Project #29604 - Stats HW

1.   Financial analysts often use the following model to

 

characterize changes in stock prices:

 

Pt = P0

 

e

 

1m- 0.5s

 

2

 

2t +sZ2t

 

   where

 

P0  =   current stock price 

 

Pt  =    price at time  t

 

m   =    mean (logarithmic) change of the stock price

 

per unit time 

 

s =    (logarithmic) standard deviation of price

 

change 

 

Z =    standard normal random variable  

 

   This model assumes that the logarithm of a stock’s price

 

is a normally distributed random variable (see the discussion of the lognormal distribution and note that the

 

first term of the exponent is the mean of the lognormal

 

distribution). Using historical data, one can estimate values for    m    and    s.    Suppose that the average daily change

 

for a stock is $0.003227, and the standard deviation is

 

0.026154. Develop a spreadsheet to simulate the price

 

of the stock over the next 30 days, if the current price

 

is $53. Use the Excel function NORMSINV(RAND( ))

 

to generate values for Z. Construct a chart showing the

 

movement in the stock price.

 

 

 

 

6.   Using the generic profit model developed in the section  Logic and Business Principles  in  Chapter   9   , develop a financial simulation model for a new product proposal and construct a distribution of profits under the following assumptions: Price is fixed at $1,000. Unit costs are
unknown and follow the distribution.
Description: MAC:Users:USER:Pictures:Screen Shot 2014-05-01 at 1.13.38 PM.png

 

 

 

Implement your model using  Crystal Ball  to determine

 

the best production quantity to maximize the average

 

profit. Would you conclude that this product is a good

 

investment? (Data for this problem can be found in the

 

Problem 6  worksheet in the Excel file   Chapter   10    Problem

 

Data. )

 

 

 

7.   The manager of the apartment complex in Problem 9

 

of  Chapter   9    believes that the number of units rented

 

during any given month has a triangular distribution

 

with minimum 30, most likely 34, and maximum 40.

 

Operating costs follow a normal distribution with mean

 

$15,000 and a standard deviation of $300. Use  Crystal

 

Ball  to estimate the 80%, 90%, and 95% confidence intervals for the profitability of this business.

 

 a.   What is the probability that monthly profit will be

 

positive?

 

 b.   What is the probability that monthly profit will

 

exceed $4,000?

 

 c.   Compare the 80%, 90%, and 95% certainty ranges. 

 

 d.   What is the probability that profit will be between

 

$1,000 and $3,000?

 

 

 

 

 

8.   Develop a  Crystal Ball  model for the garage band in

 

Problem 11 in  Chapter   9    with the following assumptions. The expected crowd is normally distributed with

 

a mean of 3,000 and a standard deviation of 400 (minimum of 0). The average expenditure on concessions

 

is also normally distributed with mean $15, standard

 

deviation $3, and minimum 0. Identify the mean profit,

 

the minimum observed profit, maximum observed

 

profit, and the probability of achieving a positive profit.

 

Develop and interpret a confidence interval for the

 

mean profit for a 5,000-trial simulation.

 

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Due By (Pacific Time) 05/01/2014 11:00 pm
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