We consider a portfolio selection problem with n assets and N periods. At the beginning of...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
We consider a portfolio selection problem with n assets and N periods. At the beginning of each period, we re-invest our total wealth, redistributing it over the n assets using a fixed, constant, allocation strategy * ER" , where 72 € 20,Σ" = 1 In other words, if W(t-1) is our wealth at the beginning of period t, then during period t we invest Xi W(t-1) in asset i. We denote by 2(t) the total return during period t, i.e., 2(t)=W(t)/W(t-1). At the end of the N periods our wealth has been multiplied by the factor N II X(t) i=1 We use a discrete stochastic model to account for the uncertainty in the returns. We assume that during each period there are m possible scenarios, with probabilities Aj, j = 1,..., m . In scenario j, the return for asset i over one period is given by Pij . Therefore, the return 2(t) of our portfolio during period t is a random variable, with m possible values P₁,... P and distribution T₁ = P(x(t) = px) The target for the investment strategy is to maximize the log long term relative wealth LogLT RW Task = lim N log N 772 W(N) W (0) Show that LogLT RW = log(px) Tj according to the considered discrete stochastic model We consider a portfolio selection problem with n assets and N periods. At the beginning of each period, we re-invest our total wealth, redistributing it over the n assets using a fixed, constant, allocation strategy * ER" , where 72 € 20,Σ" = 1 In other words, if W(t-1) is our wealth at the beginning of period t, then during period t we invest Xi W(t-1) in asset i. We denote by 2(t) the total return during period t, i.e., 2(t)=W(t)/W(t-1). At the end of the N periods our wealth has been multiplied by the factor N II X(t) i=1 We use a discrete stochastic model to account for the uncertainty in the returns. We assume that during each period there are m possible scenarios, with probabilities Aj, j = 1,..., m . In scenario j, the return for asset i over one period is given by Pij . Therefore, the return 2(t) of our portfolio during period t is a random variable, with m possible values P₁,... P and distribution T₁ = P(x(t) = px) The target for the investment strategy is to maximize the log long term relative wealth LogLT RW Task = lim N log N 772 W(N) W (0) Show that LogLT RW = log(px) Tj according to the considered discrete stochastic model
Expert Answer:
Answer rating: 100% (QA)
LogLT RW t 1 N log Wt1 Wt As 1 WtWt1t where t denotes the return during period t we can rewri... View the full answer
Related Book For
Financial Accounting and Reporting a Global Perspective
ISBN: 978-1408076866
4th edition
Authors: Michel Lebas, Herve Stolowy, Yuan Ding
Posted Date:
Students also viewed these mathematics questions
-
In the complex notation there is a clever device for finding the time average of a product. Suppose f(r, t) = Acos (k ?? r ?? wt + a) and g(r, t) = B cos (k ?? r ?? wt + b). Show that (fg) = (1/2) Re...
-
List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...
-
Mrs. B, recently widowed and in her mid to late 40s, is a senior executive working for a Singapore-based multi-national corporation with SGD 10 billion in global sales. She has a son aged 20 and a...
-
What are the premises for successful paleostress analysis?
-
A friend says to you, I dont understand how taxable temporary differences can be liabilities and how deductible temporary differences can be assets. It seems to me that these temporary differences...
-
In Exercises sketch each scalar multiple of v. (a) 4v (b) -1/2v (c) 0v (d) -6v v = (-2, 3)
-
Air flows in a horizontal 100-ft-long, 24-in. \(\times 24\)-in. duct at the rate of \(5000 \mathrm{ft}^{3} / \mathrm{min}\). The air then flows through an expansion into \(200 \mathrm{ft}\) of 36-in....
-
Strong Welding Equipment Company produces and sells welding equipment nationally and internationally. Following is information about two divisions. REQUIRED A. Calculate each divisions ROI. B....
-
5. A three-stage, single acting compressor is required to compress 135m of free air per hour from 1bar to 64bar. Prove that with complete intercooling the stage pressure ratio should be equal to the...
-
Derive and solve the equation of motion for the mass m in terms of the variable x for the system shown. Neglect the mass of the lever AOC and assume small oscillations. C k2 k1 ww TxB = bo cos ot A a
-
After watching the video on British companies sourcing from China and the logistics coordination that is needed to maintain quality and throughput and reading the comments of Mark Richardson of the...
-
The purchase of new office furniture for a boardroom has caused conflict between two factions within a company. One faction argues that the company should buy modern furniture, which will cost 24...
-
a. A range of office furniture includes a chunky hardwood table weighing \(18 \mathrm{~kg}\) and a much lighter table with a \(3.0 \mathrm{~kg}\) virgin aluminium frame and a \(3.0 \mathrm{~kg}\)...
-
The chief goal of the private sector is effciency.Why? The primary focus of the public sector is equity. Why? It is quite possible to be highly effcient yet ineffective. It is also possible to be...
-
Disposable knives and forks are ordered by an environmentally-conscious pizza house. The shape of each (and thus the length, width and profile) are fixed, but the thickness is free: it is chosen to...
-
Why is healthcare reform such a contentious issue in the United States? Why have public and private efforts been unsuccessful in fully addressing the challenge of affordable health care? What role(s)...
-
Johnson, Incorporated acquired 90 percent of Nemec Enterprises on November 1, 20x5. As of that date, Nemec had inventory with a market value of 60,000 greater than the book value and long-term debt...
-
What are the three kinds of research types? Explain each type.
-
JSC Aeroflot Russian Airlines (Aeroflot) was formed as a joint stock company following a government decree in 1992. The 1992 decree conferred all the rights and obligations of Aeroflot Soviet...
-
Haeffner PLC is an accounting firm. Some of its clients face the following situations. For each, it is assumed that a reliable estimate can be made of any outflows expected: 1. On 9 December X1 the...
-
Saint Gobain, a France-based global enterprise, is involved in the production and sales of flat glass and building materials. It reports in its financial statements for the year ended 31 December...
-
The comparative statements of financial position of Borra Services as at 30 June 2024 and 2025 and the statement of financial performance for the year ended 30 June 2025 are shown overleaf....
-
The following comparative statements of financial position and statement of financial performance are for the business of Low Dollar Shop Pty Ltd. Additional information 1. All sales and purchases of...
-
The financial statements for the business of Autocare are shown below. Required (a) Prepare the statement of cash flows for Autocare for the year ended 30 June 2025, using the direct method. (b)...
Study smarter with the SolutionInn App