Question

In: Statistics and Probability

Suppose you are given the following end of year stock price data for Random Inc. stock....

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

Solutions

Expert Solution

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


Related Solutions

Suppose you are given the following end of year stock price data for Random Inc. stock....
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
Suppose you are given the following end of year stock price data for Random Inc. stock....
Suppose you are given the following end of year stock price data for Random Inc. stock. Assume the returns are normally distributed, calculate the minimum value that an investor eared during any given year of the sample. (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
Suppose you are given the following end of year stock price data for Random Inc. stock....
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
Suppose that you are given the following information about the stock price/dividends for a company: Year...
Suppose that you are given the following information about the stock price/dividends for a company: Year Beginning of Year Price Dividend Paid at Year-End 2016 $80 $3 2017 $85 $4 2018 $78 $2 2019 $82 $2 If the company's stock price is $85 per share at the end of 2019, what is the arithmetic average return for an investment in XYZ over the period? What is the geometric average return for an investment in XYZ over the period? (Do not...
Use the​ end-of-year stock price data in the popup​ window, (data below) to answer the following...
Use the​ end-of-year stock price data in the popup​ window, (data below) to answer the following questions for the Harris and Pinwheel companies. a. Compute the annual rates of return for each time period and for both firms. b. Calculate both the arithmetic and the geometric mean rates of return for the entire​ three-year period using your annual rates of return from part a. ​(Note: you may assume that neither firm pays any​ dividends.) c. Compute a​ three-year rate of...
You are given the following data                        Year            HPR of Stock A &nb
You are given the following data                        Year            HPR of Stock A      HPR of Stock B      HPR of Stock C                          2017                12%                            16%                         12%                         2018                 14%                            14%                         14%                         2019                 16%                            12%                         16% (1) Calculate expected rate of return for each stock (2) Calculate standard deviation for each stock (3) Calculate coefficient of variation for each stock. If you will choose only one stock for investment, which stock will you choose? Why? (4) How much is correlation coefficient...
Two stocks has the following year-end stock prices and dividends: Stock 1 Stock 2 Year Price...
Two stocks has the following year-end stock prices and dividends: Stock 1 Stock 2 Year Price Dividend Price Dividend 1 $70 $150 2 $75 $1 $163 $2 3 $74 $1 $156 $2 4 $80 $2 $173 $1 Which stock has a higher annual average capital gain yield over the four years? Which stock has a higher average dividend yield?If T-bill rate is 2.0 percent, which stock has a higher average nominal risk premium based on the annual average total return?What...
Suppose the current stock price is $120 and the stock price in a year can be...
Suppose the current stock price is $120 and the stock price in a year can be either $150 or $100. The risk-free rate is 2% per year, compounded annually. Compute the price of a European put option that expires in a year. The strike price is K=$130 (Hint: This is a put option case, not a call option. Be careful when you compute the cash-flow at expiration date. All other calculations should be the same as call option case.)
You are given the following information concerning options on a particular stock:    Stock price =...
You are given the following information concerning options on a particular stock:    Stock price = $62 Exercise price = $60 Risk-free rate = 5% per year, compounded continuously Maturity = 3 months Standard deviation = 45% per year    a. What is the intrinsic value of each option? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations.)     Value   Call option $   Put option $    b. What is the time...
You are given the following information concerning options on a particular stock:    Stock price =...
You are given the following information concerning options on a particular stock:    Stock price = $76 Exercise price = $75 Risk-free rate = 6% per year, compounded continuously Maturity = 6 months Standard deviation = 31% per year    a. What is the intrinsic value of each option? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations.)     Value   Call option $      Put option $       b. What is the time...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT