Question

Jake had a stock with returns of 4%, -5%, -15%, and 16% in 2004, 2005, 2006, and 2007. The Avg. return of the stock for 5 years perioed 2004 – 2008 was 13%:

            A – Whats the return for year 2008?

            B – What is standard deviation for the all five years of the stock?

Answer 1

Let, returns be denoted by x_i

Given   = 13% = 0.13

Therfore,

Hence, returns in 2008 will be 0.65 - (0.04-0.05-0.15+0.16) = 0.65

Standard deviation of the returns for all 5 years can be calculated using the STDEV.P function in Excel. We consider the data given as population rather than sample because the data set provided is the only set of data that is of interest to us. We are not interested in returns before 2004 or after 2008 or for that matter return on any other stock.

The standard deviation calculated using Excel would be 27.94%

The formula for calculating standard deviation of a population is where is the population mean and n is the number of observations.

So the answers are

A - 65%

B- 27.94%