# Trade off between risk and return

Problem Description: It is a well known principle of finance that when investing, there is a trade off between risk and return, i.e. in order to earn a higher return, one must assume greater risk . Stock returns are calculated as the percentage change in price over a given period. Risk is measured by the variability (or volatility) of these returns. You are part of an analytical team working for a large investment bank. Management is considering two investments: A or B. Before doing so, they have asked your team to prepare a report on the risk and return profiles of these two investments. You will use descriptive statistics and your knowledge of continuous distributions to complete this task. The returns data (measured annually) for the two investments are given in the Excel file: investment Monday.xls Required: a. Estimate descriptive statistics for each investment via Excel. Compare the two investments. Be sure to comment on the central tendency, variability and shape of these two investments (Note: use the most appropriate measure when comparing the variability of two distributions). Based on your findings, which investment would you choose and why? b. For your chosen investment, assume that the returns are normally distributed with a mean and standard deviation (as estimated in (a) rounded to the nearest integer). Answer the following questions: i. Find the probability that returns will exceed 55% ii. Find the probability that returns will be between 22% and 36% iii. Find the probability of making a loss iv. If you are given a choice between the top 3% of returns and a return of 48%, which option would you choose? v. Between what two values of returns (symmetrically distributed around the mean) will 48.6% of all possible returns contained? c. What are the limitations of your analysis?

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