Articles

Investing for the Future

In Statistical Analysis, Statistics on July 24, 2010 by David Tagged: , ,

This past spring, I took a class on statistical finance at Rice. It’s mindboggling how many different ways people seek to manipulate the market, perform arbitrage, or otherwise “game” the system. I guess in a way, that’s to be expected with large sums of money at stake, low cost of entry, and what appears to be a clear relationship between insight and profit. The mentality also seems like, “If I can outsmart the market, why shouldn’t I? Someone else would most certainly do it if they had the opportunity and would get an edge over me.”

That said, I think the stock market, options, and futures are full of fascinating economic problem with creative challenges and interesting questions. Stock markets are rather black box – a lot of the approaches don’t really begin to attempt to understand the underlying mechanisms behind fluctuations or why stock prices change, but rather seek to capture momentum or short-term movements to get a quick profit. Personally, I think there are serious problems with the idea of stocks – I don’t think a company can have constant changes in value when it’s the same company at either price A or price B. This makes it really prone to speculation, and you are always in need of more players to enter the market to keep the bubble going.

Anyways with those caveats described, I just wanted to describe an interesting investing strategy that I learned in the class called the MaxMedian Portfolio. The idea is simple. Each year, you look at the stocks in the S&P500, and choose the top stocks with regard to median daily return from the previous year. You hold the stocks for a year, and the rebalance the following year. This strategy seeks to capture momentum – if a company is on the upswing, chances are it’ll keep going up. There’s more inertia going up, then coming down (remember my previous statement about bubbles? Generally, the majority of the players in the market want prices to keep going up.)

The interesting thing is the portfolio performs really well. If we run the simulation of running this strategy for the past 20 years, we would have made 25-fold our initial investment back. This is much better than the 5-fold return from investing in either the Dow Jones Industrial Average (DJIA) or the Standard and Poor’s 500 (S&P500). It does appear that this kind of strategy just amplifies the overall movement of the market. Between 2001 and 2003 with the bubble bursting, this strategy lost more money than investing in either of the indexes. I think this suggests that if you think the market will continue to grow and be good, it might be good to try this portfolio selection strategy.

To make sure this is not due to random chance alone, I simulated what would happen if I randomly chose 20 stocks from the S&P500 each year and followed a strategy of rebalancing each year. The following graph is a distribution of results from following this random strategy. Although it is possible to perform better than the MaxMedian strategy, the MaxMedian strategy is at the 75 percentile. I take it to mean this is better than random chance, although this random strategy ironically performs better than the market. Perhaps it’s because the stocks are chosen from the S&P500, which are generally larger and more established companies.

Anyways, I’ve just begun to dabble and put my money where my mouth this. The top performers for the past year have been AIG, AIV, GNW, TIE, and GCI. I avoided AIG, because it really seems like it was a strong benefactor of the bail-out and all the crap, but I put some money in equally the other four stocks. So far, they seem to be doing well, but we’ll see how it is in a year or so!

The code to import past year’s data from Yahoo Finance, generate median daily returns, and sort by returns is posted at: http://github.com/douyang/Statistical-Finance/downloads. So is the code for analyzing the past historical data and simulation based on choosing random stocks. Code is in R and python. Enjoy!


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