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# Prize Bonds: How the math works

This is a very popular financial instrument built to leverage willingness of people to take a ‘chance’. It’s probabilities at play. Through prize bonds, the gov. raises debt & instead of paying interest to everyone, it pays a jackpot to a few.

There is a 0.0002% chance to win the first prize in a year, and that is still better than the probability of dying in a plane crash (c. 0.0001%), so those who are afraid of flying, there are higher chances of you winning the jackpot, than dying in a plane crash. Imagine that.

Now lets look at the PKR 750 prize bond. The first prize is PKR 1.5 million, the second prize is PKR 500k (there can be 3 winners for the second prize), and the third prize is PKR 9,300 (there can be 1,696 winners for the third prize.

The government gives out the following ‘winnings’ at every prize bond draw of PKR 750 bond.

First Prize: PKR 1.5m * 1 = PKR 1.5m
Second Prize: PKR 500k * 3 = PKR 1.5m
Third Prize: PKR 9,300 * 1,696 = PKR 15.772m

Total winnings distributed by the government: PKR 18,772,800

There are four draws in a year, so total ‘winnings’ distributed by the government in on full year is: PKR 18.77m * 4 = PKR 75.09m

So we now know that every year, Government pays out PKR 75.09m on a single series of a PKR 750 prize bond.

Now how many prize bonds of PKR 750 are in issuance? One ‘series’ has 999,999 bonds — which means that 999,999 bonds with value of PKR 750 each were sold by the government to raise PKR 749.99m (PKR 750 * 999,999).

So the amount raised by Government is PKR 749,999,250.

The winnings distributed is PKR 75,091,200. So the ‘cost of debt’ for the government is around 10.01% in the case of prize bonds.

The current rate on Behbood Savings Certificates is around the same. In-effect, the cost of prize bonds is largely with long term GoP debt.

As an investor, you can either invest in long term GoP bonds and get a sure shot return per annum, or you can try your luck and get a prize bond, with a probability of 0.68% of winning anything (even the smallest prize) in one year.

There may be years when you don’t win anything, and then there might be a fluke year where you win the jackpot!

Bonus: You can also teach kids how money laundering works.

P.S. Some numbers may be slightly off, but song remains the same.