# Pilot Study

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As using the same method with the main paper, we got the four similar tables there. Firstly, we got monthly returns of 200 stocks in ASX from data stream, and used them to calculated standard deviations. Moreover, the table 1 was made out below (in order to maintain a neat, all the data we retain all four decimal places.) In the first table, when we made eight stocks as a portfolio, the rate of portfolio standard deviation to standard deviation of a single stock has been nearly 50%. We also found that the ratio will be constant at 0.2217 if we make more than 100 stocks as a diversified portfolio. These two main points are similar to the main article, but the difference is only the data. Elton and Gruber found that 10 stocks portfolio got the rate of near 50%, and the rate would be constant at 0.39 when they made a 200 stocks portfolio. The main reason we thought is that the different between the two markets’ size.
In addition, we used the two functions as the original paper to get the result of figure 1.

Certainly, the SML we made as the similar condition, we also used ten randomly selected stocks as a portfolio G (10), and the diversified portfolio of ten stocks as P (10). The line should be 200-stock line. We got the result the risk premium became to 6.4%, and the standard deviation of P (200) and G (10) were 2.96% and 14.61% respectively. We got a big difference between these two standard deviations, contrast with the main research. Therefore, the expected return of P (10) exceeded more much than expected return of G (10), which was 15.32. As the result, the huge difference existed probably because the ASX market is more stable than SP 500 market.
As supporting the figure 1, we retrieved the Treasury bill rate of Australia and call money rate from 2000 to 2005, in order to get the expected alpha. The table 2 had been made out:

We got the expected difference equalling to 1.73%, which is larger than

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