The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

is in effect shared by the insurer and the insured. A policy in which the insurer pays 75%

of the cost of any claims would be an example. This type of policy might commonly be

described as a “75% coinsurance” policy, or as a “75/25” policy.

Coinsurance is very often a feature of health insurance policies, and will be discussed

in that context in the next section. It is less common with casualty policies, though

there are exceptions. Property insurance policies often carry a provision for coinsur-

ance if the property is insured for less than its full value. For example, suppose that

you own a warehouse that, together with its contents, is worth $2,500,000. It is very

unlikely that you would ever suffer a complete loss—even a serious fire would probably

not completely destroy the entire warehouse and all of its contents. You might decide,

then, to save some money on the premium by buying insurance coverage only up to

$1,500,000.

The problem that this presents, though, is that the insurance premium for a $1,500,000

policy was most likely based on the potential claims of a property worth $1,500,000. The

likelihood of a claim running near that coverage limit on your facility is much greater than the

probability of a claim running near the limit for a $1,500,000 facility. Therefore the $1,500,000

premium would not adequately cover the potential for claims on your warehouse.

Insurers may address this issue by including a coinsurance clause, a policy provi-

sion stating that if the property is insured for less than its full value, the insurer will

provide coverage only for claims at the percent of full value for which the property is

insured.

Example 13.1.9 Your warehouse and its contents are worth $2,500,000. You insure

the property for $1,500,000. Your policy contains a coinsurance clause. There is a fi re,

and you incur a $1,200,000 loss. How much will your insurance pay?

You have insured the property for

$1,500,000___________

$2,500,000

0.60
60%

of its full value. Your insurance will cover 60% of the claim: (60%)($1,200,000) 


$720,000.

Coinsurance clauses often include a provision that coinsurance will not apply if the prop-

erty is insured for more than a given percent of its full value. Eighty percent is a com-

mon minimum; a policy that includes this provision would be referred to as having an

“80% coinsurance clause.” Note that there is potential for confusion with this wording; the

phrase “80% coinsurance” could also be interpreted to mean that the policy carries 80/20

coinsurance on all claims. It will usually be clear from context which way it should be

interpreted.

Example 13.1.10 Your warehouse and its contents are worth $2,500,000.

You insure the property for $2,000,000. Your policy contains an 80% coinsurance

clause. There is a fi re, and you incur a $1,200,000 loss. How much will your

insurance pay?

You have insured the property for

$2,000,000

___________

$2,500,000

0.80
80%

of its full value. This meets the minimum requirement, so coinsurance does not apply. Your

claim is covered in full.

How Deductibles, Coverage Limits, and Coinsurance Affect Premiums

It stands to reason that the higher a policy’s deductible, the lower its premium, and vice

versa. Similarly, the higher the coverage limit, the higher the premium. Insurers may pro-

vide for this by presenting rates as a formula based on coverage limits and deductibles, by

13.1 Property, Casualty, and Liability Insurance 531