Basic Business Statistics, Student Value Edition
14th Edition
ISBN: 9780134685113
Author: Mark L. Berenson, David M. Levine, David F. Stephan, Kathryn Szabat
Publisher: PEARSON
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Chapter 13, Problem 50PS
a.
To determine
Find the approximate market model.
b.
To determine
Find the expected return from SPUU index if S&P 500 index gains
c.
To determine
Find the expected return from SPUU index.
d.
To determine
Determine the type of investors who can be attracted and who stay from leveraged index funds.
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
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Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Chapter 13 Solutions
Basic Business Statistics, Student Value Edition
Ch. 13 - Prob. 1PSCh. 13 - If the values of X in Problem 13.1 from 2 to 25,...Ch. 13 - Fitting a straight line to a set data yields the...Ch. 13 - The production of wine is a multibillion-dollar...Ch. 13 - Zagat’s publisher restaurant rating for various...Ch. 13 - Is an MBA a golden ticket? Pursuing an MBA is a...Ch. 13 - Starbucks Coffee Co. uses a data-based approach to...Ch. 13 - The value of a sports franchise is directly...Ch. 13 - An agent for a residential real estate company in...Ch. 13 - A box office analyst seeks to predict opening...
Ch. 13 - How do you interpret a coefficient by of...Ch. 13 - If SSR= 36 and SSE=4, determine SST and then...Ch. 13 - If SSR=66 and SST=88, Compute the coefficient of...Ch. 13 - If SSE= 10 and SSR=30, compute the coefficient of...Ch. 13 - If SSR=120, Why is it impossible for SST to equal...Ch. 13 - In problem 13.4 on page 493, the percentage of...Ch. 13 - In problem 13.5 on page 493, you used the summated...Ch. 13 - In Problem 13.6 on page 494, a prospective MBA...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - In problem 13.8 on page 494, you used annual...Ch. 13 - In problem 13.9 on page 494, an agent for a real...Ch. 13 - In problem 13.10 on page 494, you used You tube...Ch. 13 - The following results provide the X Values,...Ch. 13 - The following results show the X Values,...Ch. 13 - In problem 13.5 on page 493, you used the summated...Ch. 13 - In problem 13.4 on page 493, you used the...Ch. 13 - In problem 13.7 on page 494, you used the plate...Ch. 13 - In problem 13.6 on page 494, a prospective MBA...Ch. 13 - In problem 13.9 on page 494, an agent for a real...Ch. 13 - Prob. 30PSCh. 13 - Prob. 31PSCh. 13 - The residuals for 10 consecutive time periods are...Ch. 13 - The residuals for 15 consecutive time periods are...Ch. 13 - In Problem 13.7 on page 494 concerning the...Ch. 13 - What is the relationship between the price of...Ch. 13 - Prob. 36PSCh. 13 - A freshly brewed shot of espresso has three...Ch. 13 - The owners of a chain of ice cream stores have the...Ch. 13 - You are testing the null hypothesis that there is...Ch. 13 - Prob. 40PSCh. 13 - Prob. 41PSCh. 13 - In problem 13.4 on page 493, you used the...Ch. 13 - Prob. 43PSCh. 13 - In problem 13.6 on page 494, a prospective MBA...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - Prob. 46PSCh. 13 - In Problem 13.9 on page 494, an agent for a real...Ch. 13 - In Problem 13.10 on page 494, you used you used...Ch. 13 - The volatility of a stock is often measured by its...Ch. 13 - Prob. 50PSCh. 13 - Prob. 51PSCh. 13 - Movie companies need to predict the gross receipts...Ch. 13 - Prob. 53PSCh. 13 - Prob. 54PSCh. 13 - Prob. 55PSCh. 13 - Based on a sample of n=20, the latest-squares...Ch. 13 - Prob. 57PSCh. 13 - In Problem 13.4 on page 493, you used the...Ch. 13 - In Problem 13.7 on page 494, you used the plate...Ch. 13 - In Problem 13.6 on page 494, a prospective MBA...Ch. 13 - Prob. 61PSCh. 13 - Prob. 62PSCh. 13 - In problem 13.10 on page 494, you used YouTube...Ch. 13 - Prob. 64PSCh. 13 - Prob. 65PSCh. 13 - When is the unexplained variation (i.e., error sum...Ch. 13 - Prob. 67PSCh. 13 - Prob. 68PSCh. 13 - Prob. 69PSCh. 13 - How do you evaluate the assumptions of regression...Ch. 13 - When and how do you use the Durbin-Watson...Ch. 13 - Prob. 72PSCh. 13 - Can you use movie critics’ opinions to forecast...Ch. 13 - Management of a soft-drink botting company has the...Ch. 13 - Measuring the height of a California redwood tree...Ch. 13 - You want to develop a model to predict the asking...Ch. 13 - You want to develop a model to predict the taxes...Ch. 13 - An analyst has the objective of predicting the...Ch. 13 - An accountant for a large department store has the...Ch. 13 - On January 28, 1986, the space shuttle Challenger...Ch. 13 - A baseball analyst would like to study various...Ch. 13 - Can you use the annual revenues generated by...Ch. 13 - In Problem 13.82 you used annual revenue to...Ch. 13 - During the fall harvest season in the United...Ch. 13 - Refer to the discussion of beta values and market...Ch. 13 - The file CEO 2016 includes the total compensation...Ch. 13 - In Problem 13.8, 13.20, 13.30, 13.46, 13.62,...
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- Problem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forward
- In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0 given (under the measure P) by d.St 0.03 St dt + 0.2 St dwt, with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to price an option on this stock (which we name cubic put). This option is European-type, with maturity 3 months (i.e. T = 0.25 years), and payoff given by F = (8-5)+ (a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure Q. (You don't need to prove it, simply give the answer.) (b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2. (c) Let X = S. Find the Stochastic Differential Equation satisfied by the process (Xt) under the measure Q. (d) Find an explicit expression for X₁ = S3 under measure Q. (e) Using the results above, find the price of the cubic put option mentioned above. (f) Is the price in (e) the same as in question (b)? (Explain why.)arrow_forwardThe managing director of a consulting group has the accompanying monthly data on total overhead costs and professional labor hours to bill to clients. Complete parts a through c. Question content area bottom Part 1 a. Develop a simple linear regression model between billable hours and overhead costs. Overhead Costsequals=212495.2212495.2plus+left parenthesis 42.4857 right parenthesis42.485742.4857times×Billable Hours (Round the constant to one decimal place as needed. Round the coefficient to four decimal places as needed. Do not include the $ symbol in your answers.) Part 2 b. Interpret the coefficients of your regression model. Specifically, what does the fixed component of the model mean to the consulting firm? Interpret the fixed term, b 0b0, if appropriate. Choose the correct answer below. A. The value of b 0b0 is the predicted billable hours for an overhead cost of 0 dollars. B. It is not appropriate to interpret b 0b0, because its value…arrow_forwardUsing the accompanying Home Market Value data and associated regression line, Market ValueMarket Valueequals=$28,416+$37.066×Square Feet, compute the errors associated with each observation using the formula e Subscript ieiequals=Upper Y Subscript iYiminus−ModifyingAbove Upper Y with caret Subscript iYi and construct a frequency distribution and histogram. LOADING... Click the icon to view the Home Market Value data. Question content area bottom Part 1 Construct a frequency distribution of the errors, e Subscript iei. (Type whole numbers.) Error Frequency minus−15 comma 00015,000less than< e Subscript iei less than or equals≤minus−10 comma 00010,000 0 minus−10 comma 00010,000less than< e Subscript iei less than or equals≤minus−50005000 5 minus−50005000less than< e Subscript iei less than or equals≤0 21 0less than< e Subscript iei less than or equals≤50005000 9…arrow_forward
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