Carl Icahn, who has gotten rich by spotting good investment opportunities, will celebrate his 78th birthday in a few weeks. Most people have retired by that age and maybe Icahn should think about it too amid signs he may be losing his tech investing touch.

Consider his high-profile stake in Apple Inc. Icahn sent an open letter to Apple shareholders yesterday in which he extolled the exciting possibilities for televisions made by Apple. He thinks that the company can profitably compete against the likes of Samsung Electronics Co. Ltd., LG Electronics Inc., and Sony Corp. in the burgeoning market for ultra-high definition displays. These televisions retail for $3,000 to $40,000, depending on size. Icahn expects Apple to sell 25 million units at the price of about $1,600.

Considering that TVs almost always get cheaper, it's possible that UHDs will sell for that in a few years. However, lower prices would almost certainly come at the expense of profitability as the technology becomes commoditized. The collapse in operating margins within the television segments of global electronics manufacturers over the past 15 years tells this story -- and also probably explains why Apple has never shown any interest in making big-screen TVs.

Television maker operating margins. Source: Bloomberg Industries.
Television maker operating margins. Source: Bloomberg Industries.

Yet Icahn thinks Apple could sell 25 million units "at a gross margin of 37.7%, which would be consistent with that of the overall company." Gross margins aren't the same as operating margins, so that number isn't comparable to the previous chart. However, it's still probable that Icahn's estimate of future profitability is too optimistic. For comparison, gross margins at television manufacturers are only about 20 percent -- down from about 30 percent in the industry's heyday in the late 1990s and early 2000s.

Television maker gross margins. Source: Bloomberg Industries.
Television maker gross margins. Source: Bloomberg Industries.

Icahn has also been berating EBay Inc. to spin off its PayPal electronic-payments unit. Although some analysts argue that EBay is undervalued, it isn't obvious that separating the auction platform from the payments system would solve that problem. There's even good reason to think that PayPal's position as a money-transfer service is bolstered by its integration into the EBay marketplace platform. EBay's boss, John Donahoe, recently wrote a post on the company's blog explaining that "eBay represents approximately one-third of PayPal's revenue and well over half of its profits. eBay continues to generate 30 percent of Paypal's new users – at zero acquisition cost. And in 2013, eBay was a significant contributor to PayPal’s profit growth." Moreover, EBay is a "significant source of low-cost capital for PayPal." It sure seems as if the two businesses are better together than apart.

Finally, consider Netflix Inc. The video-streaming service just reported solid quarterly results. Icahn sold more than half of his stake three months ago -- against the advice of his son, Brett. Bloomberg reports that the elder Icahn would have been $196 million richer if he hadn't sold. (Icahn still owns about 4.5 percent of the company, according to data compiled by Bloomberg.) In Carl Icahn's defense, his stake had almost quintupled in value between the time he bought and the time he started cutting back. Even so, he may have been premature in selling. As my colleague Barry Ritholtz wrote in November, many investors cash out of winning positions too early.

Icahn's immense self-made fortune is a testament to his investing prowess. Do these recent missteps make you wonder if he still has it?

(Matthew C. Klein is a writer for Bloomberg View. Follow him on Twitter.)