Why does it make sense for a company to purchase insurance?

Purchasing insurance decreases the likelihood of having to raise costly external costly. Having to raise costly capital could cause a firm to forgo new investment and profitable projects, or cause new projects to be unprofitable. Insurance prevents the firm form having to use internal funds to pay for losses. It also decreases the likelihood of financial distress which affects the conditions at which claimants contract with the firm. Because the firm would have to pay claimants for risk, it is cheaper to purchase insurance to cover those risks.

What are the assumptions for the CAPM to work?

In order for the CAPM to work, the firm has to be publicly traded and have many shareholders with diversified portfolios. CAPM assumes that management of a firm is risk neutral and there are no agency problems. It also assumes that there are no taxes or transaction costs. CAPM is a model that suggests that risk management does not add value to a firm. The problem with that is the assumptions under CAPM are unrealistic. In a real market, there are taxes and transaction cost and management does not always make risk neutral decisions. For these reasons, risk management can add value to a firm when done efficiently.

Why does risk management create value?

The goal of risk management is to maximize the the value to shareholders by minimizing the cost of risk. It is known that risk is costly. Risk management enables a firm to identify risk and exposure, this allows them to protect themselves against those risks.