其實上星期就已經想談談Facebook收購Whatsapp，因為從教學角度看這實在是一個很好的案例。

首先，到底190億美元的收購價有多高？以Whatsapp一年一人一美元的收費模式，未計營運成本都要190億人年才能回本。就算有將來有十多億用家，這價錢還是需要數十年後才有賺。

我們也可以從另一個各度，看看科技業的兩大巨無霸—Apple與Google—在2013財政年度到底用了多了錢於收購上：Apple以14.07億買下最少七間公司，Google則以14.48億買下18間。這也就是說，Facebook在Whatsapp一間公司上所用的收購資金，比Apple加Google全年合起來還要多六倍。

Facebook願意以天價買下Whatsapp，當然是看中其4億5千萬活躍用戶。事實上，在發展一日千里的網絡，Facebook已經「out」了。只要觀察一下身邊的年輕人，就會發現他們對Whatsapp的投入程度遠超Facebook。去年從中大經濟系畢業的梁永行同學，畢文論文收集了同系同學用Whatsapp等即時短訊軟件的習慣。他除了證明各短件的新增用戶數目和現有用戶數目是有著正關聯—這是經濟學中所謂的「Network Effect」—還發現Whatsapp的增長放緩速度是一眾軟件中最少的。不過綜觀歷史，即時短訊軟件此起彼落似乎才是常態：ICQ、MSN不也曾紅極一時？

另一點值得留意的是，190億中有150億都是股票。有讀過企業財務的同學可能有學過，企業在自身估值高時會特別願意以股本作併購，因為每一股都代替了大量的現金資產。而以現時Facebook的110倍市盈率，相較Google的30倍以至Apple與Microsoft的13倍，肯定算是高了。如果大家相信Facebook估值過高，那它願意以同樣過高的價錢收購Whatsapp就不是那麼希奇了。

Apparent Theft at Mt. Gox Shakes Bitcoin World

Economists have for a while been asking whether Bitcoin is a good store of value, for reasons ranging from demand to ease of entry. Now a bigger problem emerged: security. The Mt. Gox closedown is the biggest incident so far, but it is far from the first (see https://bitcointalk.org/index.php?topic=83794.0#post_toc_17).

Even without the transaction malleability issue, I see one of the biggest attractiveness of Bitcoin—access to your money unfettered by government control—instinctively as a two-edged sword. If you want no one to monitor your actual identity, then no one is monitoring whoever-took-your-money’s either. As such, I really do not see why people would trust their private keys with service providers, but storing them privately is just as safe as putting your money under your mattress either.

Let’s say you have a variable that you know is constant within each group, what is the best way to preserve it during a collapse operation in Stata? You might think taking the first value (firstnm) must be the fastest, since it theoretically only requires 1 step per group. If that is the case, you are in for a surprise—Stata is actually better in calculating the mean.

Here are the simulation results for 100 groups of 1000 randomly generated observations, averaged over 30 runs:

collapse mean 0.0443
collapse median 0.1062
collapse min 0.0844
collapse max 0.0657
collapse count 0.0456
collapse firstnm 0.0473
collapse lastnm 0.0464

The measurements are reported in seconds. The relative speed is quite stable to variations in number of groups and observations. Base on my analysis of the underlying algorthims collapse uses, the reason why firstnm is so slow is that an order-preserving sort has to be performed on the data, and order-preserving sorts are slow relative to non-preserving ones. To confirm this is true, I ran the test with just one group of 100k observations:

collapse mean 0.0614
collapse firstnm 0.0508

And as expected, firstnm is now faster. The calculation of mean also slows down more than that of firstnm as the number of groups decrease.

Base on my simulations, calculation of mean is faster when there are as little as 3 groups, so mean is the way to go in most cases.