Investment Analysis

Qestion1 Data description and risk measurements

The data description of 5 assets is presented by the table1.1

Table 1.1

Portfolio

Market Capitalization

(in EUR billion) Weights

(w) Average monthly

return(μ) Standard Deviation

KLM 4.8282 2.5% 0.698% 16.383%

AHOLD 16.0442 8.3% 0.655% 12.011%

HEINKEN 18.4926 9.6% 0.721% 7.111%

SHELL 114.682 59.3% 0.452% 6.696%

UNILEVER 39.4007 20.4% 0.679% 7.114%

The expected monthly return of the portfolio is calculated as: Rp=w’μ=0.547%

The risk of portfolio is calculated by the

σ_p^2=w’Σw= 0.38% σp= 6.20% (Σ can be found in Appedix 1.1)

Suppose the initial wealth to be €250,000, the monthly 99% Value at Risk is computed in the following equation:

VaR=Wt(2.33×σ-μ)= 34740.69

In order to calculate the GUISE, we need to compute the geometric monthly return using the method: geometric average= arithmetic average- 1/2 σ^2

Annualized σ = monthly σ×√12=6.20%×√12=21.47%

Annualized geometric average return= 0.547%×12-0.5×0.21472= 4.258%

GUISE is calculated by x(0.10)=0.3125×x(0.01)+0.4375×x(0.05)+0.2500×x(0.10)

Table 1.2

Investment 250000

μ 4.258%

σ 21.47%

H 1/12

z_0.01 -2.326

z_0.05 -1.645

z_0.10 -1.282

x_0.01 217201.52

x_0.05 226572.19

x_0.10 231731.77

GUISE 224933.75

VaR (value at risk)is the maximum amount that we are going to lose with a certain probability. In this case, there is 1% possibility of the conditions that we will lose more than €34740.69 with an investment of €250000. On the other hand GUISE described the expected payoff in the 10% worst scenario. Here we could expect €224933.75 as payments in the worst case. It implies that the loss in the worst 10% stage will be €25066.25, which is smaller than 99%