Which type of preferred shares can be redeemed by the issuing company at any time?

Callable preferred shares are designed with specific features that allow the issuing company to redeem them at its discretion, often at a predetermined price after a certain date. This provides the company with financial flexibility, especially in scenarios where interest rates decline, enabling them to buy back shares and potentially reissue new ones at a lower cost.

In contrast, cumulative preferred shares focus on the accumulation of unpaid dividends, ensuring shareholders receive their dividends even if payments are missed in the past. Convertible preferred shares offer a right for shareholders to convert them into common shares, providing potential appreciation but lacking the redemption feature. Participating preferred shares may provide additional dividend benefits or a share in the residual assets upon liquidation, but do not confer the right to be redeemed at the issuer's discretion like callable preferred shares do.

Thus, the distinctive characteristic of callable preferred shares is the company's ability to redeem them at any time, making this the correct answer.