Shares of Walt Disney were down 3.7% Thursday to $82.73, hitting their lowest level in nearly three-and-a-half years, with some investors betting that a further price drop is on the cards in the next few months.

Disney stockholders are scrutinizing the company's turnaround plan after chief Bob Iger earlier this month promised a mix of price hikes across its streaming properties, more ads and cost cuts to lift the business.

On Thursday, Disney options were busier than usual with some 195,000 contracts traded by around 1 pm ET (1700 GMT).

Trading sentiment leaned toward bearish bets with put options that would guard against the stock slipping below 80 by mid-September and mid-October, and were among the most actively traded contracts, according to data from options analytics firm Trade Alert.

Put options convey the right to sell shares at a fixed price in the future. Disney's stock was also dragged by weakness in the broader market as investors turned cautious ahead of U.S. Federal Reserve Chair Jerome Powell's speech later this week.

In Disney's earnings report on Aug. 9, Iger acknowledged the entertainment company faces a "challenging environment" in the near-term and the company's shares have dropped over 5% since the time.