CROSS REFERENCE TO RELATED APPLICATION(S)
The present application is a divisional of and claims the priority of U.S. patent application Ser. No. 11/453,370, titled “MATCHED FILTER APPROACH TO PORTFOLIO OPTIMIZATION”, filed on Jun. 15, 2006.
FIELD OF THE INVENTION
This invention relates to methods and apparatus for distributing funds among a set of investments.
BACKGROUND OF THE INVENTION
Suppose one has some capital to invest in the stock market. How does one go about investing it? One can try picking “good” stocks at low prices and selling them later at higher prices. That age old strategy although quite simple conceptually, is very difficult to implement. Stocks are inherently risky since they move up and down in a seemingly haphazard fashion on a variety of inputs and the common wisdom says that one should not keep “all eggs in one basket”, but rather spread out the investment so as to minimize the risk.
In the 1950s Harry Markowitz, then a graduate student at the University of Chicago, fine-tuned this idea, laying the foundations of the modern portfolio theory. Markowitz\'s idea is easy to understand. Let us concentrate on picking stocks. The strategy is to pick the right mix of stocks that minimizes the overall risk in terms of losing money that is invariantly caused by the stock values moving below their purchased prices. Stocks move up and down, sometimes violently, causing great volatility in term of the total portfolio value. Markowitz\'s basic idea was to keep this volatility low by picking the right mix of stocks. One would like to keep the total portfolio value fluctuations to a minimum at all times, i.e. no big variations, and if there are any variations they should amount to small jitters. Actual stock variations are of course beyond one\'s control, but what is controllable is which specific stocks to add to the overall portfolio from the total pool, and how much of each stock. The idea is to use the right mix of right stocks to minimize the overall volatility. After all the basic goal of a fund manager is to protect the portfolios under his management from losing their values and hopefully increase their return values or the overall gain. The specific stock holdings and their relative importance within the portfolio are unimportant both to the fund manager and to the investor, so long as the portfolio “makes money”, or performs well.
Thus two quantities play a role in portfolio selection—the overall risk, and the overall return or gain. Obviously, the overall risk needs to be minimized, and the overall return or gain should be maximized at the same time. Various strategies can be designed using these conflicting goals.
For a random variable, the variance is a good measure of the spread of the random variable around a mean value, and hence volatility minimization for stocks or investments, can be achieved in terms of portfolio variance minimization.
To quantify these ideas, let P represent an overall portfolio consisting of m stocks where si(n) represents the ith stock price at time index n and ai>0 the weight factor associated with the ith stock. Note that the unit of time can be hours, days, months or years depending on the investment duration. Clearly
