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# Daily vs. Monthly Compounding

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I need an explanation how to resolve this question or an example

#### Solution Preview

Please see the calculations in the attached Excel sheet.

Given the same nominal rate, more frequent compounding will always result in a higher effective rate, because ...

#### Solution Summary

We compare daily and monthly compounding, showing the exact calculations for each and which results in a higher effective rate.

\$2.19

## Various Calculations Given Time Series of IBM Stock Prices

1. Download time series of daily and monthly prices for IBM for 1963-2009.

2. Compute the sample mean, median, variance, skewness, kurtosis, min, and max for continuously compounded, i) daily and ii) monthly returns. Compare the same for simple returns.

a. Are there any differences in skewness of daily and monthly returns?
b. Are there any differences in skewness of continuously compounded versus simple
monthly returns?
c. Are there any differences in kurtosis of daily and monthly returns?
d. Are there any differences in kurtosis of continuously compounded versus simple
monthly returns?

3. Do the followings for daily and monthly continuously compounded returns:
a. Plot the time series returns. What can you say about the picture?
b. Plot the histograms and tell what you infer about the true distribution of the stock returns. Hint: Is the return distribution normally distributed?
c. Do part a and b for simple returns. Compare the results with the ones for continuously compounded returns. Describe any notable features.

4. Download time series of daily and monthly prices for the daily S&P index for 1963-2009. Compute continuously compounded returns and plot time-series as well as the histogram. Compare to daily IBM return results in Q1.

5. Compute the sample auto-covariances and auto-correlations for both daily and monthly continuously compounded returns for k=1,...,22 for both IBM and the S&P index. Plot the autocorrelation functions. Do you see any differences between the S&P index and IBM?

NOTE: The source data can be found on Yahoo/Google finance

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