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Time Series Properties of Stock Returns, Comparative Analysis of High- and Low-Frequency Data

Introduction

Fama (1970) suggests that stock returns exhibit random walks through time. This means that one cannot observe any trend in the movement of returns on assets and that returns cannot be forecasted based on information about past returns. Following Fama (1965) and Mandelbrot (1963), the unconditional distribution of returns has been found to be Lepturokurtic, skewed and exhibits volatility clustering. This means that returns are not normally distributed as one may expect them to be and using them in models that assume normality can lead to misleading findings. Returns have been widely used to determine the risks of a company as well as determine the cost of capital to be used in making investment decisions. The question then arises. How frequent should the data used in estimating risk and determining the cost of capital be observed? Should it be monthly, daily, weekly or annually?

Conclusion

Based on the above analysis, one can conclude that the statistical properties of daily returns are different from those of monthly returns. Moreover, returns observed over a high frequency are approximately normally distributed and thus have better statistical properties. However, to make better decisions, it is important to combine both primary and secondary data.

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