After the Alibaba IPO, the market is on average expecting that Yahoo's CEO Marissa Mayer is going to destroy $11 billion dollars in shareholder value. That's how much the operating company of Yahoo is valued at when stripped of its cash, Alibaba and Yahoo Japan holdings.
This is actually a little harsh. There are some tax issues which would lower the $11 billion number slightly. On top of this - Alibaba is currently very hard for an arbitrager to short. Once it becomes easier to borrow Alibaba stock it is likely that the implicit negative valuation of the core Yahoo business will shrink.
Investors are guessing that a significant portion of proceeds from Yahoo's Alibaba stake are going to go towards value destroying acquisitions that boost the importance of the CEO at the expense of shareholders. When Facebook bought Instagram, they made a good decision to buy a nascent competitor who understood the mobile space. When Yahoo bought Tumblr for $1.1 billion, Mayer spent $750 million of that cost on intangible assets in an attempt to try make Yahoo relevant/cool, with the side effect that the person running Yahoo would also be more relevant*.
Mayer can prove the doubters wrong in one of two ways. The easiest way is to find a tax advantageous way to return money and shares to the shareholders. The harder way is to make acquisitions like the market expects, but to buy companies that will actually generate earnings for the core operating company.
Mayer taking the hard approach is the most likely, but she has committed to returning at least 50% of the proceeds of the Alibaba IPO to Yahoo shareholders. Given that this payback, it is really hard to destroy as much value as the market is currently pricing in . They are probably paying too much attention to Yahoo's past acquisitions of GeoCities and Broadcast.com.
And given how cheaply Yahoo is currently trading, this entire discussion could be moot. Yahoo itself could be bought before we have a chance to find out what Mayer would have done with its influx of money.
*It's important to note that Tumblr's value has gone up if value is measured on a basis of how many users the service has, but it has disappointed the market in that it has been harder than expected to generate revenue from these users.