The three questions definitely are key ones and fortunately I can say yes to some of them. I feel like they are actually correlated since target school => great alumni network resource => high chance to land internships and for non-targets they need to network their ass off and get pretty luck. I mean that's why those non-target hero stories exist, isn't it?
They are absolutely correlated. Success isn't built overnight. You can't suck from HS to College with lousy GPA and crappy school, and only hope for a miracle or with one GRE score to erase all your wrongs. Sure you might get lucky, but life isn't a lottery. A lot of people here seem to hope to get those coveted position through less than stellar background, and we should be really skeptical about their results. All major programs had invested heavily in hiring practitioners as faculty (not cheap), educating hiring managers about their programs, curriculum planning, and alumni coordination to establish themselves. If you want to go to a graduate program, accept nothing but the best. A graduate program that cannot help you distinguish yourself from other job applicants is not worth going at all (especially if you come from other disciplines or foreign countrie).
In terms of trading, what's the value of personal accounts? Do they care about it as much as how smart you are? I'm confused with this because banks are going to train you anyways, will they prefer a smart guy and teach him or someone who got a decent record but already developed his own strategies?
It depends. After all, traders make their lunch through trading profit. And for prop shops, profit and alpha seeking is by far the one and only criterion you need for a job. But as
financeguy mentioned, things get a bit complicated with banks. If you compare a trading desks to an Apple store, the sales people are the front area greeters, the traders are the technicians, the back office are the shipping specialists, and the financial instruments are the ipads. Your ability to trade isn't nearly as important as your ability to put the components together correctly and communicate with your clients. Sell-side traders focus more on hedging the market exposure of their inventories, so you work in teams to make sure your bank doesn't get run over by market volatility. (or that's my understanding of them. I only worked in prop)
And for forex derivatives, does one really need to know stochastic calculus (so that he or she can understand the product) just for trading? I'm sure there are people who don't know high-level math trade well, but what about the more general cases?
Stochastic calculus (SC) is only used for designing pricing and hedging strategies. You then use the calculated result as a benchmark to adjust your quotes and
hedge your exposures accordingly through arbitrages make sure you don't violate arbitrage bounds (thanks
Yike Lu). So for those, you need a thorough understanding of all the greeks (and their behaviors under different market condition) to explain to your clients and control your risks.
For directional trades (prop trading), however, SC is far less useful than general economics and common sense. As computerize trading proliferates and arbitrage margins get depressed, the real money in trading is in directional trading where forecasting and time series analysis are way more important.