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The Role of Mathematics in Investment Decision-Making: An Applied Study
of Mathematical Expectation and Variance Criteria
tebessa.dz-mohammed.rouabhia@univ
tebessa.dz-latifa.bahloul@univ
.
Investment is a process of forecasting the future and making influential
decisions that carry both risks and opportunities. Investment decisions present
investors with challenges and opportunities they cannot ignore, as they constantly
strive to make optimal choices to achieve financial gains. A significant challenge
facing investors involves data analysis, risk estimation, and potential gains. This is
where the importance of mathematics comes into play.
Mathematics is not just a theoretical science but a powerful tool that enables
the analysis of information and the formulation of accurate conclusions. In the world
of investment, mathematics can guide decisions and increase their precision. Whether
you are trying to estimate the present value of a specific investment, analyze stocks, or
manage an investment portfolio, mathematics equips you with powerful tools to make
informed decisions.
This research aims to explore the pivotal role played by mathematics in
investment decision-making. We will examine how mathematical models and
quantitative analysis are used to estimate value, manage risks, and enhance
investment performance. Case studies and practical applications will be presented to
illustrate how mathematics is employed in making smart investment decisions.
Kaywords: Investment – Risk Management – Project Evaluation – Return and Risk –
Investment Decision Making – Investment – Investment Decision.
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1
1 J.L Bailly et des autres , Macroéconomie , 2eme édition , Aubin imprimeur, paris , 2006, pp 101-102
1
FBCF
QS
I= FBCF+DS
2
3
2
1
2
3
1
.
.2
2
. 3
3
4
ردنأ ميلو فطاع 1
2
3
4
1
2
3
DRDélai de Récupération
DR=I0/CF
I0
CF
DR
DR
1
2
3
DR
TRC(Taux de Rendement Comptable
TRC= RN'/I0*100
RN'
I0
TRC
VAN (La Valeur Actuelle Nette
VAN = ΣCFi=1…n (1+t) –i+vR (1+t) -n -I0
VAN = CFi [(1-(1+t) -n) /t] -I0
CFivRI0
nt
VAN
VAN
VAN
(Taux de Rentabilité Interne) TRI
1
TRIVAN
ΣCFi=1…n (1+TRI) –i+ vR (1+t) -n = I0
TRI
VAN1 t1VAN2t2
TRI = t1 + [VAN1/ (VAN1-VAN2)] * (t2-t1)
VAN1t1
VAN2t2
t1t2
-1
.
1
IPIndex Profitability
IP = (ΣCFi=1…n (1+t) -i) /I0
CFit I0
n
o IP
o IP≤
VAN
EVANƩPiVAN
I0
Pi
VAN
VAN = ΣCFi=1…n (1+t) –i+vR (1+t) -n -I0
E(VAN)= (1+t) –*E(CF1)]+….+ (1+t) –n*E(CFn)]+ (1+t) –n*E(VR)]- I0
o E(VAN)
o E(VAN)
2
VVAN=∑ E(VAN^2)-[E(VAN)]^2
V(VAN)=∑i=1…i=n(1+t)^-i*v(CFi)
1 - هسفن عجرملا ص ،16.
2 -
1
P1P2
I0 : P1NI0 : P2N
P1
CF1
Pi
CF2
Pi
1
2
3
60
70
80
0.3
0.4
0.3
50
60
70
0.4
0.3
0.3
P2
CF1
Pi
CF2
Pi
1
2
3
30
62
90
0.3
0.4
0.3
50
80
100
0.4
0.4
0.2
182
230
P1P2
%VR CF
P1
P1
CF1
Pi
Pi CF1
P CF1^2
CF2
Pi
Pi CF2
P CF2^
1
2
3
60
70
80
0.3
0.4
0.3
18
28
24
1080
1960
1920
50
60
70
0.4
0.3
0.3
20
18
21
1000
1080
1470
70
4960
59
3550
-E(VAN)
E(VAN)= (1+t) –*E(CF1)]+….+ (1+t) –n*E(CFn)]+ (1+t) –n*E(VR)]- I0
1 -
E(VAN)=[(1.1^-1)*(70)]+[(1.1^-2)*(59)]-100 =12.39 >0
V(VAN)
V(VAN)=∑i=1…i=n(1+t)^-i*v(CFi)
VVAN (1.1^-1)*[4960-(70^2)] + (1.1^-2)*[3550-(59^2)] = 111.59
P2
P2
CF1
Pi
Pi CF1
P CF1^
CF2
Pi
Pi CF2
P CF2^
1
2
3
30
62
90
0.3
0.4
0.3
09
24.8
27
270
1537.6
2430
50
80
100
0.4
0.4
0.2
20
32
20
1000
2560
2000
182
60.8
4237..6
230
72
5560
-E(VAN)
E(VAN)= (1+t) –*E(CF1)]+….+ (1+t) –n*E(CFn)]+ (1+t) –n*E(VR)]- I0
E(VAN)=[(1.1^-1)*(60.8)]+[(1.1^-2)*(72)]-100 =14.77 >0
V(VAN)
V(VAN)=∑i=1…i=n(1+t)^-i*v(CFi)
VVAN (1.1^-1)*[4237.6-(60.8^2)] + (1.1^-2)*[5560-(72^2)] =802.52
P2
P1
I
II
-
III
J.L Bailly et des autres , Macroéconomie , 2eme édition , Aubin imprimeur, paris ,
2006, pp 101-102