# 7.3: Risk and the investor


Firms cannot grow without investors. A successful firm's founder always arrives at a point where more investment is required if her enterprise is to expand. Frequently, she will not be able to secure a sufficiently large loan for such growth, and therefore must induce outsiders to buy shares in her firm. She may also realize that expansion carries risk, and she may want others to share in this risk. Risk plays a central role in the life of the firm and the investor. Most investors prefer to avoid risk, but are prepared to assume a limited amount of it if the anticipated rewards are sufficiently attractive.

An illustration of risk-avoidance is to be seen in the purchase of home insurance. Most home owners who run even a small risk of seeing their house burn down, being flooded, or damaged by a gas leak purchase insurance. By doing so they are avoiding risk. But how much are they willing to pay for such insurance? If the house is worth $500,000 and the probability of its being destroyed is one in one thousand in a given year then, using an averaging perspective, individuals should be willing to pay an insurance premium of$500 per annum. That insurance premium represents what actuaries call a 'fair' gamble: If the probability of disaster is one in one thousand, then the 'fair' premium should be one thousandth the value of the home that is being insured. If the insurance company insures millions of homes, then on average it will have to pay for the replacement of one house for every one thousand houses it insures each year. So by charging homeowners a price that exceeds $500 the insurer will cover not only the replacement cost of homes, but in addition cover her administrative costs and perhaps make a profit. Insurers operate on the basis of what we sometimes call the 'law of large numbers'. In fact however, most individuals are willing to pay more than this 'fair' amount, and actually do pay more. If the insurance premium is$750 or \$1,000 the home-owner is paying more than is actuarially 'fair', but a person who dislikes risk may be willing to pay such an amount in order to avoid the risk of being uninsured.

Our challenge now is to explain why individuals who purchase home insurance on terms that are less than actuarially 'fair' in order to avoid risk are simultaneously willing to invest their retirement savings into risky companies. Companies, like homes, are risky; while they may not collapse or implode in any given year, they can have good or bad returns in any given year. Corporate returns are inherently unpredictable and therefore risky. The key to understanding the willingness of risk-averse individuals to invest in risky firms is to be found in the pooling of risks.

This page titled 7.3: Risk and the investor is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Douglas Curtis and Ian Irvine (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.