

On the other hand, my numbers could be wrong. MS Excel can't come close to calculating totally accurate odds for such a vast number of possibilities (...try calculating factorial 399,400!), but I would expect my approximations are very close.

Would be good if you and postman_pat gave us an update a couple of times yearly. I'll do likewise if I take the plunge.

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Will do..anyway got my numbers in post today,checked them...guess what!!..won €50

My wins so far are

Week 1: 1 x 50

Week 2: nothing

Week 3: nothing

Week 4: 2 x 50

Week 5: 1 x 50

Week 6: 1 x 50

Pleased with that so far and if it continues for a year the return will be just over 2% net, higher than I'd get with a one year fixed term deposit.

I confess to getting quite excited at 12:30 every Friday logging onto prizebonds.ie and knowing that there is a good chance that I'll win 50 quid.

Also, I put my winning cheques into ten year Solidarity Bonds so I'm compounding my returns. Handy that the minimum amount for SBs is 50 euro.