Why not Prize Bonds? Expected 3% tax-free

I understand the expected payout rate of Prize Bonds is 3% of deposits. Of course it's tax free, so the real expected 'interest' rate is more than 4%, and access is at only a 7 day delay.

Of course, the actual payout you receive may be more or less than 3%, but if you're 'risk neutral' and would otherwise be paying DIRT, why aren't Prize Bonds among the most competitive investments available now? Am I missing something?

Based on some figures I did last year:

The prize bond fund is around €1.05billion.
So there are around 168 million bonds in issue (each bond worth €6.35).

The prize structure is as follows:
€1,000,000 x 12 per year
€20,000 x 52 per year
€1,000 x 260 per year
€250 x 520 per year
€75 x whatever number is required to make the total pot of prizes 3%

The total prize fund is €1.05billion * 3% = €31.5 million per year.

Let's say you hold €6,350 in bonds - that's 1000 bonds out of the 168 million in issue.

Over a year, your chance of winning €1m is (1,000 / 168,000,000) * 12.
It's the chance that one of your 1,000 bonds is picked out, from the 168 million in issue, multiplied by the 12 chances you have to win the jackpot in each year.

In other words, you'll win the jackpot every 14,000 years per average.
The chance of winning the €1m prize is so negligible that it should be excluded from your expected return.

However, of the €31.5million paid out each year, €12m of that is made up of the jackpot. If you consider prizes that you actually have a chance of winning, only €19.5million is paid out each year. The interest rate, excluding the jackpot is €19.5million / €1.05billion or 1.86%.

Less attractive methinks.

Let's say you have €6.35 million to invest, then you can buy a million prize bonds, and your chance of winning the jackpot is much higher - you'll win it every 14 years on average. So for a long term investor with considerable funds, prize bonds may be a worthwhile investment. For everybody else, the current prize structure (weighted towards large but infrequent prizes) means returns are poor.

I agree with Camlin here. Prize Bonds fool the unwary into thinking that they have a higher expected return than they really do.

Prize Bonds
The company was set up in 1989 to operate the scheme for the Minister for Finance. The scheme is now operated on behalf of the National Treasury Management Agency (NTMA) which manages the national debt on behalf of the Minister for Finance. In 1999 the company submitted a successful tender to operate the scheme for a further 10 years until September 2009.

An Post is responsible for the accounting, marketing and the conduct of the draw. The administration is carried out by FEXCO in Killorglin, Co.Kerry.
Prize Bonds are a flexible, secure, state guaranteed investment. The top prize in the monthly Jackpot prize draw is €1,000,000. A top weekly Star prize of €20,000 is awarded each week. With a minimum purchase of €25, that's a huge return on your investment.


Draws are held every Friday with over 2,500 prizes ranging between €75 and €20,000. Every eligible €6.25 Prize Bond is automatically entered in the weekly draw no matter how old.


The more Prize Bonds you hold the greater the possibility of you getting a substantial return on your money.


The Prize Bond Company Ltd. is a joint venture operated between An Post and FEXCO.

The number of prizes awarded each week depends on the total size of the Prize Bond fund. It is currently calculated at a variable rate of 3% of the fund size per annum. This provides over 2,500 prizes every week.
Tax-free
All winnings are tax-free. In Ireland winnings are not liable to Income Tax, Capital Gains Tax, or D.I.R.T. (Deposit Interest Retention Tax).

Prize Bond holdings at 31 December, 2008

Number of separate Prize Bond holdings 5.61 million
Fund value €803.5 million

Source: The Prize Bond Company Limited Annual Report 2008

Analysis
The capital is very safe. You don’t risk the money you put in, only what interest you’ll get, and Prize Bonds are operated by An Post which is backed by the State.


What are the odds of winning :
The odds of any single bond winning the top prize are about 1 in 5.6 million (the number of bonds in circulation)
However the minimum investment is €25.

For comparison the odds of any one bond winning the £1M jackpot in the UK Premium bonds is now over 40 billion to 1.

You’re likely to win even less than the interest rate.
The value of prizes paid out is determined by an interest rate, which is currently 3%. This means if you owned every Prize bond in existence, the amount won over a year would be equal to 3% of what you put in.
So very roughly, on average for every €100 put into Prize Bonds, you'd expect a €3 annual return.


Yet because of the way the prizes are allocated, the majority of people will win much less than the interest rate anyway.


Don’t think of it as ‘winning’
The great attraction is ‘the lottery effect,' the chance of winning a dream, and there is of course the chance of winning a million. Equally you could be the next space-walking astronaut, and you’re odds probably aren’t that dissimilar!


The fact the payouts are commonly referred to as a ‘win’ rather than an ‘interest payment’ is psychologically devious. Comments like, “my friend wins €75 every few months” mislead; on clinical evaluation, someone with €10,000 of Bonds should ‘win’ €300 a year; that’s roughly €25 every month; yet the same cash in State Savings Certificates issue 17 could ‘win’ the equivalent of €470 a year.


Worse still, compare the Prize Bond interest to the average rate of inflation. Over the period Jan 1926 to May 2010 the average rate of inflation in the USA was 3.01%pa, German Consumer Price Index since 1948 averaged 2.61%oa, UK Retail Price Inflation since 1947 averaged 5.58%pa and the Harmonised Eurozone Inflation rate has average 1.95% since Feb 1996 which means that on average one should expect that the rate of inflation is almost certainly about the same as the the Prize Bond interest rate, so any cash you have in bonds is only increasing at best at the same as that of the prices of everyday goods. This means by holding bonds the real amount of money you have is not increasing.


Are they ever worth it?
Look at Prize Bonds with a clinical financial eye. Some will win more than the average, not many, but a few. And if you're that lucky person, this is a great return. Yet the odds of winning big get very long.


Prize Bonds aren’t as good as they first appear
It's all about the actual prize distribution. The following is the prize structure:

Monthly Jackpot Prize
12 x €1,000,000

Weekly star prize €20,000 is awarded each week

5 prizes @ €1,000

10 prizes @ €250

Over 4000 @ €75

Why most people win less than the interest rate

Even though Prize Bond rates stack up poorly compared to decent savings rates, even that’s still misleadingly generous; the real expected payout is much less, as it's massively skewed by the distribution of the prizes.

This is tricky to understand, so let me start with a simple example. Suppose there a contest offered a €1,000,000 prize and allowed a million people to buy a ticket costing €1. It could then be argued the average winnings per ticket were €1, even though 999,999 people would win nothing.

A similar, though less drastic, effect is happening with the Prize Bond interest rate; it says the payout is 3%, so you'd expect to win €3 per €100. Yet of course this is impossible, there isn't a €3 prize; you can either win nothing, €75, or more than €75. The big jackpot prizes, won by a miniscule number of people, skew the payout average and make the interest rate look much more generous than it is.

The situation that this throws isn’t a pleasant concept for Prize bond holders expecting an average of 3%pa.

On the surface Prize Bonds don’t look to be too complex. The winners are happily listed on the website with enough data to allow anyone with a calculator to work out the chances of any one bond winning a single prize over a month.

Yet to work out the chance of someone with a larger holding say five thousand bonds winning more includes countless variables. To win €1000 in one go could be one €1000 prize, or four €250 prizes, or a combination of smaller prizes; yet to win more than €500 holds scores of variables.

Plus of course, the draws are monthly, so if you’re calculating the assumed winnings over 5 years; it actually means you’re calculating the interaction of probabilities for over 60 draws to get the various answers.

To calculate the probability of winning is virtually impenetrable. You would need to use a very advanced multinomial probability equation.

Marc, I'm afriad that your analysis is deeply flawed.
Here are a few points that I picked out from your post

Marc said:

I Prize Bonds fool the unwary into thinking that they have a higher expected return than they really do.

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Do you know what expectancy means. THe expectancy is still 3% regadless of the distribution of prizes

Marc said:

Yet because of the way the prizes are allocated, the majority of people will win much less than the interest rate anyway.

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And those that win win several times more.

Marc said:

The fact the payouts are commonly referred to as a ‘win’ rather than an ‘interest payment’ is psychologically devious.

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It is effectively a gamble with your interest. You've alreadu pointed out that most people get nothing and others get a lot.

Marc said:

someone with €10,000 of Bonds should ‘win’ €300 a year; that’s roughly €25 every month; yet the same cash in a savings account could ‘win’ over €41 every month or €500 a year.

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Where the hell have you found a 5% return after DIRT. That would be an amazing rate of return.

Marc said:

Worse still, compare the Prize Bond interest to the current rate of inflation, which is almost certainly higher than the Prize Bond interest rate,

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Where are you getting your rate of inflation? Last time I looked it was around 1% and was negative only a short while ago.

Marc said:

The situation that this throws isn’t a pleasant concept for Prize bond holders expecting an average of 3%pa.

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I don't think prize bond holders do expect an average return of 3%. Most people are looking for a possibility to win big without losing their savings. Surely, it is a far superior way than the lottery to achieve this.

I think 3% after DIRT is a great expected return.As long as you understand it is a gamble but given it is a higher rate (after DIRT) than anyone else is offering, it is a gamble with positive expectancy

Has anyone got a source for the expected return of 3%. I can't find anything on the website?

OK, let's think about this from both a theoretical and practical perspective.....

Example: The expected return from investing in stocks is positive and is determined by the equity risk premium and capital asset pricing model. I have a positive expected return from investing in stocks whenever I buy according to the CAPM.

However, from a practical perspective if I had invested in the MSCI World Index in say Jan 2000 my actual return has been -2.26%pa. This is not to say investing is stocks is bad idea, I just had a bad experience. Let's call it bad luck.

So, you say the expected return for an investor in Prize Bonds is 3% and the distribution of the prizes doesn't matter. Correct from a theoretical perspective. Provided that you;

(a) held every prize bond in existence for
(b) an infinite period of time,

then your expected return is theoretically 3%pa.

Now, let's consider this from a practical perspective
(a) I'm not rich enough
(b) is impossible.

You say that you "don't think prize bond holders do expect an average return of 3%" I would argue that savers putting their hard earned into Prize Bonds must have a positive expected return and I would suggest that the expectation is 3% since;

(a) This is what the marketing material says it is
(b) This is exactly the point the original poster was making

My point is simply this, the way in which the prize fund is distributed means that the chances of winning the occasional large prize are extremely slim and this means that the average actual return (in practical terms) is less than 3% for most savers.

I think the important point to communicate here is that on average (and on average we are all average) anyone buying Prize Bonds will probably (and this is what matters) not "win" 3%pa. Prize Bonds are therefore a bad investment. Period.

The CAPM is irrelevant and makes no assumption about a positive expected return from stocks anyway.

You are correct that expected and actual returns rarely match and just becasue they don't match, it doesn't mean the original expected return calculation was wrong.

For Prize Bonds, expected and average return are 3% whatever way you look at it.
What you are talking about is the median return.

Say there are 11 poasible oucomes of prizes (all equally likely)

0,0,0,0,1,2,3,4,5,6,100000

The expected return here is 9092.82
The median is 2.

You are correct that the median for prize bonds is much less than 3%.

You can't have it both ways, a steady 3% return with the possibility of big prizes.

Well, it doesn't sound too bad to me. It's correct to say that the return is 3%, but this isn't guaranteed, it's an average return.

I'd say that someone with about 3,000 'invested' would make about 3% or a little under. I'd be interested in seeing a calculation showing how much under,.. I'd guess that someone with 3,000 Euros worth might earn 2.6% and someone with 30,000 Euros worth would earn closer to 2.8%... anyone know or care how to calculate this? It's clear that someone who owned them all would earn exactly 3%, and someone with 25% of the total would likely also win 3%.

I'm basing the on the fact that only 16 prizes a week are greater than 75 Euro, and there are 2,500 prizes of 75 or less... so I'm not sure of the skewing effect of the massive prizes. I'm going to look at the figures and report back... I don't think I'll be capable of a complete answer, but maybe just some pointers.

The chance of winning a life changing amount has to be taken into account, even if it is a very small chance.


edited to add: for bonus points, can someone say what percentage of the total prize bonds fund must one person own in order that they have a 50-50 chance of obtaining a return of exactly 3%.. (they will also have a certain probablity of winning more, or less, both of these should make up the other 50 of the 50-50 chance)


I'm assuming here that the expected return increases as the number of prize bonds owned goes up, but this might be a mistake... the expected average return for everybody, or for each prize bond is 3%... is there actually a skewing effect due to the prizes or not?

But the chance of winning a huge amount is real. The average expected return is also 3%, which isn't bad.

There is a skewing effect of the prize structure, but we haven't yet seen any figures to illustrate how large it is. Large holders may win more than 3% per year, making it a more attractive investment for them.

I don't think the skewing effect is very large, or significant, PROVIDED that the number of prize bonds held exceeds a certain number, .. perhaps 3,000 Euros, but definitely for amounts of around 30,000 or more...

And for amounts of 30,000 or so, then the chance of winning the big prizes may become significant. And winning a large amount would be life changing, which is hard to quantify.

It's better than the lotto I'd say.


edited to add.
Ok, the skewing effect is real and is quite large... this is because a huge amount of the prize fund is given out in very large prizes.. about 40% or more of the total prizes is given out in the 1,000,000 prize.. so I now think that the expected average return would be more like 1.8% or so,.. and the remaining 1.2% is what you pay for the chance of winning the 1,000,000.

Basically what Camlin90 said in the second post...

Still better than the lotto I reckon.

According to the Annual Report and accounts for the year ended 2008 the total prize fund was €20,259,775 from a total fund of just over €803M

There are slightly over 5.6M separate holdings in issue.

So, if everyone held the same number of bonds, the odds of any one household winning the Jackpot each month are about 1 in 5.6M.

To put that into some perspectice, the odds of being on a flight which results in at least one fatality whilst on a plane operated by the top 25 airlines with the best accident rates is about one in 5.4 Million.

Or, according to the UK Met Office, the odds of being struck by lightning are about 1 in 3 million.

Finally, from the Mirror Newspaper (so it is almost certainly made up) the odds of left handed people being killed while using a right handed product 1 in 4,400,000.

96.754% of statistics are made up on the spot - Spike Milligan.

The figures don't seem to add up.

If there are 5.6m bonds, and the price is 6.35, then there'd be only 32 million Euro or thereabouts in the fund.

Would there not be about 123million prize bonds, each at 6.25... giving about 803 million?

So the odds are worse now... about 1 in 10 million of winning the top prize once in a year, per prize bond.

Still not bad in my opinion... if someone diverted their 6.25 lotto money to buying a prize bond each week... after five years they'd have 250 bonds... or a 1 in 40,000 chance of winning the top prize per year.

Joe, you are correct 5.6m is the number of separate holdings or "households"

I don't have a copy of the latest accounts so I can't verify Camlin's numbers at the start of this thread. However, if all households held the same number of bonds, then the chances of a household winning the jackpot would be 1 in 5.6 M. But we know that everyone doesn't have the same allocation of bonds.

The crux of this problem therefore is working out the probability of winning based on a variable holding of bonds over a variable period of time. Sadly, this isn't as easy as dividing the prizes by the number of bonds.

The maths to do this has been cracked in the UK for Premium Bonds and the program took 3 months to develop by a post-doctoral cosmology statistician. The program takes 6 hours to run each month to update the numbers.So, back of fag packet guesses at the chances of winning will probably be extremely wide of the mark.

Marc said:

Dubrov, I don't understand your point.

I thought that the CAPM said (and I paraphrase here) that the expected return from a stock equals the investors' required rate of return which in turn equals the cost of equity capital for a stock.

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Expected return is an inpuit to the model. I guess if the expected return never exceeds the risk free-rate then it would never be worth investing so I take your point. It is very subjective though when it comes to stocks.

Anyway, I think we are sort of agreeing. The difference comes from CAPM assuming that investors are risk-averse. i.e. they requrie a higher return for higher risk.

This is normally the case for investors. However, some people actually would like higher risk and Prize Bonds may may sense for them. Lottery players are similar in this respect albeit with much lower expected returns.

I'm not saying prize bonds are the best investment in the world but they have their place alongside other products.

A guy I work with won 3 prize bonds about 3 years ago and won €75 this week on one of those, I told him that he should buy 3 more with the €75 as he is very lucky. I have some with a good number of years and have never won anything on them, but I do know a few people that have won €75, so I live in hope!

As with all investments, it is all depending on your clear understanding of the risks involved which a lot of people dont have.

Don't forget, this country is full of people who didn't realise that buying a highly leveraged investment property with an interest only mortgage was a high risk investment.

The average return from the prize bonds may be theoretically 3%, but in reality, as the figures here has shown, the actual average return for someone with prizebonds, is much lower and probably close to 0%.
This is only a problem if you dont realise this and believe the marketing blurb that your "investment" is safe and haven't realised that your "investment" is being eroded over time by not keeping pace with inflation.

I have a small number of prize bonds, which I consider a gamble, but a lower risk gamble than the lotto or the horses.

I have examined the odds of winning in a little more detail. I have made a surprising discovery!

I'm assuming the following...
Total fund = 800 million.
total prizes, per year = 3% = 24 million
total of 12 x 1,000,000 prizes = 12 million
number bonds = 128 million


prizes = 12 x 1,000,000, one draw per month
1 x 20,000 per weekly draw
5 x 1,000 per weekly draw
10 x 250 per weekly draw
this leaves 2710 prizes of 75 Euro per weekly draw



Ok, so asking what the expected average return is is the wrong question, as the answer is always 3%, no matter how you look at it. So different questions need to be asked, such as .. how many bonds does one need to own in order to have a 50-50 chance of winning 3%, in a single year?



But I asked some other questions... for example, what proportion of your winnings should come from each of the prize values?, and this leads to an interesting discovery. Previous to 2007 there was no 1,000,000 prize, then in 2008 there was 4, now there are 12 x 1,000,000 per year.


Each bond worth 6.25 should get 3% per year, which would be 18.75 cents per year... so how much is contributed to this from each of the prize values????

Well, currently, with 12 x 1,000,000 prizes, the breakdown of each prize value is...
1,000,000 contributes a massive 9.4 cents to the 18.75 cents, more than half!!! The bread and butter 75 Euro prizes contribute less, at 8.26 cents per year.

This is a huge change... when there were only 4 x 1,000,000 draws then the million prize only contributed a paltry 3.13 cents per year, and the 75 Euro prize contributed a massive 14.5 cents to the 18.75 cents yearly total.

So increasing the number of 1,000,000 has drastically changed the game... now you are contributing over half of your supposed winnings to gambling on winning the top prize, which is unlikely. Previously you were only gambling about 15% of your winnings.

So now it is far more like an exceptionally fair lottery, with nearly perfect fairness, but no advantageous odds, they are very slightly below fair odds,.. not quite exactly fair due to rounding issues.



I also calculate that in order to have a 50-50 chance of winning your fair 3% in 75 Euros prizes you must own 455 Bonds, worth approx 2,840.. but I'm not 100% certain of this calculation. Some advice on how to add odds would be appreciated.



For example the odds of getting heads once in a coin toss is 50%... but getting one head from two throws is 75% (you can also get two heads), and getting exactly one head from two throws is 50%.

So if the odds of winning a prize per Bond are 1/10 say... what are the odds if you own two bonds, and either or both can win?.. is it 2/10? This is confusing as if you own 100 Bonds then the odds are 10-1 in your favour if you simple added the odds... so that can't be correct.

And considering coin tosses... it's not clear how the odds of .5 on each throw, lead to odds of .75 when considering two throws???? But the .75 odds are absolutely correct, from two throws....

Nice post.

It shows that if you have a decent enough size of bonds, you can roughly expect to be saving half the interest earned and gambling the other half to win the big prize with fair expectancy/

JoeBallantin said:

So if the odds of winning a prize per Bond are 1/10 say... what are the odds if you own two bonds, and either or both can win

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You easiest thing is to think abot this another way.

The odds of either or both to win = 1 - odds of both to lose

The odds of both losing are
(9/10 * 9/10) = 81/100

So The odds of either or both winning = 1-81/100 = 19/100

Another way is:

THe odds of exactly one winning is 2 * 1/10 * 9/10 = 18/100
(The two is because this can happen 2 ways, Bond A wins and B loses or viceversa)
THe odds of both winning= 1/10 & 1/10 = 1/100

Ths sum of the two still adds to 19/100

Hi

That's great, thanks for the tips on combining odds.

So now I have new figures for the probability of winnning certain prizes with certain
degrees of certainity. This idea of 'Degree of Certainity' is a good one. I got it from the following link.
http://saliu.com/theory-of-probability.html

The guy gives good info on how to calculate odds when doing multiple trials. I have to learn a little about logs before I can re-arrange some of the equations to get good answers.


But I've got the following so far.. still not sure if this is actually correct or not.

How many Bonds must one own in order to win the expected 3%, from only 75 euro prizes, with the following Degrees of Certainity.

50% certainity = 630 Bonds, value 3,938 Euros
99% certainity = 4,181 Bonds, value 26,130 Euros
99.9% certainity = 6,271 Bonds, value 39,194 Euros
99.99% certainity = 8,362 Bonds
99.999% certainity = 10,452 Bonds

These figures for the Bonds are increasing in a arithmetic sequence when I add extra 9s to the 99.999%.. I don't think this is correct, I think the numbers should increase geometrically.. which is why I think I may have made a mistake.

i.e 2,4,6,8,10 = arithmetic
2,4,8,16,32 = geometric

I'm interested in getting a full solution, any help, tips or pointers would be great.

Cheers

I was thinking about this recently. I've studied probability but I really couldn't be bothered doing the math. What I have done though is I've bought 6,400 prize bonds (total spend €40,000). They way I see it I am forgoing around €600 in interest but if I only win a few €75 prizes it will reduce that. My capital is safe so I have limited downside (my interest or the erosion of my capital due to inflation over the period I keep the bonds) and a chance of a good upside. I will only keep them for six months as I think that they are a horrendous long term investment.

I have always been sceptical of prize bonds, as although I know quite a few people who have won decent prizes in the lotto, I have never met anyone who won a red cent on a prize bond. If I don't win anything (not even a €75 prize) I will have confirmed (for myself) that they are a waste of time.

I would never do this in a high interest rate environment but now is not a bad time to have a flutter.