Chapter 3 fx rate risk monitoring and controls

Managing Market Risk Under The Basel III Framework
Copyright © 2016 CapitaLogic Limited
Chapter 3
FX Rate Risk
Monitoring and Controls
Managing Market Risk Under The Basel III Framework
The Presentation Slides
Website : https://sites.google.com/site/quanrisk
E-mail : quanrisk@gmail.com

Copyright © 2016 CapitaLogic Limited 2
Declaration
Copyright © 2016 CapitaLogic Limited.
All rights reserved. No part of this presentation file may be
reproduced, in any form or by any means, without written
permission from CapitaLogic Limited.
Authored by Dr. LAM Yat-fai (林日林日林日林日辉辉辉辉),
Principal, Structured Products Analytics, CapitaLogic Limited,
Adjunct Professor of Finance, City University of Hong Kong,
Doctor of Business Administration (Finance),
CFA, CAIA, FRM, PRM.

FX rate risk monitoring
FX rate risk controls
Outline

A paradox of VaR
A foreign currency investment was made several
days ago
When the FX rate goes down
VaR decreases
Unrealized loss increases
When the FX rate goes up
VaR increases
Unrealized profit increases
VaR only tells the future downside of a foreign
currency investment
No information about the unrealized loss

Stop loss limit
Stop loss amount
The maximum loss of an investor on his foreign currency
Stop loss limit
The FX rate at which an investor will start to sell his foreign currency to
avoid additional loss beyond the stop loss amount
For a small quantity of foreign currency
Stop loss can be done quickly
For a very large quantity of foreign currency held by a financial institution
It takes several days to perform stop loss to avoid the downward pressure on
the FX rate as a result of fire sale
How many days needed to arrange an order disposal?
Assume 10 days
But during these 10 days, the FX rate may continue to go up or down
Assume a very bad situation will happen in the coming 10 days
99% confidence level

Worst case loss
Specification
At the end of a T-day holding period (10-day)
At the qth percentile confidence level (99th percentile)
Worst case value
The minimum potential value of the foreign currency portfolio at the
end of the holding period with the worst (1 - q%) situations excluded
Expected value + VaR
Worst case loss
The maximum potential loss relative to the acquisition cost with the
worst (1 - q%) situations excluded
Worst case value - Acquisition cost
Example 3.3
Example 3.4

Worst case loss
Value0
0
Worst case value
Expected value
Value-at-risk
1 - q%
q%
T days
ValueT
Unrealized
loss
Worst case loss
Acquisition cost

Worst case loss monitoring
To monitor daily the worst case loss of a
foreign currency portfolio
To take mitigation actions if the worst case
loss exhibits an extraordinary behaviour
Daily calculations of
Worst case value
Worst case loss

FX rate monitoring
To monitor daily the FX rates of the foreign
currencies in the portfolio
To take corresponding mitigation actions if
any FX rate exhibits an extraordinary
behaviour
Daily calculations of
% change
Example 3.5

Percentage change
Early detection with % changes
What is today’s percentage change relative to
the most recent 500 trading days?
Emergency – extremities (+1%)
Warning – wing regions (+1% to +5%)
Attention – side regions (+5% to +10%)
Normal – middle region (-10% to 10%)

Daily percentage changes
80% = 400 days

Concentration of FX rate risk
Herfindahl-Hirschman index
When highly concentrated → 1
When highly diversified → 1 / M
M
2
k
k=1
2M
k
k=1
Component VaR
HHI =
Component VaR
 
 
 
∑
∑

Concentration of FX rate risk
Alternative form
Pros
Half the number of VaR calculations
Cons
Individual currency VaR carries less economic meaning
in a foreign currency portfolio
M
2
k
k=1
2M
k
k=1
Individuial currency VaR
HHI =
Individual currency VaR
 
 
 
∑
∑

Concentration of
foreign currency value
Alternative form
Pros
Readily available from investment records
Cons
Ignored the effects from holding period dispersion and
diversification effect
( )
M M
22
k k k
k=1 k=1
2 2M M
k k k
k=1 k=1
Value n S
HHI = =
Value n S
   
   
   
∑ ∑
∑ ∑
Example 3.6

FX rate risk monitoring
Outline

Why mitigating FX rate risk?
Return driven by risk
Why mitigating FX rate risk?
Stop unrealized loss
Lock in unrealized profit
Risk increased beyond tolerance level
Change of risk aptitude

FX rate risk factors
for a currency portfolio
FX rate risk
Value
Quantity (+)
Holding period
dispersion
FX rate (+)
Standard
deviation (+)
Holding
period (+)
Diversification
effect
Concentration of
foreign currencies
(+)
% change
dependency (+)

Controlled by investor
Quantity ↓
Holding period ↓
Concentration ↓
Re-balancing
Not controlled by investor
FX rate
Standard deviation
% change dependency
Derivatives

Re-balancing
Theoretical approach
Sell the original foreign currency portfolio
Buy and hold a new foreign currency portfolio
Assume that there is no transaction cost
In practice
Only buy/sell the difference between the new and
original portfolios
To reduce the transaction cost

Re-balanced worst case loss
Original portfolio
Acquisition cost Acquisition day
Current value Today
Re-balanced loss = Current value - Acquisition cost
Re-balanced portfolio
Re-balanced cost Today
Worst case value = Expected value + VaR
Worst case loss = Worst case value - Re-balanced cost
Re-balanced loss + Worst case loss

Value0
0
Worst case value
Expected value
Value-at-risk
1 - q%
q%
T days
ValueT
Re-balanced
loss
Worst case loss
Acquisition cost
Example 3.7
Example 3.8
Re-balancing
Re-balanced
worst case loss

Chapter 3 fx rate risk monitoring and controls

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