We've written a lot recently about the worsening odds on premium bonds, broadly concluding that . Yet over 23m Britons own them - far outnumbering those who invest in shares. So it's interesting to compare premium bonds not to cash savings accounts, but to equities.
They have a lot in common. Both offer uncertain returns, but in different ways. My table, constructed with the help of Moneysaving Expert's premium bond calculator, shows the differences. It shows the probabilities of various returns to a £30,000 investment over a 12-month period. The equity pay-offs are estimated on the assumptions of a five per cent return (just above the current yield on the All-share*) and volatility of 32.4 per cent: Euronext's FTSE 100 volatility index. I've expressed the probabilities as parts per 10,000 to avoid lots of zeros in the last column; don't regard them as accurate to this degree. I've chosen £30,000 as that's the maximum permissible investment in premium bonds.
Premium bonds vs shares: pay-off probabilities
| Investment gain | All-share | Premium bonds |
|---|---|---|
| Less than 0 | 4387 | 0 |
| Less than £500 (1.7%) | 4594 | 9607 |
| More than £1,000 (3.3%) | 5210 | 70 |
| More than £5,000 (16.7%) | 3590 | 7 |
| More than £10,000 (33%) | 1937 | 3 |
| More than £50,000 (166%) | 0.003 | 0.5 |
The figure in brackets is the percentage of £30,000 represented by that particular gain. The probabilities are parts per 10,000
You can see that these distributions of returns differ in three ways:
• Premium bonds offer no chance of a nominal loss - your capital is safe - whereas equities offer a big one - over a two-in-five chance.
• The odds of a reasonably nice return are vastly greater on equities. The chances of making £5000 or more are around 500 times better on shares than on premium bonds.
• The odds of a really spectacular gain are actually better on premium bonds. You have a one in 18,381 chance of winning £50,000 on premium bonds. That's minuscule. But it's around 200 times better than the odds of such a gain on shares**.
However, the average investor strongly prefers premium bonds' distribution of returns to shares' distribution. He is happy to accept an expected return of just 1 per cent on premium bonds, but would turn his nose up if someone offered him similar returns on the equity market. Behavioural finance tells us a lot about why this should be:
• The marginal utility of wealth is non-linear. For most of us, another £5,000 won't change our lives. But £50,000 might. So we pay extra - in terms of foregoing returns - for assets that offer a better chance of paying £50,000.
• Loss aversion. We don't want to lose money. You can do this with equities, but not premium bonds. So we accept lower returns on the latter as a quid pro quo.
• The buzz of gambling. With premium bonds, we get a little frisson of excitement each month as we check whether we've won - a buzz which is not diminished by the fact that we can't lose. There's no such buzz from looking at what the stock market has done.
• Blindness to opportunity costs. The truth is that premium bonds do lose us money - because we could get a better interest rate, on average, on building society deposits. This is not an absolute loss, though - it's a gain foregone. And we tend to underweight these, relative to out-of-pocket losses.
• Mental bundling. If the FTSE 100 rises just 41 points, you make more money on a £30,000 tracker fund in a day than you would in an average year on premium bonds. But this £300 gain would probably make you less happy than an equivalent amount of premium bond prizes.
There's a reason for this. Because we know equity returns are volatile, we mentally bundle up today's gain with yesterday's (and tomorrow's!) loss - and vice versa. We take little joy in a good day for the market because this is the price we pay for insulating ourselves from the pain of a bad day.
By contrast, a win on premium bonds isn't tied to any bad news. It's pure fun.
• Mental accounting. Many of us regard shares and premium bonds differently. Shares are a "serious long-term investment for our pension", whereas premium bonds are "a bit of fun", with the prizes to be used to buy treats - little ones at current rates. So we just don't think of them as alternatives, with premium bond holdings as being a sacrifice of potential equity returns.
• Tangible money. A premium bond prize comes in material form - a cheque - whereas an equity gain is merely an addition to some account, so it looms less large in our mind. Better still, the cheque is from the government; I like to think my cheques are written out by Gordon Brown personally, in his own blood.
Herein, though, lies an awkward fact. Most of these motives are completely irrational. So, might it be that our love of premium bonds - which I share - is not wholly founded in reality? Still, the government needs all the help it can in raising money....
* This implies an expectation of almost zero price growth over the next 12 months or an equity premium of 3.1 per cent over 12 month Libor. Tweaking this number obviously changes the numbers in the table but - unless you assume a very strange expected return - does not affect the substance of what follows.
** This assumes equity returns are normally distributed. Assuming a power law distribution with exponent three substantially improves the chances of equities doing this well. But the odds are still 13 times better for premium bonds than for shares.
*** Full disclosure: I own the maximum amount of premium bonds allowed!
