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 lose more than -3% in a year, Prob(Ret<-3%). (Enter percentages as decimals and round to 4 decimals). Year Price 2005 43.65 2006 44.01 2007 45.77 2008 53.04 2009 45.67 2010 59.05 2011 46.88 2012 49.24 2013 43.99 2014 42.67 2015 48.14

Answer 1

given data set:

Year	Price
2005	43.65
2006	44.01
2007	45.77
2008	53.04
2009	45.67
2010	59.05
2011	46.88
2012	49.24
2013	43.99
2014	42.67
2015	48.14

we need to find probabaility when return goes below -3%(-0.03) in 1 year.

We are given total 11 years of prices.

From this we can caluclate 11 - 1 = 10 returns of 1 year difference.

So, Total return for 1 year difference is given in below table:

Year Price Return Return(%) 2005 43.65 2006 44.01 0.008247423 0.825% 2007 45.77 0.039990911 3.999% 2008 53.04 0.158837667 15.884% 2009 45.67 -0.138951735 -13.895% 2010 59.05 0.292971316 29.297% 2011 46.88 -0.206096528 -20.610% 2012 49.24 0.050341297 5.034% 2013 43.99 -0.106620634 -10.662% 2014 42.67 -0.03000682 -3.001% 2015 48.14 0.12819311 12.819%

Note: The second last return is -3.001% which is also more than -3%.

Mean Return = 0.0196

Return Standard Deviation = 0.149

We will perform all calculations without considering percentage.

We need to fin probabaility where investor loses more than -3% or -0.03 times value

We need to find probabaility of below shaded area i.e for X < -0.03

Since = 0.0196 and = 0.149

We need to convert above pronlem in terms of z score

So, z = (X - ) /

z = (-.0.03 - 0.0196) / 0.149

z = -0.332

So, now we need to find probability for P (z < -0.332).

Checking in z score table we get

P (X < -0.03) = P (z < -0.332) = 0.3707