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MMLU-Pro / 514 / Consider a strategy of the form (γ,0,0) for the investment wheel. Show…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Consider a strategy of the form (γ,0,0)(\gamma, 0, 0) for the investment wheel. Show that the overall factor multiplying your money after nn steps is likely to be (1+2γ)n/2(1−γ)n/2(1+2\gamma)^{n/2}(1-\gamma)^{n/2}. Find the value of γ\gamma that maximizes this factor.
Plain-text mathematical notation (without MathML)
Consider a strategy of the form (γ,0,0) for the investment wheel. Show that the overall factor multiplying your money after n steps is likely to be (1+2γ)^(n/2)(1−γ)^(n/2). Find the value of γ that maximizes this factor.
Original LaTeX notation
Consider a strategy of the form $(\gamma, 0, 0)$ for the investment wheel. Show that the overall factor multiplying your money after $n$ steps is likely to be $(1+2\gamma)^{n/2}(1-\gamma)^{n/2}$. Find the value of $\gamma$ that maximizes this factor.

category

business

options

  1. 0.80
  2. 0.25
  3. 0.10
  4. 0.33
  5. 0.50
  6. 0.66
  7. 1.00
  8. 0.20
  9. 0.40
  10. 0.75

src

theoremQA-Finance

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Source and history

upstream_id / Original problem ID
514
task_id
c3980802-a16e-5c21-bd29-e000ba6cde90
task_key
default--test--514
task_revision_id
1
config / split
default / test

Official source

initial import