1. No category

Equity-Based Insurance Guarantees Conference
November 18-19, 2013
Atlanta, GA
Lessons Learned: “What is the Cost of Your
Hedging Program?”
Frank Zhang
Lessons Learned:
“What is the Cost of Your Hedging Program?”
Equity Based Insurance Guarantees Conference
13:15-14:00
November 19,
19 2013
Atlanta, GA
Frank Zhang, CFA, FRM, FSA, MSCF, PRM
Vice President, Risk Management (ALM and VA Risk Mgt)
Pacific Life Insurance Company
1
Disclaimer
This presentation contains the current opinions of the author and not of my employer Pacific
Life Insurance Company or the Society of Actuaries. Any such opinions are subject to
change without notice. This presentation is distributed for educational purposes only.
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2
Table of contents
 The question of “the cost of hedging”
 Basics of derivatives pricing and dynamic hedging replications
 Review of the question of “the cost of hedging”
3
3
The question of “the cost
of hedging
hedging”
4
4
One of the most asked questions
 What is the cost of hedging?
 Does it depend on the point of view from the person asking the question?
5
5
Is it the hedge losses you see each year?
Q3 2008, Company 1: “… the capital markets in the third quarter represented a real
challenge for any dynamic hedging program as equity fell and volatility soared.
These factors contributed to a GMWB loss of $133 million pre-tax in the third
quarter”
Q4 2008, Company 1: “In the fourth quarter, the GMWB hedging program managed
through the tremendous volatility of the markets reasonably well. We finished
with an after tax loss of $384 million. This was driven mostly by our under
hedged vega position, basis risk and intraday market volatility."
All company information is from public company earnings calls
6
6
Is it the cost of guarantees?
Q3 2008 Company 2: “In addition to reducing our risk profile and decreasing our
exposure to changes in hedging costs, this rebalancing has protected our
customers from substantial account value declines through recent financial
market conditions.”
Q2 2013 Company 3: "Our risk managed fund strategies on our VA products
continue to anchor new deposit flow... These solutions embed volatility
management inside client accounts, enhancing account value stability and
lowering our hedging costs."
Q3 2008 Company 4: “…increase in volatility that causes an increase in our hedging
cost..”
All company information is from public company earnings calls
7
7
Is it the Milliman Hedge Cost Index™ (MHCI)?
MHCI provides the estimated hedging cost for a hypothetical lifetime guaranteed
minimum withdrawal benefit (“Lifetime GMWB”) block. The expected hedge costs
are calculated using product features for a generic Lifetime GMWB in line with
product designs common in the market. Likewise, the modeling assumptions are
based on typical actuarial and behavioral assumptions widely used by VA writers
in the market place.
MHCI- Expected Hedge Cost
130
120
(bps)
110
100
90
80
70
MHCITM is provided by Milliman Financial Risk Management LLC
Jul--13
Apr--13
Jan--13
Oct--12
Jul--12
Apr--12
Jan--12
60
8
8
Is it the hedge breakage or ineffectiveness?
Q3 2008, Company 3 : “The breakage in the quarter can be attributed to a
combination of basis risk, currency movements and the impact of an extreme,
intraday volatility..“
Q3 2008 Company 2: “The
The adjusted operating income we report also includes
breakage between changes in the values of our living benefit guarantees and our
hedging instruments. With the turbulent financial markets in the current quarter,
we experienced negative breakage of $37 million…”
Q1 2009 Company 2: “In the Annuity business, we've we have consistently reflected
the impact of hedging breakage within adjusted operating income. The hedging
breakage represents the difference between changes in fair value of the
embedded derivative liabilities to our living benefits, and changes in value of the
derivatives we use to hedge these liabilities or guarantees.
All company information is from public company earnings calls
9
9
Is it the cost of macro hedging?
Q4 2012 Company 1: "the cost structure of our macro hedge program has improved,
which is now estimated to be approximately $75 million to $100 million annual
cash spend, down from the previous $200 million to $250 million."
Q4 2012 Company 5: "The
The notional value for our macro hedging program increased
in the quarter resulting in higher expected hedging costs.“
Q2 2013 Company 5: " During the second quarter, we took advantage of favorable
market conditions to improve the effectiveness of our hedging program by adding
$2 billion in guarantee value to our dynamic hedging program... And in addition,
we unwound macro hedge positions to maintain our equity risk targets. In the
early part of the third quarter, we also added an additional $5.7 billion in
guarantee value to our dynamic hedging programs in the U.S. and Japan. The
reduction in (macro) hedge positions increased our second quarter core earnings
by approximately $20 million"
million
All company information is from public company earnings calls
10
10
Is it the losses from change in assumptions?
Q3 2013 Company 2: "The $1.7 billion loss from product-related embedded
derivatives and hedging was largely driven by reducing our assumed level of
lapses on variable annuity contracts based on our annual actuarial review. While
lower assumed lapses contributed to a positive unlocking for our AOI results,
they produced a charge here because of the capital markets assumptions we are
required to use for embedded derivatives under GAAP.“
All company information is from public company earnings calls
11
11
Does the cost depend on when/how the hedging is built?
Q2 2013 Company 3: "I think what you see at a lot of companies is companies that
weren't protected -- didn't have hedge programs in place coming into the crisis
and had to build those hedge programs at costs that are probably twice what we
had to spend to put that hedge program in place."
All company information is from public company earnings calls
12
12
Cost in business projections
Company 2 2013 Investor Day: “base scenario projection with 8% equity grow
return.” “the hedge costs in this analysis or in the business is to think of it as like
a cost of goods sold. This is the sum cost for doing business with optional living
benefits.”
“In the stress scenarios, we adjusted our hedge effectiveness assumption. So in the
baseline assumption, we're assuming 100% hedge effectiveness. In the stresses,
we're assuming 80%. So we've accounted for some increased cost associated
with hedging and in stress."
All company information is from public company earnings calls
13
13
Basics of derivatives pricing
and dynamic hedging
replications
14
14
Capital market one price – Risk neutral valuation
 Derivatives can be replicated using risk free instruments
 It turns out risk neutral pricing is a very convenient trick to simplify derivatives
calculations
 Risk neutral replications is dynamic hedging
 The objective of dynamic hedging is to fully fund at maturity/payoff the derivatives
obligations whatever happens
Martingale or risk neutral measure: Ht = EQ(HT|Ft)
Girsanov theorem and Radon-Nikodym derivative:
R l ti
Relationship
hi between
b t
risk
i k neutral
t l and
d reall world
ld measures
15
15
Dynamic replications
– Whether or not market goes down
 Example of GMAB block with $5M option value

Two paths of market performance of replicating strategies

Whether or not market goes down – the hedging is to track against the change in liability with
small net P/L
Dynamic
y
Hedge
g Performance ((Hedging
g g Target
g vs. Hedge
g Assets))
160,000
140,000
25,000,000
AV
120,000
20,000,000
100,000
15,000,000
80,000
60,000
Account Value
A
Hedged ta
arget vs. Hedging
g Assets
30,000,000
10,000,000
Hedged Target = GMAB Liability
40,000
5,000,000
20,000
Hedging Assets = Prem + P/L
-
0
100
Option Value
200
300
Cum Futures G/(L) + PV of Option Premium
400
500
Weeks
Account Value
16
16
Dynamic replications
– Whether or not market goes up
 Example of GMAB block with $5M option value

Two paths of market performance of replicating strategies

Whether or not market goes up – the hedging is to track against the change in liability with
small net P/L
Dynamic
y
Hedge
g Performance ((Hedging
g g Target
g vs. Hedge
g Assets))
12,000,000
180,000
AV
140,000
8,000,000
,
,
120,000
6,000,000
100,000
80,000
4,000,000
Hedged Target = GMAB Liability
60,000
Acco
ount Value
Hedged ta
arget vs. Hedging
g Assets
160,000
10,000,000
2,000,000
40,000
20,000
Hedging Assets = Prem + P/L
(2,000,000)
0
100
Option Value
200
300
Cum Futures G/(L) + PV of Option Premium
400
500
Weeks
Account Value
17
17
Hedging with options vs. dynamic delta hedging
 Does dynamically delta hedging cost less than using options?

The following example show that without paying for option price but dynamically hedging
from time zero

The difference (of option premium) is carried forward with interests and paid back later,
whether
h th th
the market
k t is
i up or down
d
Dynamic Hedge Performance (Hedging Target vs. Hedge Assets)
AV
25,000,000
160,000
140,000
20,000,000
120,000
15,000,000
100,000
Hedged Target = GMAB Liability
10,000,000
80,000
5,000,000
60,000
-
40,000
(5,000,000)
20,000
Hedging Assets = P/L
“saved” initial option prem will be paid back at end plus interest
(10,000,000)
0
100
Option Value
200
300
Cum Futures G/(L) + PV of Option Premium
Accountt Value
Hedged ta
arget vs. Hedging
g Assets
30,000,000
400
500
Weeks
Account Value
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18
Hedge breakage with dynamic delta hedging
 Dynamic delta hedging cost without the initial option premium

There is always a “breakage” or cost of financing every single period due to accrued
interest from the option premium

This will be a bigger problem when interest rate is higher
 Dynamic delta hedging can not lock in the guarantees perfectly

The breakages depend on the realized volatility during the hedging periods (gamma cost)

If the realized volatility is higher, the cost of hedging (negative hedge breakage) will be higher

Dynamic delta hedging is buy-high-and sell-low

This is the way how dynamic delta hedging will eventually pay for gamma
 Dynamic delta hedging does not necessarily save company money, relative to static
hedging with options

Uncertain results of using delta hedging without gamma hedging to cover tail events

Option premium (rider fees) will have to be collected over time
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19
Dynamic hedging boils down to gamma risk
2. Why volatility matters
 Higher
Hi h realized
li d volatility
l ili iincreases cost off d
dynamic
i h
hedging
d i program

Hedge cost increases during periods when underlying funds moves sharply, resulting in
elevated transaction costs and increased “buy-high-and-sell-low” round trip trades

Volatility equals cost of options
One up-anddown-cycle
Account Value and Dynamic Hedging
160,000 Sell at lower and lower prices,
AFTER market is down
140,000 120,000 Accou
unt Value
100,000 80,000 60,000 40,000 Buy at higher and higher prices,
AFTER market is up
20,000 ‐
0
50
100
150
200
250
300
350
400 Time
20
20
Review of the question of
“the
the cost of hedging”
hedging
21
21
The Milliman Hedge Cost Index™ (MHCI)
MHCITM provides the estimated hedging cost for a hypothetical lifetime guaranteed
minimum withdrawal benefit (“Lifetime GMWB”) block. The expected hedge costs
are calculated using product features for a generic Lifetime GMWB in line with
product designs common in the market. Likewise, the modeling assumptions are
based on typical actuarial and behavioral assumptions widely used by VA writers
in the market place.
MHCI- Expected Hedge Cost
130
120
(bps)
110
100
90
80
70
Jul-13
Apr-13
Jan-13
Oct-12
Jul-12
Apr-12
Jan-12
60
Hedge cost here is the cost of option embedded in the VA guarantees
MHCITM is provided by Milliman Financial Risk Management LLC
22
22
The cost of guarantees is estimated future cost of
hedging
Q3 2008 Company 2: “In addition to reducing our risk profile and decreasing our
exposure to changes in hedging costs, this rebalancing has protected our
customers from substantial account value declines through recent financial
market conditions.”
Q2 2013 Company 3: "Our risk managed fund strategies on our VA products
continue to anchor new deposit flow... These solutions embed volatility
management inside client accounts, enhancing account value stability and
lowering our hedging costs."
The cost of option embedded in the VA guarantees is the estimated
future cost of hedging that replicates the claim payoffs
All company information is from public company earnings calls
23
23
Hedge breakage is against hedging target
Q3 2008, Company 3 : “The breakage in the quarter can be attributed to a
combination of basis risk, currency movements and the impact of an extreme,
intraday volatility..“
Q3 2008 Company 2: “The
The adjusted operating income we report also includes
breakage between changes in the values of our living benefit guarantees and our
hedging instruments. With the turbulent financial markets in the current quarter,
we experienced negative breakage of $37 million…”
Q1 2009 Company 2: “In the Annuity business, we've we have consistently reflected
the impact of hedging breakage within adjusted operating income. The hedging
breakage represents the difference between changes in fair value of the
embedded derivative liabilities to our living benefits, and changes in value of the
derivatives we use to hedge these liabilities or guarantees.
Q3 2008 C
Company 4
4: ““…increase
i
iin volatility
l tilit th
thatt causes an iincrease iin our h
hedging
d i
cost..”
Against a hedging target, hedge breakage is the cost of hedge!
All company information is from public company earnings calls
24
24
What are some typical hedge breakages?
 What they are?

Difference between targeted liability and hedging assets

Typically implied as cost of hedging by most companies at their earnings calls
 Capital market hedge targets

Delta, Vega (Mark-to market based on expected vol), Rho

Gamma (realized vol against expected vol)

Basis risk (funds
(funds, indices
indices, trading instruments)
 And many other more subtle items easily missed

Actual vs. expected decrements

Accrued/borrowed interests

Time decay and liability roll

Future expected fees vs. reserve fees

Higher order or cross Greeks

Etc
Etc.
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25
These hedge losses are hedge breakages
Q3 2008, Company 1: “… the capital markets in the third quarter represented a real
challenge for any dynamic hedging program as equity fell and volatility soared.
These factors contributed to a GMWB loss of $133 million pre-tax in the third
quarter”
Q4 2008, Company 1: “In the fourth quarter, the GMWB hedging program managed
through the tremendous volatility of the markets reasonably well. We finished
with an after tax loss of $384 million. This was driven mostly by our under
hedged vega position, basis risk and intraday market volatility."
These losses are actually hedge breakages
All company information is from public company earnings calls
26
26
Dynamic replications
– Delayed hedging during initial up or down market
 Example of GMAB block with $5M option value

Dynamic hedging delayed for 2 years when market went up

Delayed hedging missed out the losses from initial up market and resulted in “permanent”
gains
Dynamic Hedge Performance (Hedging Target vs.
vs Hedge Assets)
160,000
140,000
30,000,000
AV
120,000
25 000 000
25,000,000
100,000
Market went up
20,000,000
80,000
Hedging Assets = Prem + P/L
15,000,000
60,000
Start hedging
Acco
ount Value
Hedged ta
arget vs. Hedging
g Assets
35,000,000
10,000,000
40,000
5,000,000
20,000
Hedged Target = GMAB Liability
-
-
0
100
Option Value
200
300
Cum Futures G/(L) + PV of Option Premium
400
500
Weeks
Account Value
27
27
The estimate of future cost of hedging depend on
when/how the hedging is built
Q2 2013 Company 3: "I think what you see at a lot of companies is companies that
weren't protected -- didn't have hedge programs in place coming into the crisis
and had to build those hedge programs at costs that are probably twice what we
had to spend to put that hedge program in place."
• The cost of option embedded in the VA guarantees is the estimate
of future claims cost hedged by dynamic replication
• Delayed hedge locked in losses, resulting higher cost of covering
for the claims
• Cost of guarantees is not “locked in” unless hedged immediately
All company information is from public company earnings calls
28
28
Hedge breakage with assumption or model change
 A change in between liability run created mark-to-market impact not mitigated by hedging
 Such as change in interest rate, volatility, actuarial assumptions, or models
300
Hedge Effectiveness - Assets vs. Liabilities
200
Liability
100
$
Assets
Breakage
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-100
100
Time
-200
-300
300
Hedge Effectiveness ‐ Assets vs. Liabilities (with MTM Change)
200
Liability
Assets
Breakage
100
$
0
1
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-100
100
Time
-200
This liability MTM change impact is
missed by hedging and causes additional loss
-300
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29
Cost of change in assumptions or models
 Non-capital market components

Change of actuarial assumptions
 Missed Greeks


Assuming constant or updating frequently enough

Interest rate

Implied or assumed volatility
The impact of change constant assumption

Interest rate (Rho G/L)

Implied or assumed volatility (Vega G/L)
 Model changes
At the end of day, CEO of the company is responsible for its business
performance, no matter what is the reason
30
30
Change in assumptions means lower hedge
effectiveness
Q3 2013 Company 2: "The $1.7 billion loss from product-related embedded
derivatives and hedging was largely driven by reducing our assumed level of
lapses on variable annuity contracts based on our annual actuarial review. While
lower assumed lapses contributed to a positive unlocking for our AOI results,
they produced a charge here because of the capital markets assumptions we are
required to use for embedded derivatives under GAAP.“
Uncertain models and assumptions are the key differences between
insurance hedging and bank’s hedging programs
All company information is from public company earnings calls
31
31
Cost of no hedging
 No hedging – No hedge breakage

No replicating the liabilities

Could pocket gains or suffer losses, but will not have any certainty for outcome
 Company might make an implicit assumptions about the market

This is often true about volatility or interest rate
 Decision not to hedge might be related to GAAP/STAT accounting

SOP 03-1 products

Statutory AG43 and C3P2 “flaws”
 Cost of hedging vs
vs. cost of no hedging

Difference between hedge and unhedged can be attributed separately

There could be hidden cost to show up as surprise
32
32
Cost and benefit of hedge program operations
 Operating cost of hedging program setup/operations

Transactions costs

Systems, people and operations
 Benefit of hedging program capabilities

Benefit of ability to prevent large financial losses

Cost of hedging program operations is small compared to what companies have lost during the
financial crisis

Ability to prevent similar losses is valuable
33
33
Macro hedge program – Conservative hedging
 Macro hedges may not target dynamic replications

Usually conservative and sometimes target the tail stress scenarios
 Gains/losses are directly booked if there is no matching liability

Over the long run, the market is not in tails and the macro hedges tend to lose money
 Initial industry movements after the recent financial crisis

Moving
g from economic hedge
g to more of statutory
y hedge
g

Those hedges may cost money
 Most recent industry trend

Reduce macro hedge and back to more economic hedge

To reduce the cost of non-matching macro hedge
34
34
Macro hedging typically costs money
Q4 2012 Company 1: "the cost structure of our macro hedge program has improved,
which is now estimated to be approximately $75 million to $100 million annual
cash spend, down from the previous $200 million to $250 million."
Q4 2012 Company 5: "The
The notional value for our macro hedging program increased
in the quarter resulting in higher expected hedging costs.“
Q2 2013 Company 5: " During the second quarter, we took advantage of favorable
market conditions to improve the effectiveness of our hedging program by adding
$2 billion in guarantee value to our dynamic hedging program... And in addition,
we unwound macro hedge positions to maintain our equity risk targets. In the
early part of the third quarter, we also added an additional $5.7 billion in
guarantee value to our dynamic hedging programs in the U.S. and Japan. The
reduction in (macro) hedge positions increased our second quarter core earnings
by approximately $20 million"
million
Recent movements from macro hedge to dynamic hedge to
reduce macro hedge cost
All company information is from public company earnings calls
35
35
Hedging with or without a target
Q3 2013 Company 7: “… fair value hedging programs, where we largely have an
accounting match, continue to be effective. Fair value hedging without an
accounting match resulted in a loss of EUR 116 million, in line with expectations.
Strong equity market performance drove losses on both the equity collar hedge,
as wellll as on th
the macro h
hedge.“
d “
All company information is from public company earnings calls
•
Hedge
breakage/effectiv
eness is used for
hedging program
matched with
liability target
•
Hedge without
li bilit match
liability
t h
(macro hedge)
can be costly in
“good” market
36
36
Business projections – Optimistic ongoing business
 What about the potential cost of equity hedging, when equity market is projected to
return 7-9%, as many companies’ strategic plans even in current low rate
environment?
 What about the potential cost of interest rate hedging, if rate is projected increase by
2-3% in two years?
 What about the potential cost of equity hedging in DAC projects, where the expected
equity returns are more than 7-9%?
37
37
Projection example
Company 2 2013 Investor Day: “base scenario projection with 8% equity grow
return.” “the hedge costs in this analysis or in the business is to think of it as like
a cost of goods sold. This is the sum cost for doing business with optional living
benefits.”
• In normal business projections hedge program “cost” money
• Even though the hedge results offset the future claims (reserves)
All company information is from public company earnings calls
38
38
Risk management goals
 Goals
#1 Reduce the expected cost of future guarantees
Unc
certainty
#2 Reduce the uncertainty of cost of providing actual future guarantee claims
Initial option value sold
= Future expected cost
Difference between target
and actual is breakage
Goal #1
Before Time 0
Goal #2
Hedging to lock in the cost of providing guarantees
Final Payoff
39
39
Key Takeaways
 Cost of guarantees is the estimate of future hedge cost

Lock in the cost of guarantee with hedge immediately after the product is sold to reduce breakage

The best strategy to reduce the cost of guarantees is by product design

No hedging expose company to risk and increase earnings/capital volatility (with implicit cost)
 Cost of hedging against a matching target

Hedge breakages – hedge assets against hedged liabilities

Plus some cost of hedge program – systems, people, liquidity, operations, accounting mismatch
 Cost of hedging against no matching target

Macro hedge may or may not have specific replicating liability target to track against

Paying for the tail events that may or may not happen normally (over the long time on average)

Oft necessary tto protect
Often
t t capital
it l and
d solvency
l
 Best way to reduce hedging program breakage

Improve hedge program effectiveness (against the hedged target)

Focus on hedging performance attribution

Tighten all components of hedge breakages, such as fund basis, fund volatility, policyholder
optional behavior
40
40
Frank Zhang, CFA, FRM, FSA, MSCF, PRM
E il [email protected]
Email:
k h
@
ifi lif
LinkedIn: www.linkedin.com/in/zhangfrank
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