I want to ask you guys a question. How many of you have ever invested in stock market? Raise your hand. OK. Thanks. Do you think investment is easy? In bookstore, we can always find lots of investment books talking about “N steps to make easy money from investment”. They instill you an illusion “Come on. It’s not rocket science. It is easy for you”. However, is it really easy?
Before we continue, let me introduce you three financial terms. The first one is portfolio(投資組合) which means a combination of stocks. The second is hedge(避險) which means to eliminate the investment risk. And the third term is option(選擇權) which is a kind of financial instrument. You don’t really need to know what option is in details, just remember that stock can hedge the option risk.
OK. Now, let’s look at this equation. Do you know what does it mean? Of course you don’t know. Otherwise I can get off the stage now. This is a control equation originally from space technology. Suppose I am in a spaceship that keeps still at its position. One day, due to the gravitational force of the moon, the spaceship deviates from its original position. The equation describes how to control the spaceship to move back to its original position accurately and how much extra fuel needed for this movement. In practice, solving this problem is quite complicated. However, that equation is applied by many investment banks today to hedge option risk. Think about that. Suppose our options price deviates from its original value, by that control equation, we can use the stocks to hedge the option price deviation. So, our profit is protected. We say that this is kind of Rocket Science in our field, difficult to solve but vivid.
Another story or say application is about wireless communication. Suppose we have a fix amount of base stations, we want to know where we should place these base stations so that the signal coverage area can be maximized. This signal coverage
problem can be viewed as a resource allocation problem in mathematics. Since resource are limited. It is unrealistic to cover every corner of the region. However, with the help of mathematics, we can guarantee these base stations cover the maximum area. This concept can be used in stock investment because our money is also limited. (For example, we may buy the stocks of TSMC, Chunghwa Telecom, MediaTek and Fubon Financial to form our portfolio.) Here our target is to find out the optimal shares of stocks we have to buy so that we will have maximum profits in the end. Again, maximizing profit in the end corresponds to maximizing the coverage area in wireless communication. You can see it is not easy at all. That’s why I told you it is a rocket science. In fact, investment problem is more complicated because we need to care for the loss but that’s not my point here.
Resource allocation can be found in many fields; such as minimizing the energy consumption for the rocket, minimizing the area of integrated circuit. Even our mentor-mentee matching can also be viewed as a resource allocation problem. Nowadays, investment becomes so complicated that involve financial theory, the methods of engineering, the tools of mathematics and the practice of computer programming. It is not that trivial as those books claim. Hence, the only conclusion I give you is that: don’t just believe in your feeling for investment or otherwise you will pay for it.
Toastmaster of the evening!