14/11/14
La gestione del rischio di tasso di
interesse
4 strategies
1.  Adopt interest repricing positions which
hedge (lock in) the bank’s net interest
income
2.  Adopt interest repricing positions which
hedge the bank’s present value (stabilize its
share price)
3.  Anticipate correctly all significant interest
rate movements
4.  Do nothing to protect or optimize NII or sP
2
1
14/11/14
Opportunistic approach to
interest rate structural exposure
Approaching peak
Approaching trough
Shorten funding maturities
Lenghten funding maturities
Begin to lenghten investment
maturities
Begin to shorten investment
maturities
Acquire investments
Sell investments
Expand fixed rate loans
Restrict fixed rate loans
3
Strategies 1 & 2
•  Geared to keeping the sheep on an even keel
•  Compatible with shareholders’ best interest
•  Where’s the problem?
•  Mutually exclusive: cannot hedge bank’s NII
and the bank’s economic value
SIMULTANEOUSLY
–  Strategy 1 requires the level of NII to be insulated
from changes of interest rates
–  Strategy 2 requires the level of NII to be
responsives to changes of interest rates
4
2
14/11/14
Hedging exposures
•  Changing funding strategy
•  Changing repricing characteristics
•  Switching out of some type of investments
and into others
•  Enter a variety of derivative contracts
5
8-6
Hedging Interest Rate Risk
•  Derivatives Used to Manage Interest Rate Risk
–  Financial Futures Contracts
–  Forward Rate Agreements
–  Interest Rate Swaps
–  Options on Interest Rates
•  Interest Rate Caps
•  Interest Rate Floors
•  Interest Rate Collars
6
3
14/11/14
MAIN CHARACTERISTICS OF
DERIVATIVES CONTRACTS
7
8-8
Financial Futures Contract
•  An Agreement Between a Buyer and a Seller
Which Calls for the Delivery of a Particular
Financial Asset at a Set Price at Some Future
Date
•  Futures Markets
–  The Organized Exchanges Where Futures
Contracts are traded
•  Interest Rate Futures
–  Where the Underlying Asset is an InterestBearing Security
8
4
14/11/14
8-9
Background on Financial Futures
•  Buyers
–  A buyer of a futures contract is said to be long
futures
–  Agrees to pay the underlying futures price or
take delivery of the underlying asset
–  Buyers gain when futures prices rise and lose
when futures prices fall
9
8-10
Background on Financial Futures
•  Sellers
–  A seller of a futures contract is said to be
short futures
–  Agrees to receive the underlying futures price
or to deliver the underlying asset
–  Sellers gain when futures prices fall and lose
when futures prices rise
10
5
14/11/14
CLEARING HOUSE
Underlying asset
BUYER
SELLER
Funds
Underlying A.
BUYER
funds
C.H.
Underlying A.
SELLER
funds
n  Adequate capital
n  System of margins
11
FINANCIAL FUTURES – I MARGINI
n  Initial margin
o  Legato alla massima variazione giornaliera del prezzo
o  Da versare in cash o titoli
o  Remunerato
o  Restituito alla chiusura della posizione
n  Variation margin
o  Conseguenza del “mark-to-market” giornaliero della
posizione
o  Pagato o ricevuto alla/dalla C.H. entro le 10.00 del
giorno successivo
o  “Zero-sum” game
n  Commissioni
o  Negoziate tra aderente alla C.H. e istituzione/cliente
dipendono da volumi negoziati e livello di servizio
12
6
14/11/14
8-13
Most Common Financial
Futures Contracts
•  U.S. Treasury Bond Futures Contracts
•  Bund futures Contracts
•  Three-Month Eurodollar Time Deposit Futures
Contract
•  30-Day Federal Funds Futures Contracts
•  One Month LIBOR Futures Contracts
13
Bund future
Caratteristiche del contratto
Obbligazione a 10 anni emessa dal German
Federal Government e con una cedola pari al
6%.
Sottostante
Quotazione
È quotato in percentuale con due decimali
Variazione minima
del prezzo
1 tick = 0.01 percentuale = 10€
Dimensione del
contratto
100.000€ nominali (valore del sottostante
*100.000/100)
14
7
14/11/14
Most common STIR (Short-Term Interest Rate futures)
CCY SOTTOSTANTE NOTIONAL
BPV
BORSE
LIFFE
CME,
SIMEX,
GLOBEX
CME
TIFFE
LIFFE
LIFFE
EUR
3M EURIBOR
1 MIO EUR
25 EUR
USD
3M LIBOR
1M USD
25 USD
USD
JPY
GBP
CHF
1M LIBOR
3M LIBOR
3M LIBOR
3M LIBOR
3 MIO USD
100 MIO JPY
500.000 GBP
1 MIO CHF
25 USD
12.500 JPY
12.5 GBP
25 CHF
15
FINANCIAL FUTURES –3M EURIBOR
n  Trattato sul LIFFE (borsa elettronica)
o  Sottostante: deposito di 90 giorni (act/360)
o  Le scadenze
ú  non seriali (DEC, MAR, JUN & SEP)
ú  seriali (le altre)
o  Last trading day: 3° lunedi del mese
o  Settlement day: 3° mercoledi del mese
o  Prezzo: 100 – tasso euribor implicito
o  Tick Value :
1.000.000 ∗ 0.005% ∗
INDICE
90
= 12,5EUR
36000
o Delivery: “cash settled” per differenziale con il Settlement Price
16
8
14/11/14
8-17
Futures vs. Forward Contracts
–  Futures Contracts
•  Traded on formal exchanges (CBOT, CME, etc.)
•  Involve standardized instruments
•  Positions require a daily marking to market
–  Forward Contracts
•  Terms are negotiated between parties
•  Do not necessarily involve standardized assets
•  Require no cash exchange until expiration
•  No marking to market
17
F.R.A.: I PARAMETRI
n  I fixing
o  EURIBOR: tasso a cui fondi denominati in euro vengono offerti da
una primaria banca ad un’altra (quindi un tasso “lettera”). Calcolato
come media di 43 contribuzioni (escludendo il 15% delle quotazioni
più alte/basse), calcolato a cura della FBE in ogni giornata operativa
Target alle 11.00 CET
o  LIBOR: tasso a cui fondi (denominati in varie divise) vengono offerti
da una primaria banca ad un’altra. Calcolato come media di “n”
contribuzioni di primarie controparti attive sulla piazza londinese
(8/12/16 a seconda della divisa), viene calcolato dalla BBA alle
11.00 London time
18
9
14/11/14
F.R.A.: LA “TIMELINE”
n  La linea del tempo di un FRA 6x12
TRADE
DATE
FIXING
DATE
SETTLEMENT
DATE
6M
MATURITY
DATE
12M
19
Elementi di un FRA
•  Capitale nozionale (N)
•  Data di negoziazione
•  Data di decorrenza (t, settlement date), in cui
inizia il finanziamento futuro
•  Data di scadenza del finanziamento (maturity
date, T)
•  Tasso di interesse fissato (tasso FRA)
•  Tasso di mercato (reference rate)
20
10
14/11/14
F.R.A.: IL VALORE
n Il valore del FRA a scadenza
n  Il valore del FRA è rappresentato dal differenziale tra il tasso
contrattuale e il reference rate (LIBOR/EURIBOR), scontato al
settlement date.
TRADE
DATE
FIXING
DATE
SETTLEMENT
DATE
6M
FRA =
MATURITY
DATE
12M
DFRA
360
DFRA #
&
$1 + rLIBOR ∗
!
360 "
%
N ∗ (rFRA − rLIBOR ) ∗
N ∗ (rFRA − rLIBOR )∗
DFRA
360
21
F.R.A.: in sintesi……
Il venditore del FRA:
Il compratore del FRA:
o  Paga il tasso FRA
o  Riceve il LIBOR
COMPRATORE
VENDITORE
o  Paga il LIBOR
o  Riceve il tasso FRA
TASSI
SALGONO
INCASSA IL
DIFFERENZIALE
PAGA IL
DIFFERENZIALE
TASSI
SCENDONO
PAGA IL
DIFFERENZIALE
INCASSA IL
DIFFERENZIALE
22
11
14/11/14
8-23
Interest Rate Swap
A Contract Between Two Parties to
Exchange Interest Payments in an
Effort to Save Money and Hedge
Against Interest-Rate Risk
23
Interest Rate Swaps: i flussi
n 
GAMBA
VARIABILE
GAMBA
FISSA
FLUSSI CERTI
Netting
FIXING EURIBOR STIMATI
24
12
14/11/14
Interest Rate Swaps: le gambe / “legs”
n  Fixing e pagamenti: la gamba fissa
Pagamento
ú  Importo costante
ú  Annuale
n  Fixing e pagamenti: la gamba variabile
Pagamento
ú  Importo variabile
ú  Trimestrale/Semestrale
25
8-26
Interest –Rate Swap
26
13
14/11/14
La diffusione degli swap: il vantaggio comparato
•  La circostanza secondo cui le aziende si finanziano
nel mercato dei capitali dove hanno un vantaggio
relativo maggiore, indipendentemente dalle
proprie aspettative di andamento dei tassi,
permette lo sviluppo degli swap per trasformare i
prestiti da fisso a variabile e viceversa.
27
La diffusione degli swap: il vantaggio comparato
Esempio:
Condizioni di accesso al mercato dei tassi (prestiti 10 anni):
Soc. A
Soc. B
Fisso
4.20%
4.50%
Variabile
Euribor3m +10 b.p.
Euribor 3m +25 b.p.
Supponiamo che A voglia finanziarsi a tasso variabile (aspettativa di
riduzione dei tassi a breve) e viceversa B.
Rivolgendosi ai mercati in cui si ha un vantaggio comparato e
successivamente concludendo un IRS si ottimizza la propria posizione
competitiva riducendo i costi di indebitamento.
28
14
14/11/14
La diffusione degli swap: il vantaggio comparato
4.20%
A
B
Eurib 3m
Eurib 3m
+25bp
4.20%
INVESTITORI TASSO
FISSO
INVESTITORI TASSO VARIABILE
Risultato:
La Soc. A si finanzia ad Euribor 3m flat .
(-4.20% +4.20% -€3m euribor)
Realizza un risparmio reale di 10 b.p.p.a.
La Soc. B si finanzia al tasso fisso del 4.45%
(€3m euribor - €3m+25 b.p. – 4.20%)
Realizza un risparmio reale di 5 b.p.p.a.
29
Swap e intermediazione
finanziaria
3,90%
OPERATORE A
4,22%
intermediario
euribor
OPERATORE B
euribor
30
15
14/11/14
Un IRS “particolare : l’Overnight Indexed Swap
Overnight Indexed Swaps: definizione
n  Contratto tra due controparti che prevede lo scambio di un
flusso di interesse a tasso fisso contro un tasso ottenuto
attraverso la composizione di “n” tassi overnight (es.: Eonia)
TASSO FISSO
A
B
“n” TASSI O/N
composti
n 
Riproduce fedelmente la “meccanica” di un deposito
interbancario reinvestito/finanziato sull ‘overnight
31
Overnight Indexed Swap:la comparazione con il
deposito interbancario
DEPO
O.I.S.
MATURITY
Tailor-made
Tailor-made
SIZE
Tailor-made
Standard
PRICE
Rate
Rate
MARK-TO-MARKET
No
No
MARKET
Over the Counter
Over the Counter
CREDIT RISK
Counterparty
Substitution cost
32
16
14/11/14
Overnight Indexed Swap:un esempio concreto
Esempio - 1w EURO a 0.5%, (7gg) FISSO
EONIA rates: 1-2 gg 0.45; 2-3gg 0.4625; 3-4gg 0.475; 4-5gg
0.4625; 5-8gg 0.4375
Nominale: 10 mio euro
Capitalizzazione composta:
[1+(0.0045*1/360)] X [1+(0.004625*1/360)] X [1+(0.00475*1/360)] X
[1+(0.004625*1/360)] X [1+(0.004375*3/360)] = 1.0000878501
EONIA per 7gg = (1.0000878501 -1) X 360/7= 0.004518 =
0.4518%
Interessi composti sul nominale X la durata =
10 mio*0.4518%*7/360 = 878,50 euro interessi gamba variabile
Il pagatore di tasso fisso deve pagare invece: 10 mio* 0.5%*7/360=
972,22 euro.
Al netto il compratore dell’OIS paga 93, 72 euro (il giorno dopo
la maturity)
33
8-34
Interest Rate Option
It Grants the Holder of the Option the
Right but Not the Obligation to Buy or
Sell Specific Financial Instruments at an
Agreed Upon Price.
34
17
14/11/14
8-35
Types of Options
•  Put Option
– Gives the Holder of the Option the Right
to Sell the Financial Instrument at a Set
Price
•  Call Option
– Gives the Holder of the Option the Right
to Purchase the Financial Instrument at
a Set Price
35
8-36
Most Common Option Contracts
Used By Banks
•  U.S. Treasury Bond Futures Options
•  Eurodollar Futures Option
36
18
14/11/14
8-37
Interest Rate Cap
Protects the Holder from Rising Interest
Rates. For an Up Front Fee Borrowers
are Assured Their Loan Rate Will Not
Rise Above the Cap Rate
Buyer will receive the difference:
(fixed rate/cap – variable rate)*
Notional
37
8-38
Interest Rate Floor
A Contract Setting the Lowest Interest
Rate a Borrower is Allowed to Pay on a
Flexible-Rate Loan
Seller will pay the difference:
(variable rate– fixed rate/floor)*
Notional
38
19
14/11/14
8-39
Interest Rate Collar
A Contract Setting the Maximum and
Minimum Interest Rates That May Be
Assessed on a Flexible-Rate Loan. It
Combines an Interest Rate Cap and
Floor into One Contract.
39
HEDGING WITH
DERIVATIVES
40
20
14/11/14
Types of hedging
•  Microhedging
•  Individual asset, liability or committment.
•  Macrohedging
•  Hedging entire portfolio interest risk (duration gap)
•  Found more effective and generally lower cost.
•  Basis risk
•  Exact matching is uncommon
•  Standardized delivery dates of futures reduces
likelihood of exact matching.
41
Routine vs Selective H
•  Routine hedging: reduces interest rate risk to
lowest possible level.
•  Low risk - low return.
•  Selective hedging: manager may selectively
hedge based on expectations of future
interest rates and risk preferences.
•  Partially hedge duration gap or individual assets or
liabilities
42
21
14/11/14
Effects of hedging on risk and
E(R)
Unhedged
E(r)
Selectively hedged
Fully hedged
overhedge
risk
Minimum risk P
43
F.R.A.: un esempio di microhedging
n  Il 9/06/13, un’ azienda , indebitata a tasso variabile (6m Euribor
+ 0.50%) , teme per la semestralità dic-13 giu-14 di dover subire
le conseguenze negative di un aumento del costo del denaro in
misura superiore a quanto già previsto dal mercato ;
n  Il tasso verrà fissato il 28/13 valuta 30/13. Come coprirsi da un
rialzo dei rendimenti ?
9/06/2013
28/12/2013
Funding in
corso
30/12/2013
1M
30/06/2014
Funding
futuro
Euribor
+0.50
7M
44
22
14/11/14
F.R.A.: un esempio di microhedging
n  Il tesoriere dell’azienda richiede la quotazione di un
FRA Euro “6vs12 over end”
Eur FRA 6svs12s over 30th
DEC 2.18% a 2.20%
n  Action!: a 2.20% il Tesoriere acquista 10 mln/Eur di 6v12 FRA valuta
30/13 fissando il costo del funding
9/06/2013
28/12/2013
Funding in
corso
30/12/2013
30/06/2014
Funding
futuro
Euribor
+0.50
6M
12M
45
F.R.A.: il settlement
n  Ipotizziamo un rialzo dei tassi dalla BCE nel corso della riunione
del 7/12 (+0.50), i tassi a 6 mesi si portano in area 2.40%. Il 28/12
l’Euribor per scadenza 6 mesi fissa a 2.51%.
n  Tasso applicato al “loan”: 2.51% + 0.50% = 3.01%
n  Differenziale tasso incassato sul FRA : 2.20% - 2.51%=
0.31% Differenza incassata dall’acquisto FRA da attualizzare
FRAsettle =
10ml € ∗ (2,20 − 2,51)∗
180
36000
180 #
&
$1 + 2,51 ∗
!
36000 "
%
15307,89 €
Tasso finale pagato : 3.01%- 0. 31% = 2.70%
46
23
14/11/14
8-47
Hedging with Futures Contracts
Avoiding Higher
Borrowing Costs and
Declining Asset Values
Avoiding Lower Than
Expected Yields from
Loans and Securities
→
→
Use a Short Hedge: Sell
Futures Contracts and
then Purchase Similar
Contracts Later
Use a long Hedge: Buy
Futures Contracts and
then Sell Similar
Contracts Later
47
A Short Hedge
•  A short hedge (sell futures) is appropriate for a
participant who wants to reduce spot market
risk associated with an increase in interest rates
•  If spot rates increase, futures rates will typically
also increase so that the value of the futures
position will likely decrease.
•  Any loss in the cash market is at least partially
offset by a gain in the futures market
48
24
14/11/14
Example of short Hedging
A bank anticipates needing to borrow $1,000,000 in 60
days. The bank is concerned that rates will rise in the
next 60 days
–  A possible strategy would be to short Eurodollar
futures.
–  If interest rates rise (fall), the short futures position will
increase (decrease) in value. This will (partially) offset
the increase (decrease) in borrowing costs
49
FINANCIAL FUTURES –HEDGING
15 Marzo: un azienda contrattualmente legata ad un’operazione
di finanziamento ad un anno a tasso Euribor 3 mesi + 2.5 teme
un rialzo tassi a fine anno.
Rata Finanziamento per 3 mesi (metà SETT – metà DEC)
BPV
+
_
rata
Gen.
rata
Mar.
rata
Giu.
rata
Sett.
Dic.
50
25
14/11/14
Esempio
Per coprirsi dal rischio di rialzo tassi sottoscrive a metà marzo
(t0) un contratto future scadenza Dicembre alle seguenti
condizioni:
Venduto 1 contratto future Sett. a 98.82.
Presentiamo di seguito le quotazioni successive.
Data
Quotazione
t0
98,82
t1
98,93
- Eur 275 (= 25 × 11 p.b.) nel 1° giorno
t2
98,68
+ Eur 625 [= 25 × (–25 p.b.)] nel 2° giorno
….
Scadenza
99,12
I profitti (e le perdite) sul futures sono pari a:
-Eur 750 (= 25 × 30 p.b.) nell’intero periodo
51
Esempio: il pay-off finale della strategia
Il futures ci consente di bloccare per la parte variabile
del tasso da pagare di:
• bloccare il 1,18% [= (100 – $98,82) / 100] per i 3 mesi
che iniziano dal periodo considerato.
• pagare complessivamente Eur 2950 (= 1.000.000 ×
1.18 x 90) / 36000] come somma tra:
- Eur 2200 (interessi al 0,88%, tasso di mercato alla
scadenza desunto dalla chiusura future 100-99,12)
-  750 Euro da loss da chiusura contratto future (-98,82
+ 99.12) x 25
Naturalmente al tasso cosi’ ottenuto occorre
sommare lo spread stabilito dalla
banca alla
stipulazione del contratto (2.50 %)
52
26
14/11/14
Short Hedge Example
•  On March 10, 2013, your bank expects to sell
a six-month $1 million Eurodollar deposit on
August 15, 2013
–  The cash market risk exposure is that interest
rates may rise and the value of the Eurodollar
deposit will fall by August 2013
–  In order to hedge, the bank should sell futures
contracts
53
Short Hedge Example
•  The time line of the bank’s hedging activities
would look something like this:
March 10,
10, 2005
March
2013
August 17,17,
2005
August
2013
Cash: Anticipated sale of
Sell $1 million Eurodollar
investment
Deposit
Futures: Sell a futures contract Buy the futures contract
September
2005
Sept 20,20,2013
Expiration of Sept. 2013
2005
futures contract
54
27
14/11/14
Short Hedge Example
Date
3/10/13
8/17/13
Net result:
Cash Market
Bank anticipates selling
$1 million Eurodollar
deposit in 127 days;
current cash rate
= 3.00%
Bank sells $1 million
Eurodollar deposit at
4.00%
Opportunity loss.
4.00% - 3.00% = 1.00%;
100 basis points worth
$25 each = $2,500
Futures Market
Bank sells one Sept.
2013 Eurodollar futures
contract at 3.85%;
price = 96.15
Basis
3.85% - 3.00% = 0.85%
Bank buys one Sept.
2013 Eurodollar futures
contract at 4.14%;
price = 95.86
Futures profit:
4.14% - 3.85% 3 0.29%;
29 basis points worth
$25 each = $725
4.14% - 4.00% = 0.14%
Basis change: 0.14% - 0.85%
=-0.71%
Effective loss = $2,500 - $725 = $1,775
Effective rate at sale of deposit = 4.00% - 0.29% = 3.71%
or 3.00% - (0.71%) = 3.71%
55
8-56
Basis Risk
The basis is the cash price of an asset minus the
corresponding futures price for the same asset
at a point in time
▫  For financial futures, the basis can be calculated as the
futures rate minus the spot rate
▫  It may be positive or negative, depending on whether
futures rates are above or below spot rates
▫  May swing widely in value far in advance of contract
expiration
Basis=Cash-market price (or interest rate) –
futures market price (or interest rate)
56
28
14/11/14
Macrohedge with FF
•  Number of futures contracts depends on
interest rate exposure and risk-return
tradeoff.
ΔE = -[DMA – k DML] × A × [ΔR]
Or:
ΔE = -[DA - kDL] × A × [ΔR/(1+R)]
57
Example
•  Suppose: DA = 5 years, DL = 3 years and
interest rate expected to rise from 10% to
11%. A = $100 million.
ΔE = -(5 - (.9)(3)) $100 (.01/1.1) = -$2.091 million.
58
29
14/11/14
Risk-Minimizing Futures Position
•  Sensitivity of the futures contract:
ΔF/F = -DF [ΔR/(1+R)]
Or,
ΔF = -DF × [ΔR/(1+R)] × F
F = N F × PF
59
Risk-Minimizing Futures Position
•  Fully hedged requires
ΔF = ΔE
DF(NF × PF) = (DA - kDL) × A
60
30
14/11/14
8-61
Number of Futures Contracts
Needed (macrohedge)
=
(D A - D L *k )* A
D F * Price of the Futures Contract
K = leverage
A= total assets
61
Our example
•  Suppose current futures price is $97 per $100
of face value for the benchmark 20 years, 8%
coupon bond underlying FF, contract size
minimum $100,000, duration of deliverable
bond is 9.5 years
•  NF = ?
•  What happens on BS and OFFBS when
interest rates rise by 1%?
62
31
14/11/14
8-63
Principal Uses of Option Contracts
•  1. Protecting a security portfolio through the use of put
options to insulate against falling security prices (rising
interest rates); however, there is no delivery obligation under
an option contract so the user can benefit from keeping his or
her securities if interest rates fall and security prices rise
•  2. Hedging against positive or negative gaps between
interest-sensitive assets and interest- sensitive liabilities; for
example, put options can be used to offset losses from a
negative gap when interest rates rise, while call options can
be used to offset a positive gap when interest rates fall.
63
Duration matching with swap to
immunize interest rate risk
Duration of assets? Duration of Liabilities? Duration gap?
64
32
14/11/14
Duration matching with swap to
immunize interest rate risk
65
Example of Macrohedge
Against Interest Rate Risk
•  Step 1: DA= 7.5 yrs. DL=2.9 yrs. A=$750m L=
$650m. DG = 5 yrs. Assume a 25 bp increase in
interest rates such that ΔRS /(1+RS) = + 25bp
ΔE ≈ -DGA ΔRS /(1+RS) = -5($750m)(.0025)
= - $9.375m
Step 2: Loss of $9.375million in the market value of
equity when interest rates unexpectedly increase
by 25 bp.
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Macrohedge Example (cont.)
•  Step 3: Perfect hedge would generate positive cash flows
of $9.375 million whenever spot rates increase 25 bp.
Short hedge: buy fixed for floating rate swaps.
•  Step 4: Floating rate reprices each year (Dfloat=1). Fixed
rate is equal to the 15 yr 8% coupon T-bond (Dfixed=9.33).
ΔSwap ≈ -(DFixed –DFloat)NVΔRswap /(1+Rswap) =
-(9.33 – 1)NV(.0025) set = $9.375m = ΔE
NV = $450 million
Buy $450 million of fixed for floating rate swaps in order to
implement macrohedge to immunize against ALL interest
rate risk
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Immunizing Against Interest
Rate Risk Using Swaps
•  Interest rate shock drops out of final formula (as
long as interest rates change by the same amount
in spot and futures markets):
For microhedge: NVswap = (DSPS)/(DFixed -DFloat)
For macrohedge: NVswap = (DG)A/(DFixed - DFloat)
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