Accountants record advertising expenditures as expenses when the ads are run. (A prepayment of a future ad would be recorded as an asset until the ad is run.)
The reason advertising is recorded as an expense and not an asset is the problem of measuring the future value of an ad. What amount would the accountant use for recording the advertising expenditure as an asset? (You may recall a very entertaining and memorable ad by an automobile manufacturer during a Super Bowl. Viewers ranked it as one of the best. However, a later analysis showed that the ad did not result in additional sales for the car company.)
Advertising may be valuable—even crucial for some businesses—and will lead to additional assets, but accountants and others are unable to quantify the future economic value necessary for reporting it as an asset. As a result, advertising expenditures will be reported as expenses in the accounting period in which the ads are run.