Lecture 6 Afternoon 1 .pdf - Part 2 Risk CORPORATE FINANCE...

Part 2
Risk
CORPORATE FINANCE (PSBV026NABB)
Nóra Felföldi-Szűcs, PhD
Department of Finance, Corvinus
University of Budapest
2021 FALL

Foundations of Corporate Finance
1. Time
2. Risk
!
Utility
!
The nature of risk
!
Correlation & diversification
!
Portfolio return and standard
deviations
!
Portfolio Theory
!
Systematic and issuer-specific
risk
!
Capital Asset Pricing Model &
Beta
!
Capital Structures
3. Analysis
!
Financial Statements
!
Ratios
10/25/21
This Course – the structure

Part 2.1
Risk:
Modern Portfolio Theory
CORPORATE FINANCE (PSBV026NABB)
Nóra Felföldi-Szűcs, PhD
Department of Finance, Corvinus
University of Budapest
2021 FALL

Corporate Finance, CUB - Nóra, Felföldi-Szűcs, PhD
Topics Today
Single Asset Risk
Multiple Asset Risk
Utility functions
Modern Portfolio Theory
1. Decision: Capital Allocation
2. Decision: Asset Allocation
2
FNÁ1

Corporate Finance, CUB - Nóra, Felföldi-Szűcs, PhD
Risk and investors
Which one would an average risk investor choose if the initial investment is the same for the two
opportunities?
• 100.000 USD next year
• 50.000 USD with a probability of 50% or 150.000 USD with a probability of 50% next year
" Investors are risk averse
" required return is higher for risky investments: RISK PREMIUM
" present value of risky cash flows in the future is LOWER

Corporate Finance, CUB - Nóra, Felföldi-Szűcs, PhD
Risk in finance
200
A

Prices or Returns?
Security Prices
Security Returns
Random Variable for Time Series
We generally use Returns not Prices
De-composition
Cumulation
(compounding)
300
3,000
Feb 92 Jul 97 Jan 03 Jul 08 Dec 13 Jun 19
S+P 500
-20%
-15%
-10%
-5%
0%
5%
10%
15%
Feb 92 Jul 97 Jan 03 Jul 08 Dec 13 Jun 19
S+P 500

Corporate Finance, CUB - Nóra, Felföldi-Szűcs, PhD
Measuring Risk
VARIATION OF RETURNS (income, price gains) aka PRICE VOLATILITY measures RISK
• NOT using Absolute Deviations from the mean
• very bad math e.g. compounding risk over several time periods
• Variance (average Squared Deviations from the mean)
• better math: Variances ADD
• higher weight for outliers
• Standard Deviation (square-root of the variance)
• a more intuitive measure

Corporate Finance, CUB - Nóra, Felföldi-Szűcs, PhD
Where
p
i
= probability of a state
r
i
= return at a certain state
̅ r = mean return
(NB in Statistics, estimates of σ
2
and σ are slightly different)
Single Asset Returns: Mean and Variance
Concept Symbol
Ex Post
(average ….)
Ex Ante
(expected…)
Mean Return μ, or E(r)
!
1
n
r
i
x
1
n
! p
i
r
i
Variance σ
2
, or Var
!
1
n
(ri − ̅ r)
2
x
1
n
! p
i
(ri − ̅ r)
2
Standard Deviation σ, or SD
Var Var

Corporate Finance, CUB - Nóra, Felföldi-Szűcs, PhD
Example
i.e. the Variance = 1.2
So the standard deviation ≈ √1.2 = 1.1
Event Probability Outcome
(Utility)
Squared
Deviation
Expected Squared
Deviation
A 0.1 1 (1 - 3)
2
0.1 x 4
B 0.2 2