John Hull Chapter 14.pdf - Model-Building Approach Chapter...

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
Chapter 14
Model-Building
Approach
1

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
The Model-Building Approach

The main alternative to historical simulation for
calculating VaR or ES is to make assumptions
about the probability distributions of the returns
on the market variables

This is known as the model building approach
(or sometimes the variance-covariance approach)
2

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
Microsoft Example
(page 318-319)

We have a position worth $10 million in
Microsoft shares

The volatility of Microsoft is 2% per day
(about 32% per year)

We use N =10 and X =99
3

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
Microsoft Example continued

The standard deviation of the change in
the portfolio in 1 day is $200,000

The standard deviation of the change in
10 days is
4

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
Microsoft Example
continued

We assume that the expected change in
the value of the portfolio is zero (This is
OK for short time periods)

We assume that the change in the value
of the portfolio is normally distributed

Since N (–2.326)=0.01, the VaR is
5

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
AT&T Example

Consider a position of $5 million in AT&T

The daily volatility of AT&T is 1% (approx
16% per year)

The SD per 10 days is

The VaR is
6

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
Two-Asset Portfolio
(page 319-320)

Now consider a portfolio consisting of both
Microsoft and AT&T

Suppose that the correlation between the
returns is 0.3
7

Risk Management and Financial Institutions 5e, Chapter 14, Copyright © John C. Hull 2018
S.D. of Portfolio

A standard result in statistics states that

In this case 
X
= 200,000 and 
Y
= 50,000
and  = 0.3. The standard deviation of the
change in the portfolio value in one day is
therefore 220,200
8