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Questions and Answers of
Marketing Strategy Planning
Using the OLD School data used in the previous chapter, test the following measurement theory: A researcher believes that the items greedy, no_loyal, money, material, and cheating represent a factor
Using the GoodBuy data set from the last chapter, choose 12 variables and conduct an exploratory factor analysis. Describe your results in tables and in a brief summary.
Use the OLDSKOOL data introduced in Chapter 15 for this exercise. You can download the data from the student resources located at www.cengagebrain.com. The survey captured responses to 9-Point
Conduct a repeated measures analysis using the data shown in Exhibit 17.8. Include Sales 4 as an additional within-subjects measure. How do the results compare with those shown in the chapter using
Using the data from an earlier chapter describing coffee drinking habits by the shift that workers work (shown again here), prepare a pie chart(s) and at least one other type of chart that depicts
Prepare an Exhibit similar to 16.2 that shows the per capita bottled water consumption for the countries listed. Population stats for each country can be found in the CIA factbook discussed in an
Prove that holds
Check this result by using (21.16).(21.16)
Apply Itô’s lemma to confirm this result.
Use (19.8) to prove the second equality.(19.8)
Can you see why this is true?
The solution to Problem 15.1 isShow that this result is consistent in the limit T → ∞ and T → 0.Problem 15.1Assume that actual variance has the mean reverting term structurewhere σ2∞is the
Confirm this result by using (11.17) on page 215.(11.17)
Suppose instead of (14.16) on page 294, we had chosen the schemewhere the last term in parenthesis is with respect to time τ = (m + 1)Δτ. Prove that this scheme is still explicit and use a
Use Itô’s lemma to show that the forward pricefollows the stochastic processif the dynamics of St are governed by the geometric Brownian motion (13.5) on page 250.(13.5)
Convince yourself that (11.9) is correct.(11.9)
Convince yourself that (9.67) simplifies exactly to the original RVF (9.8) on page 157, when the stochastic discount factor is deterministic, Mt = δ.(9.67)(9.8)
Iterate (9.65) one period to confirm the construction.(9.65)
Confirm that (9.63) is indeed true.(9.63)
Convince yourself that the result (9.38) is correct.(9.38)
Can you see why E[eλeI+1|Ft] = eλ2σ2∈/2 in (9.36)?(9.36)
Can you see why this condition is necessary?
Verify the last equality in (9.17).(9.17)
Verify the last equality in (9.10).(9.10)
Verify Equation (9.2).(9.2).
In linear filtering theory, |η = | v − P|μ is called the innovation, and г = PΣP′ + Ω is the prediction error covariance. The quantity K = ∑P'T-1 is called the Kalman-filter gain, and the
Can you see why this is true?
Convince yourself that with (8.16), Ω = 1/c Var [P|R〉](8.16)
Verify the Kelly-criterion (8.12) for the portfolio problem. (8.12)
Convince yourself that (8.7) is correct.(8.7)
Prove that the half life of the difference in Problem 7.1 isyears.Problem 7.1Practitioners often assume that the true yearly β of a security decays towards βMP = 1 with time. A simple model for
Practitioners often assume that the true yearly β of a security decays towards βMP = 1 with time. A simple model for such a mean reversion process iswhereShow that β̂0 is given by
Prove the second equality in (7.69) by using that B is idempotent.(7.69)
Check that by reviewing (7.28) on page 126.(7.28)
Verify Equation (6.57).(6.57)
Prove the theorem by plugging μP = λμ1 + (1 − λ)μ2 into (6.46).(6.46)
Verify this result by deriving the respective first order condition.
Show that the variance of the MVP is given by
Confirm (6.26) by using (6.25).(6.26)(6.25)
Consider the same financial market as in Problem 5.5. Imagine at t = 0 an agent forms the portfolioWhat is the payoff ∏1 of this portfolio and which security does it replicate? Can you derive the
Use a zero-coupon bond to show that the expectation value of the stochastic discount factor in Problem 5.1 isProblem 5.1Assume that von Neumann–Morgenstern-utility is a time separable functional of
Verify the first equality in (5.57).(5.57)
Verify that the portfolio selection problem and its wealth constraint is summarized in (5.16).(5.16)
Assume that the commodity prices in the optimization problem (4.34) with (4.36) are p1 = 1 and p2 = 2. Show that in the optimum u(c*1,c*2) =w/√8 holds(4.34)(4.36)
Daniel Bernoulli was the first to suggest a kind of expected utility of wealth as a solution to the St. Petersburg paradox of Problem 4.1. He used logarithmic utilityShow that the expected utility of
The trace of a square matrix is a linear functional, defined as the sum of its principal diagonal elements,A further property of the trace is tr [AB] = tr [BA], for suitable matrices A and B. Show
Show that this definition gives the correct answer for (3.10) in IR2.(3.10)
A theorem by Kolmogorov (see Arnold, 1974, p. 24) states that every stochastic process X(t), which satisfies the inequality for t > s and a particular set of numbers a, b, c > 0, has almost
Again consider the die example of Problem 2.3. Show that the property holds for A being the event of throwing an even number.Problem 2.3.Consider rolling a fair die, with X(ω) as the number of pips
Bottle-Up, Inc., was organized on January 8, 2008, and made its S election on January 24, 2008. The necessary consents to the election were filed in a timely manner. Its address is 1234 Hill Street,
Ned Norris, a widower, engaged in the transactions described below during 2017. He made only one earlier taxable gift, $1.2 million in 2014. Use this information to prepare a 2017 gift tax return
Consider a hypothetical contract called a “reversing pair” by Joshi (2008, p. 319), which consists of a long position in a forward rate agreement, running from T0 to T1, and a short position in
Check this result.
Differentiate this equation to prove the claim.
Verify the second equality.
Formulate the parity relation for a callable bond.
Confirm this statement.
Check that this statement is true.
Convince yourself that f(t, t) = r(t) has to hold.
Confirm the last equality.
Use l'Hôpital’s rule to compute limκ→0 ψ sub.(u).
How does the last equation look for log-prices xt = log St?
Check that the last equality holds.
Verify that for K = 9 we have α = 1/2.
Confirm this parity relation by adding the payoffs.
Consider the environmental conditions of the standard example 12.1 on page 230 and valuate a knockout call option with upper knockout barrier Su = 125 and American exercise right. Formulate the
Let Ft be a filtration generated by the stochastic process Xt, and τ a stopping time with respect to Xt. The stopped σ-algebra is defined by Fτ = {A ∈ F : A ∩ {τ ≤ t} ∈ Ft for all t ∈
Show that for the deterministic stopping time of Problem 12.4, the stopped σ-algebra is Fτ = Fs.
In Example 12.2 on page 231, a European binary call was valuated with the binomial formula. Price the corresponding put option in the same setting, and check whether or not your result satisfies
Convince yourself that this choice is also stable.
Sketch the payoff function of a short call position.
Sketch the payoff function for a short call and short put position.
Verify the last result formally.
Confirm this derivative.
Give a formal verification of this statement.
Verify the last statement for x = ±1.
Check that this statement is correct.
Can you see how this probability was computed?
Confirm the first equality.
Confirm the factorial relations established above.
Convince yourself that the last argument is indeed true.
Convince yourself that the Kelly-fraction of Example 8.1 is perfectly sensible for the fair coin, p = 0.5, and also for the always winning coin, p = 1.
Show that B is symmetric and idempotent.
Verify the last equation for wS = 0.
Write the first order condition for this problem.
Confirm this result.
Verify this result.
Verify this first order condition.
Provide a formal argument for the last statement.
Check that both examples satisfy the required conditions for closed convex cones.
Verify the intermediate results in Example 5.1.
Confirm the last equation.
Convince yourself that the last statement is true.
Can you see why?
Below your own activity list, make a list of the assumptions you are making. Once complete, share your list and listen to the lists of assumptions other students recorded. Are you surprised how many
In teams, discuss each individual list of five practices. The output of this step is to generate a list of 10 practices.
You are developing an expert system to play Go. Give three examples of if/then rules you might use.
Search online for advances in AI expected over the next 5 years. Which advances are the most helpful for society, and which the most concerning?
Now, start to develop a pattern-matching system. Describe three input nodes and your output node.
Each individual, using the chapter as a guide, writes down five personal practices.
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