Chapter 6 · Section 6 practice

Asymmetric Volatility and Position Sizing

0 of 4 answered

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

Question 1

For a stock index, the sign of \(\gamma\) is expected to be:

  • Negative — good news is more surprising
  • Positive — bad news raises volatility more (the leverage effect)
  • Zero — the square already captures size
  • Depends on the seed

Question 2

Two-step ARMA+GARCH means:

  • Fit ARIMA on \(r_t\), then fit GARCH on the ARIMA residuals
  • Fit GARCH on \(r_t\), then fit ARIMA on \(\sigma_t\)
  • Fit both on \(r_t\) independently and average
  • Fit ARIMA on \(r_t^2\)

Question 3

Compared with the calmest quartile, the most volatile quartile will show:

  • Much higher mean return — risk is rewarded day by day
  • Similar mean return but roughly double the sd — worse return per unit of risk
  • Negative mean return always
  • Zero sd

Question 4

Compared with buy-and-hold, the vol-targeted book should show…

  • Higher return, higher drawdown — it levers up
  • Lower return, same drawdown — scaling is a cost
  • Realised sd near 1 %, roughly half the drawdown, higher Sharpe, similar total return
  • Identical — scaling is a monotone transform