Question

Suppose you are given the following end of year stock price data for Random Inc. stock. Assume the returns are normally distributed, calculate the probability that an investor will earn more than 1.5% in a given year (e.g. Prob(Ret>1.5%)). (Enter percentages as decimals and round to 4 decimals). Year Price 2005 50.25 2006 66.49 2007 79.72 2008 83.81 2009 88.38 2010 84.39 2011 91.1 2012 82.17 2013 86.39 2014 76.35 2015 85.47 2016 86.07

Answer 1

We shall calculate the probability that an investor will earn more than 1.5% in a given year as follows:

S.No.	Years	Computation of returns	Return (%)	Whether More than 1.50%
1.	2005-2006	(66.49 - 50.25) / 50.25 x 100	32.3184	Yes
2	2006-2007	(79.72 - 66.49) / 66.49 x 100	19.8977	Yes
3	2007-2008	(83.81 - 79.72) / 79.72 x 100	5.1305	Yes
4	2008-2009	(88.38 - 83.81) / 83.81 x 100	5.4528	Yes
5	2009-2010	(84.39 - 88.38) / 88.38 x 100	(4.5146)	No
6	2010-2011	(91.10 - 84.39) / 84.39 x 100	7.9512	Yes
7	2011-2012	(82.17 - 91.10) / 91.10 x 100	(9.8024)	No
8	2012-2013	(86.39 - 82.17) / 82.17 x 100	5.1357	Yes
9	2013-2014	(76.35 - 86.39) / 86.39 x 100	(11.6217)	No
10	2014-2015	(85.47 - 76.35) / 76.35 x 100	11.7986	Yes
11	2015-2016	(86.07 - 85.47) / 85.47 x 100	0.7020	No

Since out of 11 time periods, in 7 time periods, the company Random Inc has managed to earn more than 1.50% of return in a particular time period, hence probability of earning more than 1.50% in a particular time period is given by

= 7 /11

= 63.6364%