Mathematical Journeys - Saint Ann's School

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  23    VICISSITUDES OF THE MARKET: AN EXPLORATION   Introduction JONAH KANER, ALEX SHILEN, SIMON HEDGES  This semester in our independent math research group we explored the possibility of quantitative stock analysis. The research took the form of a competition between colleagues. Our advisor, Jared Cross, selected forty-four random stocks from which we would each refine our portfolios. Our data comprised monthly closing prices over a ten-year time span, from 1990 to 2000. The research spanned three different competitions, each intended to reveal any trends in the data. One had two diametric portfolios—aimed at maximizing and minimizing gains. The next was to create five bundles with the most consistent growth, the worst performing of which we were judged on. The last was to reduce volatility. We each approached our portfolios individually, with a variety of strategies. Choosing our Portfolios Simon: I favored stocks that had seemingly healthy and sustainable growth throughout the 90s, preferring mid and large caps that were less volatile in the ups and downs of the market. In search of the stocks that I thought would perform poorly I chose stocks that seemed volatile, inconsistent, and more affected by bubbles. In choosing my stock bundle with the lowest standard deviation I chose the 5 stocks with the lowest volatility in the 90s without calculating any correlations. Alex: I looked at the slope of each stock’s price changes in an attempt to predict its future value. I postulated that in order to maximize the return of my first bundle I should select stocks with positive slopes. I envisioned consistent growth. For my minimum return I took stocks with stagnant growth, with a similar prediction—that they would adhere to their previous tendencies. My approach turned out to be wildly bipolar and my results unexpected. For my six least volatile bundles I looked for stocks with low standard deviations, relying on the same conjecture. Jonah: I went with a very simple method of buy low, sell high. When the stock was priced higher than the ten-year average, I would choose that stock as a loser, and when the stock was priced lower than the ten-year average, I would choose it to be a winner. Based on the winners and losers that I picked, I then organized them in bundles depending on their standard deviation over the 10 years of data we had. The aim was to come up with 5 bundles that all had low standard deviation over the previous decade. Results
24    The average return of all 44 stocks from 2000-2010 was 44%. Simon’s winners returned 74%, while his losers returned 73%. Both of his bundles of 10 outperformed the market, but he was unable to successfully pick 10 stocks that had a negative return during this time period. Alex’s winners returned -44% and his winners returned 109%. Alex’s results provided the most information for later analysis. Jonah’s winners went up 29%, underperforming the market, and his losers went down 8%. While Jonah underperformed the market with his winners, he was able to choose a bundle of 10 stocks that had a negative performance during this time period. Ted’s winners returned 40%, just underperforming the market. Simon’s average monthly percentage return was .19%, while his average monthly standard deviation was 3.17%. Jonah’s average monthly return was .38%, while his average monthly standard deviation was 6.58%. Alex’s average monthly return was 1.03%, while his average monthly standard deviation was 7.11%. Ted’s average monthly return was .45%, while his average monthly standard deviation was 4.5%. Winners and losers competition: Analyst Bundle of 10 “winners” Bundle of 10 “losers” Jonah 29% -8% Alex -44% 109% Simon 74% 73% Dr. Theo 40% Minimizing monthly volatility competition: Analyst Average Monthly Gain Standard Deviation Jonah 0.38% 6.58% Alex 1.03% 7.11% Simon 0.19% 3.17% Dr. Theo 0.45% 4.50% Composite of all 44 stocks 0.48% 5.84% Conclusions Our results yield, undoubtedly, confusing conclusions, as they were not at all what we predicted. After further analysis of our data we believe our results can be largely accredited to standard deviations as each of our winners and losers seem to have random performances. We found that, to correctly do this sort of analysis we would need to broaden our stock range to that of an entire market while simultaneously greatly increasing the number of stock pickers. The most interesting piece of information that we saw in our small pool of data was the result of Alex’s picks. His method, already described, seemed to provide an obvious inverse correlation between a stocks previous movement and its future movement, as the stocks that he found to have the most negative average growth between 1990 to 2000 performed extraordinarily while the stocks that had the highest average positive growth from 1990-2000 performed abysmally in the 2000-2010 period. Following up, in an attempt to substantiate the inverse correlation that we found in Alex’s prediction we widened our scope to look at the relation between past and present movements of all of the
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