The Bionic Turtle presents the first tutorial in the schedule for the 2007 FRM exam

1. Quantitative Analysis (I.1 & I.2) 2007 FRM > 1st Movie

2. Volatility What is it? 1 3 GARCH 4 EWMA 5 Key Takeaways 6 Moving average 2 Forecasting approaches Quantitative Analysis (I.1 & I.2)

3. What is it?

4. What is it?

5. What is it? Mean =1 st moment Standard deviation = 2 nd Skewness = 3 rd Kurtosis = 4 th

6. What is it? Traditional risk measure Contrast with downside measures (negative semi-variance)

7. Approaches

8. Approaches

9. Approaches Jorion calls this “ Moving average”

12. Conditional Unconditional “ Average volatility is 15%” What is the current Volatility? Implicit Embedded in market prices Conditional A function of Yesterday’s Variance (“conditional” on recent past)

13. EWMA

14. EWMA Weighted Scheme Alphas are weights, so they must sum to one

15. EWMA Weighted Scheme Alphas are weights, so they must sum to one

16. EWMA Weighted Scheme Exponentially Weighted Moving Average (EWMA) Alphas are weights, so they must sum to one In EWMA weights also sum to one, however they decline in constant ratio (lambda)

17. EMWA (cont) Exponentially Weighted Moving Average (EWMA) RiskMetrics TM (EWMA) RiskMetrics TM is EWMA with a lambda (smoothing constant) of ~0.94 Lambda is the “persistence parameter” or “smoothing constant”

18. Weighting Schemes EWMA RiskMetrics TM =  Variance n-1 + (1-  ) Return 2 n-1 = (.94) Variance n-1 + (.06) Return 2 n-1

19. Weighting Schemes GARCH(1,1) =  Variance (Average) +  Variance n-1 +  Return 2 n-1 EWMA RiskMetrics TM =  Variance n-1 + (1-  ) Return 2 n-1 = (.94) Variance n-1 + (.06) Return 2 n-1

20. Weighting Schemes GARCH(1,1) EWMA RiskMetrics TM A special case of GARCH(1,1) where gamma=0 and (alpha + beta = 1) EWMA with lambda = 0.94

21. GARCH(1,1) If gamma < 0, then GARCH(1,1) is unstable GARCH(1,1) 

34. EWMA vs. GARCH(1,1)