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# Arithmetic Average, Standard Deviation and Returns

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Calculate the arithmetic average, the geometric average, the variance and standard deviation For the S&P 500 index for the decade of 1980-1990. Do the same calculations for the S&P 500 index for 2000-2010. Compare and contrast your answers and provide explanations for the similarities and differences. Calculate the statistical measures using both annual and monthly returns, but compare and contrast using only annual data. [answer should only be approximately 1/2 page in length, spreadsheet calculations not included]

2. Find the adjusted monthly prices for the past year for both Novartis AG (NVS) and Pfizer (PFE). Assume you just inherited \$3000. You plan to use half of your inheritance in Novartis AG and the other half in Pfizer. You purchase (go long) in Novartis and sell short Pfizer. Both transactions are done using margin where the initial margin is 50% and the maintenance margin is 30%. Using only monthly prices, determine if either strategy received a margin call and if so how much. What is the return on both investments? Explain the differences or similarities in returns. [answer should only be approximately 1/2 -2/3, spreadsheet calculations not included]

#### Solution Preview

See the attached file. Thanks

1. Performance of S&P500 during different decades

The calculations for the performance of S&P500 in 1980s, 1990s and 2000s is done in Excel file. The data is analyzed both at monthly level and annual level. However, for discussion purpose, I am presenting the annual figures. Based on annual data the performance of S&P500 is shown below:
2000-2010 1990-2000 1980-1990
Arithmetic Average 1.687% 15.772% 9.98%
Geometric Average -0.485% 14.865% 9.296%
Standard Deviation 20.73% 14.93% 12.77%
Variance 0.0429561 0.0223039 0.0163112

The return during the 1990s is highest among the three decades, followed by 1980s. 2000s saw almost zero return on the S&P500 index. While the arithmetic average return is slightly positive at ...

#### Solution Summary

This post has two problems. First query shows how to calculate arithmetic average, geometric average, variance and standard deviation. Second query shows how to calculate adjusted monthly prices, returns and discusses about the similarities and differences in returns.

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