# Volatility drag - ii

**Computer Science**Level 4

This file contains 600 rows, each of which contains the daily returns of a fictional stock over the 252 trading days of 2013. Each trajectory was generated by randomly drawing a rate, \(\hat{r}_i\), from a normal distribution, centered about \(\bar{r} = 1.01\), with standard deviation \(\sigma = 0.06\), for each day, \(d_i\), in the year.

Clearly, there are a range of outcomes all of which are consistent with the statistical properties of the investment. However, if we take the median value of the value on day \(d_{252}\), we can get a good idea of the typical performance of the stock.

The **median** overall return on the year is given by \(\langle S_{252}\rangle/S_0\). By comparison, we'd expect a noise-free investment of the same average return to yield an overall value \(S_{252}/S_0 = r_0^{252} = 12.27\).

How much value are we losing to fluctuations? Download the file, analyze the data, and find the value of \(\displaystyle\langle S_{252}\rangle/S_0 \)

**Details**

- Note, \(\langle X \rangle\) indicates the median value of \(X\).