Advances in Risk Management

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Table 12.10 Optimization inputs

Panel A: optimization no. 1

Historical correlation

Historical Historical Topix S&P 500 DJ Euro

return volatility Index Stoxx 50

Topix 6.15 20.80 1

S&P 500 Index 7.10 25.38 0.55 1
DJ Euro Stoxx 50 6.59 23.52 0.45 0.81 1

Notes: First column: historical average returns determined in the long run (1976–2005) for Topix and
S&P 500 Composite; the Euro Stoxx has been computed for the period 1976–2004.
Second column: historical average volatility determined in the long run (1976–2005) for Topix and
S&P 500 Composite; the Euro Stoxx has been computed for the period 1976–2004. The methodology
is the exponential weighted with a 0.94 decay factor.
Third to fifth column: correlation matrix determined in the long run (1976–2005) for Topix and S&P
500 Composite; the Euro Stoxx has been computed for the period 1976–2004. The methodology is
the exponential weighted with a 0.94 decay factor.

Panel B: optimization no. 2

Historical correlation

Historical Historical Topix S&P 500 DJ Euro

return volatility Index Stoxx 50

Topix 6.15 20.80 1
S&P 500 Index 7.10 25.38 0.34 1
DJ Euro Stoxx 50 6.59 23.52 0.14 0.61 1

Note: Third to fifth column: correlation matrix determined applying the max negative jumps observed
in the 2003–05 period.

Panel C: optimization no. 3

Historical correlation

Historical Historical Topix S&P 500 DJ Euro

return volatility Index Stoxx 50

Topix 6.15 20.80 1
S&P 500 Index 7.10 25.38 0.8 1
DJ Euro Stoxx 50 6.59 23.52 0.69 0.96 1

Note: Third to fifth column: correlation matrix determined applying the max positive jumps observed
in the 2003–05 period.