Advances in Risk Management

RICCARDO BRAMANTE AND GIAMPAOLO GABBI 239

Table 12.11Optimization outputs

Frontier no. Portfolio 1 Portfolio 75

1 (no jumps) Return volatility 6.32 6.91
18.70 22.83

2 (negative jumps) Return volatility 6.37 6.92
16.60 21.95

3 (positive jumps) Return volatility 6.28 6.90
20.09 23.67

Notes: The table shows the return/risk values of the first optimization obtained with the historical
average values; the second optimization obtained with negative correlation jumps; and the first
optimization, obtained with positive correlation jumps.

2 this relation is, on a qualitative basis, demonstrated in all our analy-

sis; the benefits obtained in the correlation-jumps dataset are statistically

significant; and

3 in analysing only equity portfolios, errors we could make in ignoring

daily correlation jumps are around 18 percent (3.49 over 18.7) of volatility

in the less risky part of the frontier, and 7.5 percent (1.72 over 22.83) in

the most risky portfolios.

NOTES

1. If the (DW) is less than 2 (until 0), there is evidence of positive serial correlation. If
   there is no serial correlation, the DW statistic will be around 2. Finally, if there is
   negative correlation, the statistic will lie somewhere between 2 and 4


2. The other limitations are: (a) the distribution of the DW statistic under the null
   hypothesis depends on the data matrix. The usual approach to handling this problem
   is to place bounds on the critical region, creating a region where the test results are
   inconclusive; (b) me may only test the null hypothesis of no serial correlation against
   the alternative hypothesis of first-order serial correlation.

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