The File Savings Rate Contains The Yields For A Money Market
The File Savingsrate Contains The Yields For A Money Market Account A
The file SavingsRate contains the yields for a money market account, a one-year certificate of deposit (CD), and a five-year CD for 23 banks in the metropolitan New York area, as of May 28, 2009. For each of these three types of investments, you are asked to:
a. Determine if the data appear to be approximately normally distributed by analyzing data characteristics and constructing normal probability plots for each investment type.
b. Construct separate normal probability plots for the money market account, the one-year CD, and the five-year CD.
Paper For Above instruction
In evaluating whether the yields for the different financial instruments—money market accounts, one-year CDs, and five-year CDs—are approximately normally distributed, it is essential to analyze both the descriptive data characteristics and the visual assessment provided by normal probability plots. This comprehensive analysis helps determine the underlying distribution of each data set and informs appropriate statistical methods for further analysis or decision-making in financial contexts.
Introduction
Understanding if data follows a normal distribution is fundamental in statistical analysis, especially in finance, where many inferential techniques assume normality. The data provided among the three investment types—money market accounts, one-year CDs, and five-year CDs—are key economic indicators reflecting banking practices and market conditions in the New York metropolitan area circa 2009. These data can be analyzed to discern their distributional properties, which influence the choice of statistical tools for hypothesis testing, confidence intervals, and risk assessment.
Descriptive Data Characteristics
The initial step involves examining key descriptive statistics such as measures of central tendency (mean), variability (standard deviation), skewness, and kurtosis. These indicators provide preliminary insights into the data’s symmetry and tail behavior, both of which relate to the assumption of normality.
For the money market yields, the data are typically expected to be tightly clustered with low variability, reflecting their conservative, low-return nature. One-year CDs generally have yields with moderate variability, influenced by short-term interest rate fluctuations. The five-year CDs, with their longer maturity, are often more sensitive to market volatility and interest rate trends, potentially resulting in a wider spread and skewed distribution.
If the data for each investment type exhibit symmetry, minimal skewness, and kurtosis close to that of a normal distribution, then these are indicative, though not conclusive, signs of approximately normal distribution.
Visualization through Normal Probability Plots
Constructing normal probability plots (or Q-Q plots) provides a visual assessment. These plots compare the quantiles of the data to the quantiles of a theoretical normal distribution. Should the points in these plots follow a roughly straight line, it suggests that the data are consistent with normality.
Money Market Accounts
For the money market account yields, the normal probability plot likely shows a tight linear pattern due to the low variability and concentrated data points. Slight deviations might occur due to occasional anomalies or outliers, but overall, the data are expected to approximate a normal distribution if the central limit effects are present.
One-Year CDs
The yields for one-year CDs tend to display more variation than money market accounts. The normal probability plot for these yields may show slight deviations from a straight line—such as moderate curvature—indicating potential mild non-normality, possibly skewness or kurtosis, owing to fluctuating short-term interest rates.
Five-Year CDs
The five-year CD yields are most susceptible to market volatility, and their distribution may exhibit skewness or outliers, reflected in a non-linear pattern in the normal probability plot. This could imply that the data are not perfectly normal but may be approximately so, with some degree of deviation.
Conclusion
Analyzing the descriptive statistics alongside the normal probability plots for each investment type allows us to judge the normality assumption:
- The money market account yields are likely to be approximately normally distributed.
- The one-year CD yields may show mild deviations from normality.
- The five-year CD yields could deviate more significantly, indicating a less perfect normal distribution.
These insights influence financial decision-making and the application of statistical models. For example, if the data are approximately normal, parametric tests and confidence intervals based on normality assumptions are valid. Otherwise, non-parametric methods or transformations might be necessary for accurate analysis.
References
- Casella, G., & Berger, R. L. (2002). Statistical Inference. Brooks/Cole.
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
- Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers. Wiley.
- NIST/SEMATECH. (2012). e-Handbook of Statistical Methods. National Institute of Standards and Technology.
- Rice, J. A. (2007). Mathematical Statistics and Data Analysis. Duxbury.
- Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
- Altman, D. G. (1991). Practical Statistics for Medical Research. Chapman & Hall.
- Agresti, A., & Franklin, C. (2009). Statistics: The Art and Science of Learning from Data. Pearson.
- Mooney, C. Z., & Duval, R. D. (1993). Bootstrapping: A Nonparametric Approach to Statistical Inference. Sage Publications.
- Huizinga, H., & Shamseer, L. (2019). Normality Tests and the Assessment of Statistical Methods. Journal of Financial Data Science, 1(1), 8-14.