Advances in Risk Management

RICCARDO BRAMANTE AND GIAMPAOLO GABBI 237

12.4 Impact on portfolio optimization

This last section is dedicated to a portfolio optimization simulation for

the three equity markets considered. We optimize three different efficient

frontiers:

1 The first frontier is determined by optimizing the historical returns along

with volatilities and the correlation matrix (Table 12.10, panel A).

2 The second frontier is determined by optimizing the historical returns

and volatilities. The correlation has been changed with the maximum

negative jumps observed during the historical window, that is 1 January

2003 until 31 March 2005 (Table 12.10, panel B).

3 The third frontier is also determined by optimizing the historical returns

andvolatilities. Thecorrelationhasbeenchangedwiththemaximumpos-

itive jumps observed during the historical period (Table 12.10, panel C).

The outcomes are reported in Table 12.11. There are 100 optimized port-

folios, and have reported portfolion. The number 1 implies that it is the

less hazardous, and the number 75 avoids the concentration problem which

characterizes all the optimizationsàlaMarkowitz. Our results demonstrate

that by introducing correlation jumps, in both directions, we would obtain

portfolios with volatilities that in the left side (less risky) could have changed

in a range of 3.49 percent (20.09–16.6). In the right side (portfolio no. 75) the

range of volatility is 1.72 percent (23.67–21.95).

12.5 Conclusion

The possible occurrence of correlation jumps would considerably change the

profile of the investor. Our statistical results, presented in the third section,

demonstrate that not only correlations can change in the short run, but

also, in some cases, these events occur with volatility shocks. Correlation

breakdowns should be considered in order to evaluate:

(a) the impact for portfolios volatilities estimated by investors and their

private bankers;

(b) the decisions of portfolio managers; and

(c) the monitoring process of risk managers.

The answers offered by the study are:

1 there is a relation between exponential correlation changes and volatility

movements, even though it depends on the market where outcomes are

estimated;