Learning Objectives: Explain how asset return distributions tend to deviate from the normal distribution. Explain reasons for fat tails in a return distribution and describe their implications. Distinguish between conditional and unconditional distributions and describe regime switching. Compare and contrast different approaches for estimating conditional volatility. Apply the exponentially weighted moving average (EWMA) approach to estimate volatility, and describe alternative approaches to weighting historical return data.
24.5.1. John, an investment manager, is analyzing two sets of equity’s TomCow and RamCow. He noticed that RamCow stock had an average return of 7.24 bps a day but sometimes had a high volatility of return at 13.24 bps per day, while other times there was a low volatility of 3.21 bps a day. Meanwhile, TomCow has an average return of 4.28 bps a day, a VaR that does not change over time, exhibits negative values, and does not show a skewed distribution. In comparison to TomCow, RamCow is more likely to exhibit which of the below traits:
a. Regime-switching distribution
b. Unconditional distribution
c. Conditional distribution
d. Unconditionally lognormal distribution
24.5.2 Given a GARCH model where α = 0.17, β = 0.65, ω = 0.00005 and current volatility is 5%. What is the long-run average variance rate that this model will revert towards over time?
a. 0.016667
b. 0.000278
c. 0.000294
d. 0.017149
24.5.3 Gigh Inc., a publicly traded company, had a wild swing today after OPEC cut production. Gigh ended the day with a -16% loss. Prior to this (most recently), the daily volatility was estimated to be 4.40% according to the exponentially weighted moving average (EWMA) model. The EWMA model had originally assumed a lambda ,λ, of 0.70, but David wants to adjust the model’s responsiveness to recent market conditions. David notices that his error is too high, so he wants to change the model to respond more quickly to changes in volatility, so he decides to decrease λ by 0.10. After David properly adjusts lambda, what is the new volatility estimate using EWMA?
a. σ = 8.16%
b. σ = 0.66%
c. σ = 10.67%
d. σ = 1.14%
Answers here:
24.5.1. John, an investment manager, is analyzing two sets of equity’s TomCow and RamCow. He noticed that RamCow stock had an average return of 7.24 bps a day but sometimes had a high volatility of return at 13.24 bps per day, while other times there was a low volatility of 3.21 bps a day. Meanwhile, TomCow has an average return of 4.28 bps a day, a VaR that does not change over time, exhibits negative values, and does not show a skewed distribution. In comparison to TomCow, RamCow is more likely to exhibit which of the below traits:
a. Regime-switching distribution
b. Unconditional distribution
c. Conditional distribution
d. Unconditionally lognormal distribution
24.5.2 Given a GARCH model where α = 0.17, β = 0.65, ω = 0.00005 and current volatility is 5%. What is the long-run average variance rate that this model will revert towards over time?
a. 0.016667
b. 0.000278
c. 0.000294
d. 0.017149
24.5.3 Gigh Inc., a publicly traded company, had a wild swing today after OPEC cut production. Gigh ended the day with a -16% loss. Prior to this (most recently), the daily volatility was estimated to be 4.40% according to the exponentially weighted moving average (EWMA) model. The EWMA model had originally assumed a lambda ,λ, of 0.70, but David wants to adjust the model’s responsiveness to recent market conditions. David notices that his error is too high, so he wants to change the model to respond more quickly to changes in volatility, so he decides to decrease λ by 0.10. After David properly adjusts lambda, what is the new volatility estimate using EWMA?
a. σ = 8.16%
b. σ = 0.66%
c. σ = 10.67%
d. σ = 1.14%
Answers here:
