Fundamentals of Finance Lecture Notes

2660 FUNDAMENTALS OF FINANCE LEGEND : =
HEADINGS

LECTURES WEEK 1 -
WEEK 9
=
SUB -
HEADINGS

PROF . RORY MULLEN
=
FORMULAS

WARWICK BUSINESS SCHOOL ,
2021

CARLO DALLE MULE




TOPICS :
DIFFICULTY :




1. FINANCIAL ARITHMETIC • • B.

2. RISK AND EXPECTED RETURN 88 88

3. INVESTMENT UNDER CERTAINTY Be Bo

4. RISK AVERSION AND EXPECTED UTILITY • 08 •

5. OPTIMAL PORTFOLIO SELECTION Ba • or • • !
6. CAPITAL ASSET PRICING MODEL • • • Boa

7. MARKET EFFICIENCY •

8. BOND Do • • ooo
.




PRICING

9. FORWARDS AND FUTURES Be • or

10 .
OPTIONS Bo • 08 Oo ooo !


1. FINANCIAL ARITHMETIC

READINGS : •
HILLIER ET AL .
: 4. I -4.4
•
HILLIER ET AL .
: 5. I -5.3



SENSE OF TOPIC : ARITHMETIC TOOLS FOR BASIC FINANCIAL CONCEPTS . THESE

ARE FOUND THROUGHOUT FINANCE AND ARE MOSTLY BASED

ON THE TIME -
VALUE OF MONEY



SUB -
TOPICS :
1.1 :
DISCOUNTING CASHFLOWS AND NPV

1. 2 : ANNUITIES AND PERPETUITIES

1. 3 :
COUPON BONDS AND ASSET RETURNS



1. 1 DISCOUNTING CASH FLOWS AND NPU


FUTURE CASH FLOWS NEED TO BE DISCOUNTED TO FIND PRESENT VALUE



NPV OF CASH FLOWS :




É
r T ⇐+
CFT
☐Ft =
(ntpjt
PV= [ Npv = -

I +
CAR)t
+ CAR)t +




Lor •
R IS THE RELEVANT COST OF CAPITAL
•
t ARE THE PERIODS
•
I IS THE INITIAL INVESTMENT


↳ IF Npv > 0 THE PROJECT BRINGS VALUE

,1. 2 ANNUITIES AND PERPETUITIES

PERPETVITIES :




↳ CASH FLOWS RECEIVED IN PERPETUITY
IF THE ARE



pv =
Ept → AS IT IS A GEOMETRIC SERIES
SO THAT
,
THE QUESTION IS HOW MUCH MONEY

C ? /r
DO I NEED TODAY MY INTEREST IS EXACTLY → c



CF
PV = → IF THE PERPETUITY GROWS
p -
g

↳ •
G MUST BE SMALLER THAN r

•
IT IS ASSUMED THAT CASH FLOWS OCCUR AT DISCRETE

POINTS IN TIME



ANNUITIES :




↳ IF THE CASHFLOWS ARE CONSTANT AND RECEIVED FOR T PERIODS


↳ CAN BE DERIVED DIFFERENCE BETWEEN PERPETUITY STARTING
BY THE A

TODAY AND ONE STARTING AT T


±

( F- ) eF( )
^

( Ent)
1
-




( Hrt
¥
⇐
-
→ →
t

r



AT IS THE ANNUITY FACTOR

]
→ SOMETIMES

( (F-ryt
,
1-
CF
pv =
FORMULA IS DEFINED AS EF .

AI
r




IF THE ANNUITIES GROW SAME FORMULA CAN BE USED , ACCOUNTING FOR G
,




Piece
[1-4^7++1] r -


g



1. 3 COUPON BONDS AND ASSET RETURNS


COUPON BONDS :




↳ PAY CASHFLOWS AS COUPON AND FACE VALUE AT LAST PERIOD


↳ TREATED AS AN ANNUITY 1- PV OF LAST PAYMENT




GIRI] +
/
FV
^ -




Pv= ee
r Gtr)T

,ASSET RETURNS :




↳ EXPRESSED IN PERCENTAGE


↳ ALWAYS REFERRING TO A PERIOD → IN THIS CASE t → tt s


↳ TWO COMPONENTS :
VALUE GAIN AND CASHFLOW S




→
RETURN RATE IS PRICE INCREASE PLUS CASH Flows
Ptts -

Ptt EÉ^CFt
Rt , tts DIVIDED INITIAL PRICE
=
BY
pt

, 2. RISK AND EXPECTED RETURN

READINGS : •
HILLIER ET AL .
:
9. I -9.6
•
BODIE ET AL .
:
5. 4- 5.5
•
BODIE ET AL .
: 18.2



SENSE OF TOPIC :
WHENEVER THERE IS RISK ,
IT IS COMPENSATED FOR . STOCK RETURNS ,



HOWEVER , CANNOT BE PREDICTED AND ARE THEREFORE RANDOM

VARIABLES . EXPECTED RETURN IS USED INSTEAD .




SUB -
TOPICS : 2.1 :
RANDOM VARIABLES

2. 2
:
DISCRETE PROBABILITY DISTRIBUTION

2. 3 :
CONTINUOUS PROBABILITY DISTRIBUTION



2. 1 RANDOM VARIABLES :




RETURN ON STOCK :




→ FORMED BY TWO COMPONENTS :
CAPITAL GAIN AND DIVIDEND
Pttn P+tDNt+,
-




Ry =
→ CAPITAL GAINS CAN GO UNREALISED
Pt


↳ STOCK RETURNS ARE RANDOM VARIABLES :




RANDOM VARIABLE :
A NUMERIC QUANTITY THAT DEPENDS ON THE REALISATION

OF A RANDOM PROCESS



RANDOM PROCESS :
A SITUATION IN WHICH POSSIBLE OUTCOMES ARE KNOWN BUT

NOT WHICH ONE WILL HAPPEN


↳ USE OF PROBABILITY IS REQUIRED



2. 2 DISCRETE PROBABILITY DISTRIBUTIONS :




DISCRETE RANDOM VARIABLE : A RANDOM VARIABLE THAT TAKES ONLY A COUNTABLE
NUMBER OF POSSIBLE VALUES



MEAN OF DISCRETE RANDOM VARIABLE :




MEASURES
[ Nn=np(✗=xn)xn
→ CENTRALITY
µ=E(×)=


VARIANCE OF DISCRETE RANDOM VARIABLE :




→
En? p(✗ =Xn)(xn MY
MEASURES DISPERSION
02-_E[ ( ✗ -
MY] =
,
-