I have always maintained that crossing the zero bound to negative yield results in behaviour that doesn’t cross as easily and instead diverges into a new dimension of imaginary numbers that leads to craziness. But here is a thought to add to the interest rate negative absurdum files. Premium Bonds.
For non-UK readers, Premium Bonds are a UK Government perpetual bond that instead of paying the coupon as a fixed guaranteed payment, pools the interest due and allocates it to the bond holders by a lottery type draw. Bond numbers are drawn each month and prizes paid that equate to the total interest pot. There are multiple small prizes but they scale down in number to a single £1,000,000 prize per month. The bonds are always redeemable for original face value. The average yield on the bonds is currently 1.35%.
The UK National Lottery, by contrast, has a negative yield as about half of the money from the ticket sales is paid back in prize money. As we all know the ticket is not redeemable for face. So the expected yield on a lottery ticket is about -50%. Despite this monstrously negative yield people still buy them for the dream.
With public willingness to buy -50% yield you can see why the regulator has to step in and licence lotteries so that we all can’t cash in and borrow at such negative yields from the pool of dream money. But what if the State were to cross the zero yield line with their Premium Bond issues and move into negative yield territory?
The dullest and probably the most predictable way to do this would be to sell the bonds at a premium to face but as these are perpetuals pricing to maturity is not possible so instead the amount of bonds held could be scaled back depending upon the purchase date and time the Premium Bond is held, letting the holding effectively decline to near zero in a half life function.
But the really fun way of taking Premium Bonds negative yield is to follow the rules they currently abide by where the pool of interest is allocated by lottery. Now imagine if that pool of interest is negative. One (un)lucky owner of the Bond that is drawn now receives a letter
“Dear Mrs Smith, Congratulations! Your Premium Bond has been drawn and you owe the state £1,000,000”
A few thousand others will be receiving a letter saying they owe the state smaller sums.
Would they sell? Of course not because no one would like to own (in personal finance terms) unlimited downside even if the maths says there is huge chance of escaping any negative yield with a ‘miss’. The organiser of a lottery has the advantage of knowing the averaging will work for them as they own the whole market. An individual buying or issuing one ticket does not and will risk the vagaries of probability.
Which then leads me to ask how great does the capital gain of a premium bond have to be before an individual is willing to buy one to compensate the perceived risk of a one off down side hit. If you receive a 20% capital yield on your ticket what maximum down side would you be willing to bear, even at a tiny probability, to buy the ticket.
The balance between capital return and prize coupon is one of complexity that could be part of a behavioural finance study. Perhaps the way to run it is by setting up a real market test and let the market find its own level. The payoff between capital return and coupon is relatively easy in bond maths but how interesting it would be if the government was to issue a form of Premium Bond where the individual could choose the balance between negative coupon they may wear, if they are unfortunate enough to get drawn, against the yield if they don’t get drawn. As an issuer the State can gear it so the pay-off on average is always the national interest rate but it is up to the individual to choose their preference. Or they could let the market find its own level and with the proven bias towards paying over the odds for hope, as expressed by the market for -50% lottery tickets) the State may well find its borrowing cost go pleasantly negative without them even having to try. Bizarre but probable.
Credit risk on the individuals ability to pay an enormous penalty loss is of course a massive consideration, but as an experiment the results would be a benchmark in behavioural finance and risk perception.