Chapter 5 quiz

Bayesian Methods for Investment Research

0 of 10 answered

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

Question 1

After seeing 1 258 daily returns, which object lets you say “P(reward-to-t-scale > 1) = 0.99”?

  • The likelihood \(p(X \mid \theta)\)
  • The prior \(p(\theta)\)
  • The posterior \(p(\theta \mid X)\)
  • The p-value of a t-test on the mean

Question 2

In the Bayesian regression, which quantities get a prior?

  • \(x\) and \(y\)
  • \(y\) only
  • \(\beta_0\), \(\beta_1\) and \(\sigma\)
  • The residuals \(\varepsilon_i\)

Question 3

How will OLS respond to three high points at small \(x\)?

  • Slope up, intercept down
  • Slope down, intercept up
  • Both unchanged — three points cannot matter out of 103
  • Slope up, intercept up

Question 4

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 5

Stock A has only three monthly residuals averaging +8%. Stock C has sixty averaging −1%. Under the same prior and residual variance, which receives less weight on its own sample mean?

  • A, because three observations carry less precision
  • C, because negative estimates must be removed
  • Both receive the same weight
  • Neither: Bayesian estimates must equal sample means

Question 6

A model has posterior model probability 0.90 within a three-model comparison. What does 0.90 describe?

  • Its probability of positive net profit next year
  • Its relative posterior probability within the declared model set and priors
  • Its probability of being the true causal mechanism
  • Its expected annual return

Question 7

Which choice of \(\nu\) produces the fattest tails?

  • \(\nu = 100\) — essentially normal
  • \(\nu = 3\)
  • \(\nu = 30\)
  • Tail weight does not depend on \(\nu\)

Question 8

Draw 100 lines with \(\beta_0, \beta_1 \sim N(0, 10)\). At \(x = 10\), what range covers 95 % of them?

  • About ±3
  • About ±10
  • About ±30
  • About ±200

Question 9

OLS gives \(\beta \approx 1.06\). What will a Student-t likelihood give?

  • Exactly the same — beta is beta
  • Much lower, because crash days are removed
  • Slightly different in a direction you cannot predict in advance
  • Exactly 1 — the CAPM says so

Question 10

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