What is an asset? I like to explain assets as something that the company owns and from which the company will benefit in the future and assets result from past transactions. This is the same as the technical definition of assets: "Probable future economic benefits obtained or controlled by a particular entity as a result of past transactions".
Assets in the balance sheet of a company's financial statements are valued at market value or net realizable value or historical cost or amortized cost and in other ways. For example, Held to maturity marketable securities are reported at amortized cost, Short term investments at market value, Accounts receivable at net realizable value, PPE at historical cost net of accumulated depreciation, inventory at lower of cost or market.
Available for sale investments are carries at estimated fair value with any unrealized gains and losses net of taxes included in accumulated other comprehensive income or loss in stockholders equity. Unrealized losses are charged against other income (expense) net when a decline in fair value is determined to be other than temporary.