Insure against big losses

You should buy insurance against a big loss with a small chance of occurence. Look at these two cases:

Case 1:
Potential loss is $100,000. Chance of occurence is 1%. Expected cost of claim is $1,000. Premium (allowing for expense and profit margin) is $1,500.

Case 2:
Potential loss is $2,000. Chance of occurence is 50%. Expected cost of claim is $1,000. Premium (allowing for expense and profit margin) is $1,500.

Analysis:

For case 1, you cannot afford to bear a loss of $100,000. So, it is worthwhile to pay a premium of $1,500 to cover this risk.

For case 2, you can afford a loss of $2,000. It is not worthwhile for you to pay a premium of $1,500 to cover this risk, as you have to pay $500 more than the expected cost of claim (of $1,000).

It is not necessary to take insurance against small losses. It is better to bear this risk on your own.

An example is the deductible under a Shield plan. It is not necessary for you to buy insurance for this deductible, as you can take this risk on your own (or pay out of Medisave savings).