Advances in Risk Management

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40 RESID Number of observations  56 daily changes Spread between actual and ...

RICCARDO BRAMANTE AND GIAMPAOLO GABBI 237 12.4 Impact on portfolio optimization This last section is dedicated to a portfolio op ...

238 Table 12.10 Optimization inputs Panel A: optimization no. 1 Historical correlation Historical Historical Topix S&P 500 D ...

RICCARDO BRAMANTE AND GIAMPAOLO GABBI 239 Table 12.11Optimization outputs Frontier no. Portfolio 1 Portfolio 75 1 (no jumps) Ret ...

240 CORRELATION BREAKDOWNS IN ASSET MANAGEMENT Loretan, M.andEnglish, W.B.(2000)“EvaluatingCorrelationBreakdownsDuringPeriods of ...

CHAPTER 13 Sequential Procedures for Monitoring Covariances of Asset Returns Olha Bodnar 13.1 INTRODUCTION Time variability of t ...

242 MONITORING COVARIANCES OF ASSET RETURNS returns with the higher frequency are used for calculating the covariance matrix. Th ...

OLHA BODNAR 243 we estimate this quantity within an extensive Monte Carlo study. Final remarks are presented in section 13.5. Th ...

244 MONITORING COVARIANCES OF ASSET RETURNS The different estimation procedures and their influences on the distribu- tional pro ...

OLHA BODNAR 245 fortheGMVPweights. Forexample, takenL=e 1 =(1,0, ..., 0)asthepdimen- sional vector with the first element being ...

246 MONITORING COVARIANCES OF ASSET RETURNS (b) The covariance matrix ofvˆ ̃is equal to: Var(vˆ ̃)= n−p 2     (n−p 2 − 1 )  ...

OLHA BODNAR 247 where all elements ofμηat positionsq+1, 2q+1, 3q,4q−2, 5q−3,...,q+ q(q+1)2 are equal to (n ̃−p)/(n ̃−p−2) and th ...

248 MONITORING COVARIANCES OF ASSET RETURNS 13.3.1 T^2 Control chart The multivariate Shewhart control chart (Hotelling, 1947) i ...

OLHA BODNAR 249 13.3.3 Vector valued CUSUM Crosier (1988) proposed the multivariate CUSUM control chart, namely MCUSUM, that is ...

250 MONITORING COVARIANCES OF ASSET RETURNS problem is that the direction is unknown and therefore the statistic cannot be direc ...

OLHA BODNAR 251 The MEWMA chart gives an alarm when Qt=(Zt−μη)′#−Zt^1 (Zt−μη)>h 4 (13.14) where#Ztis the covariance matrix of ...

252 MONITORING COVARIANCES OF ASSET RETURNS The testing problem for the simultaneous control charts is presented by H0,t:E(η (j) ...

OLHA BODNAR 253 A large value ofsimPPCUSUMtis a hint that a change in the covariance matrix of the asset returns has occurred. F ...

254 MONITORING COVARIANCES OF ASSET RETURNS by the daily returns (Schwert, 1989). It follows from Theorem 1 that for each i, the ...

OLHA BODNAR 255 Table 13.1Control limits of the multivariate MEWMA, MEWMAas, MC1, MCUSUM,T^2 charts (section 13.3, in-control, A ...