In my opinion, I believe that financial risk acquires a systematic risk role because this type of risk is, by definition, non-diversifiable and affects all market assets to a greater or lesser extent level. No asset or company with dependence on the capital markets is safe of systematic risks. It encompasses the set of economic, monetary and social policy factors that can cause changes in the profitability of an asset as well as access to financing. All these circumstances can vary the expectations of profitability that the investors have over the assets (if we talk about equity markets), and the financing capacity of the companies (if we are talking about firms).
The business risk, I think, is non-systematic and encompasses the set of factors of a company or industry that affect the ability to generate income and profits, and once again, the financing capacity of each of the companies according to its particularities (if we talk about companies) and only to the profitability of its stock or bond (if we talk about capital markets). In this sense, business risk is non-systematic because it arises from the uncertainty surrounding a company individually for the development of its business, either by the company's own circumstances or by the sector of activity to which it belongs. Examples of these events can be a protif warning, the signing of a large contract, evolution of sales worse than its competitors than expected, a new product success, poor performance by comparison than competition, reputational risks, fraud, etc. All these events directly affect the price of the securities issued by the company (shares and / or bonds) because investors, as in the previous case, sell and buy them due to changes in expectations regarding the profitability to be obtained.
Financial risk for the firm arises from its capital structure, specifically its use of debt, preferred stock, and financial leases. This is company specific, not systematick risk in the CAPM sense. The measure can be the degree of financial leverage (DFL).
Budiness risk comes from the operating structure, that is fixed to variable cost structure, marketing strategy, et cetera. The measure can be degree of operating leverage (DOL). Agsin, this is company specific risk but would bd related to the industry (sector) the firm is in.