Martin Lewis on Premium Bonds

eskbanker

Audaxer said:

eskbanker said:

Audaxer said:

eskbanker said:

Audaxer said:

eskbanker said:

Audaxer said:
If you had £5,000 in PBs your expected win rate for a year would only be £25 (0.5%) as detailed in the table under section number 3 on the following page:

Premium Bonds: are they worth buying? - MoneySavingExpert

So you're assuming that the article is more accurate than the calculator?

Yes, because I think with average luck you are more likely to win slightly higher percentages, the more PBs you hold.

Sort of - if you have a maximum holding and keep it for many years, then eventually you should have a reasonably significant prospect of winning one of the bigger prizes that make up the difference between the 0.9% median and the 1% mean, but that factor is irrelevant if comparing, say, £5K with £25K over a year.  Rounding does have an impact, especially on small holdings or durations, but as above every bond has an equal chance every month, so it's not true in any meaningful sense that pro rata winnings are higher for larger holdings....

As every bond has an equal chance, surely the median percentage winnings is likely to be higher (although still below 1%) if you hold 25,000 bonds as opposed to 5,000 bonds?

I don't understand why you'd expect the percentage to be higher - the expected winnings in absolute terms will naturally be higher, but in percentage terms it should be constant, subject only to rounding.  However, even when rounding affects the median expected winnings, looking at the actual odds of achieving that median will paint a more complete picture, and hence my comment on the previous page about £5K and £7K both having the same median outcome over a year but different odds of achieving it.

The MSE article, and the calculator, largely ignore this last point and hence the misleading and apparently illogical presentation of expected outcomes listed in that table that you refer to.

In his on-line video (and on his recent TV show) Martin Lewis included a table showing 'Typical Luck Annual Winnings' with the following holdings and percentages:
£100 - 0%
£1,000 - 0%
£10,000 - 0.75%
£25,000 - 0.8%
£50,000 - 0.9%

That is why I'd expect the percentage likely winnings to be higher, the more bonds you hold. 

And that's why selective presentation of results like that is highly deceptive and misleading!

It may be true that the expected returns from £100 and £1000 are both zero, but the former is a 96.6% chance while the latter is 70.6%, i.e. 3.4% versus 29.4% chance of winning a prize, a huge difference.

0.75% from £10K is 68.4% over a year, but that's just because of rounding, in that the chance of at least 1% (the next prize) is just below 50%, so the median by itself isn't particularly representative - holding £10K for five years gives a median outcome of £450, i.e. 0.9% annually.

0.8% from £25K is 66.8% but the next data point chosen by MSE is 1% (42.1%), so the former is more likely than the latter but neither is really the median, in that if they calibrated their calculator to show the odds of a 0.9% return then that would be the most likely outcome.

Bottom line is that for all holdings, the median outcome is 0.9%, rounded down to the nearest multiple of £25, but where that rounding is significant (small holdings or durations) then condensing everything down to a single figure is too simplistic, so the actual odds of both the rounded down and the rounded up figures need to be measured to give a more realistic assessment.