Advances in Risk Management

36 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT far greater structure on firm preferences, information and beliefs. Sinceη ...

AMIYATOSH PURNANANDAM ET AL. 37 generates an optimal portfolioη∗ 2 =[1, 1, 0.50]T. As expected, only the position in the second ...

38 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT We endogenously determine the value of portfolio insurance by equating the ...

AMIYATOSH PURNANANDAM ET AL. 39 equated. Thus, the price of the insurance contract equalsICwo+qη=qηwo, implying ICwo=q(ηwo−η) ...

40 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT with linear complementarity conditions: { y−QQλ=−(Pη)− y≥0, λ≥0, λy= 0 ( ...

AMIYATOSH PURNANANDAM ET AL. 41 row rank,PPis positive definite. This property impliesλwPPλw≥0 which yields (λw(Pη)−)^2 ≤λw ...

42 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Henceδwois not optimal. A similar contradiction is obtained if one assumes ...

AMIYATOSH PURNANANDAM ET AL. 43 Therefore, although risk is defined in terms of thel^2 norm on portfo- lio weights, it may be co ...

44 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Our analysis incorporates market frictions such as illiquidity and trans- ...

AMIYATOSH PURNANANDAM ET AL. 45 using subadditivity. However,ρ(γηc) equals zero since this portfolio is accepted by the regulato ...

46 INCORPORATING DIVERSIFICATION INTO RISK MANAGEMENT Therefore, (λ 1 +λ 2 )(y 1 +y 2 )=λ 1 y 2 +λ 2 y 1 =λ 1 PPλ 2 +λ 2 P ...

CHAPTER 3 Sensitivity Analysis of Portfolio Volatility: Importance of Weights, Sectors and Impact of Trading Strategies Emanuele ...

48 SENSITIVITY ANALYSIS OF PORTFOLIO VOLATILITY Such models are usually categorized in the literature as Stochastic Volatility m ...

EMANUELE BORGONOVO AND MARCO PERCOCO 49 asEis not additive, and Limitation 1 would be replaced by the following (Borgonovo and A ...

50 SENSITIVITY ANALYSIS OF PORTFOLIO VOLATILITY 3.2 SENSITIVITY ANALYSIS BACKGROUND Recently, the activity in the scientific fie ...

EMANUELE BORGONOVO AND MARCO PERCOCO 51 As a consequence, ∑n s= 1 Ds(x^0 ,dx)= 1 (3.4) for example, the sum of theDi(i=1,...,n) ...

52 SENSITIVITY ANALYSIS OF PORTFOLIO VOLATILITY the impact of TRS on portfolio properties. We begin with a simple example. Examp ...

EMANUELE BORGONOVO AND MARCO PERCOCO 53 proving that ranking based onPDsis equivalent to ranking based onD (^1) s(a^0 ), for exa ...

54 SENSITIVITY ANALYSIS OF PORTFOLIO VOLATILITY 1982), the utilization of these models has become widespread, ranging from asset ...

EMANUELE BORGONOVO AND MARCO PERCOCO 55 Proposition 3 The differential importance of weightaiwith respect to σpGARCHfor any chan ...