Chapter 5 · Section 4 practice

Sequential Learning and Adaptive Risk

0 of 3 answered

These questions review the examples in the companion slides. Choose an answer, then check the explanation.

Question 1

After 253 daily updates with \(\sigma = 0.02\) and prior sd 0.002, what is the posterior sd of \(\mu\)?

  • \(\sqrt{1/(1/0.002^2 + 253/0.02^2)} \approx 0.00106\)
  • \(0.002 / 253 \approx 0.0000079\)
  • \(0.02 / \sqrt{253} \approx 0.00126\)
  • It depends on the order of the returns

Question 2

During the March 2020 crash the posterior sd of μ…

  • Widened, because the returns were extreme
  • Stayed constant
  • Kept shrinking — the update only counts observations
  • Reset to the prior

Question 3

With \(q > 0\) added every day, what happens to the posterior variance \(v_t\) in the long run?

  • It still shrinks to zero, just more slowly
  • It settles at a positive steady state
  • It grows without bound
  • It oscillates