Analysis
The table in the Result section has summarized the variance-minimizing strategies for 14 pairs of stocks randomly chosen by the wrapperFunction() in the Python program. The table also summarized whether the values of effectiveness indicator for these 14 pairs of stock (ie. whether the downside protection of applying the variance-minimizing strategy on these 14 pairs of stock outweighs potential upside that have to be sacrificed.)
Expected: first set of results (the smaller set) support my hypothesis
The effectiveness indicator is positive for 9 out of the 14 randomly chosen pairs of stocks. In other words, the variance-minimizing strategy is effective in 9 out of 14 times. This result supports my hypothesis that the variance-minimizing strategy is an effective investment strategy for a two-stocks portfolio.
Unexpected: second set of results (the larger set) reject support my hypothesis
Contrary to my expectation, increasing the number of observations from 14 pairs of stocks to 32 pairs of stocks does not give further support to my hypothesis. The effectiveness indicator is positive for only 15 out of the 32 randomly chosen pairs of stocks. In other words, the variance-minimizng strategy is ineffective over half of the times. On average, the effectiveness indicator is -7.118, showing that the variance-minimizing strategy can be quite ineffective on average. Unlike the first set of result, this second set of result rejects my hypothesis.
Unexpected: extreme values of effectiveness indicators
It should be pointed out that certain scenarios have effectiveness indicators with very low values. For example, when AMZN is the first stock, and AMGN is the second stock, the effectiveness indicator is -31.858; when T is the first stock, and AAPL is the second stock, the effectiveness indicator becomes -97.208. These examples show that although the variance-minimizing strategy can be very ineffective in certain circumstances. On the other hand, the highest value among the effectiveness indicators of the 32 pairs of stocks is only 20.361; in other words, even though the variance-minimizing strategy is effective in close to half of the times, this strategy only provides limited net benefits (ie. benefits - costs).
To summarize, this project rejects the hypothesis that the variance-minimizing strategy is an effective investment strategy. My results show that the variance-minimizing strategy is effective in less than half of the times; even when the variance-minimizing strategy is effective, this strategy only has a limited effectiveness.
The table in the Result section has summarized the variance-minimizing strategies for 14 pairs of stocks randomly chosen by the wrapperFunction() in the Python program. The table also summarized whether the values of effectiveness indicator for these 14 pairs of stock (ie. whether the downside protection of applying the variance-minimizing strategy on these 14 pairs of stock outweighs potential upside that have to be sacrificed.)
Expected: first set of results (the smaller set) support my hypothesis
The effectiveness indicator is positive for 9 out of the 14 randomly chosen pairs of stocks. In other words, the variance-minimizing strategy is effective in 9 out of 14 times. This result supports my hypothesis that the variance-minimizing strategy is an effective investment strategy for a two-stocks portfolio.
Unexpected: second set of results (the larger set) reject support my hypothesis
Contrary to my expectation, increasing the number of observations from 14 pairs of stocks to 32 pairs of stocks does not give further support to my hypothesis. The effectiveness indicator is positive for only 15 out of the 32 randomly chosen pairs of stocks. In other words, the variance-minimizng strategy is ineffective over half of the times. On average, the effectiveness indicator is -7.118, showing that the variance-minimizing strategy can be quite ineffective on average. Unlike the first set of result, this second set of result rejects my hypothesis.
Unexpected: extreme values of effectiveness indicators
It should be pointed out that certain scenarios have effectiveness indicators with very low values. For example, when AMZN is the first stock, and AMGN is the second stock, the effectiveness indicator is -31.858; when T is the first stock, and AAPL is the second stock, the effectiveness indicator becomes -97.208. These examples show that although the variance-minimizing strategy can be very ineffective in certain circumstances. On the other hand, the highest value among the effectiveness indicators of the 32 pairs of stocks is only 20.361; in other words, even though the variance-minimizing strategy is effective in close to half of the times, this strategy only provides limited net benefits (ie. benefits - costs).
To summarize, this project rejects the hypothesis that the variance-minimizing strategy is an effective investment strategy. My results show that the variance-minimizing strategy is effective in less than half of the times; even when the variance-minimizing strategy is effective, this strategy only has a limited effectiveness.