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# P1.T4.327. Implied volatility

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
AIMS: Explain the process of return aggregation in the context of volatility forecasting methods. Describe implied volatility as a predictor of future volatility and its shortcomings. Explain long horizon volatility/VaR and the process of mean reversion according to an AR(1) model.

Questions:

327.1. The graphic below (Linda Allen's Figure 2.12) illustrates three discussed approaches to portfolio return aggregation in the context of producing an single overall value at risk (VaR). The approaches are numbered (1 to 3):

According to Linda Allen, which of the following best summarizes the advantage of the second (number 2) approach?

a. It offers a theoretical justification for salvaging the assumption of normality
b. It offers a justification if the portfolio is not well-diversified
c. It avoids bootstrapping (historical simulation) altogether
d. No advantage: approach two is "not sufficiently different, in practice, from the first approach to warrant serious consideration"

327.2. Linda Allen asserts each of the following as true about IMPLIED VOLATILITY except which is false?

a. Empirical results show that implied volatility, on average, is greater than realized (historical) volatility
b. Higher implied volatility (versus realized volatility) can be rationally explained with a stochastic volatility premium
c. A key shortcoming of implied volatility is its model-dependence, especially where Black-Scholes assumes constant volatility in a lognormal diffusion process, which is unrealistic
d. Implied volatility is convenient to most portfolio types and sizes, in part because implied correlations are easy to access

327.3. The current daily volatility of an asset is 1.0%. Analyst Robert wants to annualize this volatility by applying the square root rule, and assuming 250 trading days per year: 1.0%*SQRT(250) = 15.81%. However, he is aware of two caveats. First, the asset returns exhibit mean reversion (negative serial- or auto-correlation of returns). Second, the current volatility of 1.0% is below the long run mean (LRM) volatility; i.e., the "steady state" volatility is higher than 1.0%. Which of the following is most likely true about the asset's annualized volatility?

a. Annual volatility is less than 15.81%
b. Annual volatility is equal to 15.81%
c. Annual volatility is greater than 15.81%
d. It is unclear, annual volatility might be greater or less than 15.81%