Exchange rates

Can someone explain to me how governments can “pin” currency exchange rates?

China's currency, the yuan, apparently remained pegged to the U.S. dollar for years. How did they manage this? It seems like it would be easy for a third party to arbitrage this arrangement to smithereens. Here's how.

Let's assume for the sake of argument that the "correct" exchange rate is 5 yuan = 1 usd (U.S. dollar). That is, on average, a nonperishable good that goes for 1 usd in America can be had for 5 yuan in China. Now let's say the Chinese government has, by government fiat, set 10 yuan = 1 usd. Here's my brilliant plan:

1. Buy 500 yuan worth of stuff in China.
2. Sell it for 100 usd in America.
3. Pocket 50 usd.
4. Take the other 50 usd and buy 500 yuan. You can do this at any bank that accepts the mandated exchange rate.
5. Repeat until there's no more stuff left in China, or no more consumer demand in America, or no more room for dollars in your pockets, or (as seems most likely) the banks wise up and stop giving away yuan.

Net result, you get infinite dollars. Who loses? The manufacturer in China got a fair price, as did the consumer in America. Only the bank got ripped off. So why do banks go along with exchange rate controls?

There are only a few explanations I can see. First, this brilliant plan might be impossible because the friction is simply too much. That is, the bank charges a fee for changing your money; and it costs something to ship the stuff from China to America; and there are taxes and tariffs to be paid; and occasionally you'll buy something that you can't sell for whatever reason; and you have to employ people to do the work. Maybe it's just too expensive. But I don't believe it. If this were the case, there would be no international trade.

Second, maybe the Chinese government steps in to prevent people from running this scam. They could detect that you're spending too many yuan and revoke your business permits and such. I hear the rules involving bringing currency into China are incredibly involved, so maybe this is the case.

Third, the scam is self-limiting. The more it runs, the more it drives down U.S. prices. The lower U.S. prices get, the less attractive the scam is. Likewise, the scam drives prices up in China. That TV you're buying for 500 yuan and selling for 100 usd might cost 600 yuan next month (due to greater demand) and might only bring 75 usd in America (due to greater supply). These prices are much closer to the 10-to-1 exchange rate the Chinese government desired, and they make the scam much less profitable. But even with this explanation, the scam will still run; it just doesn't "go infinite". Undervalued yuan are still being pumped out of banks in exchange for dollars worth half as much.

Fourth, maybe supporting the mandated exchange rate is just a cost of doing business for banks in China. The government requires the banks to do it, at their own expense. In exchange, they're allowed do business in China. I don't see how this would be possible. The price tag is just ridiculous.

Fifth, maybe the Chinese government somehow taps into this cycle so that every time the scam runs, the government ends up with enough in its coffers to pay for all the money it's throwing away. In that case, the higher your tax rates, the more power you have to control exchange rates.

Sixth.... maybe this is what's actually happening. It would explain the ridiculous trade deficit between China and the U.S. But if so, the Chinese central bank is paying for it—right? So in that case, how is the trade deficit a bad thing for the U.S.? Sure, it hurts domestic manufacturing, but it's not like unemployment is out of control over here. And aren't we getting cheap stuff at China's expense?