Essay About Monthly Return Of The Portfolio And Expected Payoff

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
Average monthly
return(μ)
Standard Deviation
4.8282
0.698%
16.383%
AHOLD
16.0442
0.655%
12.011%
HEINKEN
18.4926
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%
Table 1.2
Investment
250000
4.258%
21.47%
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%