Risk and Asset-Liability
Management
Professor Banikanta Mishra
Xavier Institute of Management
Risk Handling
Risk Avoidance
Risk Acceptance
Risk Transfer
Risk Sharing
Risk Exchange
Ways of Risk Management
Insurance
Hedging
Asset-Liability Management
Professor Banikanta Mishra, XIMB
2
Forward Contract: Buyer and seller agree to transact (buy/sell)
a specified amount of a given commodity/asset
at a pre-specified-date
at a contracted price (the forward price)
Futures Contract: Forward Contract with marking-to-market
Option:Option-buyer has the right and option-seller the obligation
to transact at a given price, on or before a given date
(up to a prefixed amount of a given asset)
[Call: right to buy; Put: right to sell]
Swap: Both counter-parties agree to exchange given quantities
of two given assets or two indexed flows
(e.g. $ for commodity; $ for DM; fixed $ for floating $)
Range Forward: Buyer has the right to buy at Ceiling from Seller
Seller has the right to Sell at the Floor to Buyer (=> Call + Put)
Professor Banikanta Mishra, XIMB
3
Farmer and Bread-maker
t=T
Distribution of ST
40% 25
60% 35
Expected 31
Farmer ‘s worry: Price may touch 25
Bread-maker’s worry: Price may touch 35
Professor Banikanta Mishra, XIMB
4
Farmer’s Solution
t=0
Sell wheat forward
Agree to sell
wheat @F at t=T
FORWARD SELL: SHORT
Will strictly prefer
F=31 to selling at the
Risky open-market price
In fact, Farmer would
be willing to accept a
bit less than 31 to get
rid of selling price risk

Professor Banikanta Mishra, XIMB
F = < 31
5
Bread-maker’s Solution
t=0
Buy wheat forward
Agree to buy
wheat @F at t=T
FORWARD BUY: LONG
Will strictly prefer
F=31 to buying at the
risky open-market price
In fact, Bread-maker
is willing to pay a bit
more than 31 to get
rid of buying price risk

Professor Banikanta Mishra, XIMB
F > = 31
6
F versus E(ST)
If there is
as much demand from bread-makers
as supply from farmers,
F = 31 is an ideal price
as both farmers and bread-makers
“strictly” prefer this to the risky open-market price
So, we would find that
F = E(ST) [Expected Future Spot Price at Time-T]
Professor Banikanta Mishra, XIMB
7
Contango
But, if, at t=0, there is a
net “forward” (time T) demand for wheat
(=> more willing to forward buy than forward sell),
speculators have to be enticed to take selling position
To give them an incentive to do this,
we need F > 31
=> forward price > expected future spot price
Professor Banikanta Mishra, XIMB
8
Backwardation
Similarly, if, at t=0, there is a
net “forward” supply of wheat
(=> more willing to forward sell than forward buy),
speculators have to be enticed to take buying position
To give them an incentive to do this,
we need F < 31
=> forward price < expected future spot price
Professor Banikanta Mishra, XIMB
9
Option: Call
If one has right, but not obligation, to buy @31, then at t=T
Price = 25 => Buy @25 in open market
Gain =0
Price = 35 => Buy @31 (exercise right)
Gain= 4
So, option holder can only gain or not gain at t=T,
but cannot lose (Note: Expected Gain at t=1 = 60% x 4 = $2.40)
So, she has to pay something (the call price) for this
(to the call writer, when entering into contract at t=0)
This price (or premium) should equal PV of $2.40.
Note: Call writer has obligation to sell @31 if holder wants to buy
Professor Banikanta Mishra, XIMB
10
Option: Put
If one has right, but not obligation, to sell @31, then at t=T
Price = 25 => Sell @31 (exercise right)
Gain= 6
Price = 35 => Sell @35 in open market
Gain= 0
So, option holder can only gain or not gain at t=T,
but cannot lose (Note: Expected Gain at t=1 = 40% x 6 = $2.40)
So, she has to pay something (the put premium) for this
(to the put writer, when entering into contract at t=0)
This put premium should equal PV of $2.40.
Note: Put writer has obligation to buy @31 if holder wants to sell
Professor Banikanta Mishra, XIMB
11
Rights & Obligations
Buy
Call
Put
Sell/Write
Right to buy
Obligation to Sell
Right to Sell
Obligation to buy
Professor Banikanta Mishra, XIMB
12
Options Payoff
ST > X
ST < X
Long Call
ST - X
0
Short Call
X - ST
0
Long Put
0
X - ST
Short Put
0
ST - X
Professor Banikanta Mishra, XIMB
13
t=0
t=1
t=2
t=3
t=4
t=5
Firm A*
Payments
#80
#80
#80
#80
#80
#1,000
Firm B**
Outflows
$116
$116
$116
$116
$116
$1,600
(* US Company: Loan of #1,000 @8.00%; **UK Company: Loan of $1,600 @7.25%)
$116 (t=1 to 5), $1,600 (t=5)
SWAP
Firm A
Firm B
Current
Exch Rate:
#1 = $1.60
#80 (t=1 to 5), #1,000 (t=5)
Firm A’s
Outflows
$116
$116
$116
$116
$116
$1,600
After Swap
Professor Banikanta Mishra, XIMB
14
Forward Price
Suppose Gold price now is $300 and R0T = 5%
Suppose Goldsmith needs one unit of gold at t=T
What can he do?
1. Borrow $300, buy gold now (at t=0), and hold
OR
2. Long forward @FT
Professor Banikanta Mishra, XIMB
15
Cash Flows
t=0
t =T
Strategy 1
Borrow $300
Buy gold @300
Net CF
+300
-300
0
Repay 300 (1+5%) =315
Have 1 unit of gold
Net CF
-315
Strategy 2
Long Forward @FT 0
Buy 1 unit of gold @FT
Net CF
0
Net CF
-FT
Professor Banikanta Mishra, XIMB
16
Forward Pricing Formula
So, Law of One Price /No Arbitrage Condition =>
FT = S (1 + R0T) = 315
In general, (1 + R0T) = (1 + R)T
where
FT is forward price for transaction at end of T years,
R0T is the interest-rate over T years (T-yearly rate),
and R is the Annual Interest Rate (EAR)
Professor Banikanta Mishra, XIMB
17
Hedger
Long Hedge: Goldsmith would long forward
 He is assured of buying gold @315 at t=T
Short Hedge: Miner would short forward
=> She is assured of selling gold @315 at t=T
Professor Banikanta Mishra, XIMB
18
Speculator
If speculator expects spot price at T to exceed 315,
[that is, E(ST) > F]
he would long forward (to buy @F at T)
His expected profit at T = E(ST) – F > 0
If speculator expects E(ST) < F,
she would short forward (to sell @F at T)
=> Her expected profit at T = F - E(ST) > 0
Professor Banikanta Mishra, XIMB
19
Arbitrageur
Gets into action only if FT = S (1 + R0T) = 315
If F > $315, then forward is overpriced
 He would sell (or short) forward
So, to cover his position,
he would buy asset now @ S = 300
And, to take care of his purchase price,
he would borrow $300
Professor Banikanta Mishra, XIMB
20
Arbitrageur’s Cash Flows
t=0
t =T
Short Forward @F T
Sell gold @ FT
Borrow $300
+300
Repay 300 (1+5%) =315
Buy gold @300 -300
Have 1 unit of gold to sell
--------------------------------------------------------------Net CF
0
Net CF
FT - 315
--------------------------------------------------------------Since FT > 315, Arbitrageur is guaranteed a +ve CF at t=T
Professor Banikanta Mishra, XIMB
21
What if FT < 315
t=0
t =T
Long Forward @F T
Buy gold @ FT
Short gold
+300
Deliver gold to close position
Lend $300
-300
Get back 300 (1+5%) =315
--------------------------------------------------------------Net CF
0
Net CF
315 - FT
--------------------------------------------------------------Since FT < 315, Arbitrageur is guaranteed a +ve CF at t=T
Professor Banikanta Mishra, XIMB
22
Caveat
In real world, we
Don’t borrow and lend at the same rate
Buy and sell at the spot market at the same rate
Buy and sell forward at the same rate
We borrow/lend @ bank’s lending/deposit rate
We buy/sell on spot @ dealer’s ask/bid price
We buy/sell forward @ dealer’s ask/bid price
Professor Banikanta Mishra, XIMB
23
No-Arbitrage F
Then, the No-Arbitrage Forward Pricing Formula
does not any more give
an equation or equality
But instead dictates
a range
within which F must lie
Professor Banikanta Mishra, XIMB
24
Hedging: Objective
To reduce risk,
Not to increase ERR
Professor Banikanta Mishra, XIMB
25
Hedging Basics
CF at t=T
State
Asset 1
Asset 2
Asset 3
1
28
2
-2
2
22
-1
2
Professor Banikanta Mishra, XIMB
26
Hedging Strategy
• What position in Asset-2 would hedge
exposure?
• What position in Asset-3 would hedge
exposure?
Professor Banikanta Mishra, XIMB
27
Long + Short
CF at t=T
State
1
2
Long
+
Short
1 Unit Asset 1 2 Units Asset 2 TOTAL
28
-4
24
22
+2
Professor Banikanta Mishra, XIMB
24
28
Long + Long
CF at t=T
State
Long
+
Long
1 Unit Asset 1 1.5 Unit Asset 3 TOTAL
1
28
-3
25
2
22
+3
25
Professor Banikanta Mishra, XIMB
29
Date
Price of Security y
Price of Security x
1
2
...
T
$Y1
$Y2
...
$YT
$X1
$X2
...
$XT
Yt = a + b Xt + ut
=>
DYt = b DXt + et
=> If price of x goes up by $1,
then price of y would go up by $b on the average
=> If you are long (short) ONE unit of y,
then hedge by going short (long) in b units of x
Professor Banikanta Mishra, XIMB
30
Let b = 1.6
Then, DYt = 1.6 DXt + et
=> For each $1.0 change in the price of x,
there is a $1.6 change in the price of y in the same direction
Price of 1.6 units of
x changes by
$1.6
$1.6
$3.2
$8.0
Long (Short) Position
In This
If Price of 1 unit of
x changes by
Price of 1 unit of
y changes by
(on the average)
$1
$1
$2
$5
Gets Canceled By
$1.6
$1.6
$3.2
$8.0
Short (Long) Position
In This
Professor Banikanta Mishra, XIMB
31
If D%Yt = b D%Xt + et,
then (DYt / Yt) = b (DXt / Xt) + et
=> DYt = b (Yt / Xt) DXt + et
So, b = b (Yt / Xt)
where Yt and Xt represent the current levels of y and x resp.
If duration of Y is Dy and that of x is Dx,
then, for 1% change in interest-rate,
D%Yt = Dy% and D%Xt = Dx%
=> D%Yt = (Dy% / Dx%) D%Xt
=> b = Dy% / Dx% = Dy / Dx
b = (Dy / Dx) x (Yt / Xt) = (Dy x Yt) / (Dx x Xt)
Professor Banikanta Mishra, XIMB
32
t = 1 Sep
Expects to
Issue on
t = 1 Nov
90-day CP
@ Pcp
Sell short
90-day
TB Futures
@ 96.62
offset
cum MTM
t = 1 Dec
t= 1 Mar
maturing on
To sell
90-d TB
@ f1-Dec
Close short
90-d TB Fut
@f1-Nov
t = 1 Feb
maturing on
To buy
90-d TB
96.62 - f1-Nov @ f1-Dec
Gain (loss) in the Futures position partially/fully offsets loss (gain) in CP issue
Hull: Options, Futures, and other Deriv.
33
Possible Interest-Rates on 1 November
Lower
Expected
Higher
(unchanged)
Sell CP @
(Rate)
96.43
(3.70%)
+0.51
+0.33
95.92
(4.25%)
-0.69
-0.45
95.23
(5.00%)
f1-Nov
96.95
96.62
96.17
CF from
1 Futures
Position
-0.33
0.00
+0.45
96.10
95.92
95.68
1.5 Fut
Position
-0.50
95.93
0.00
95.92
+0.68
95.91
Professor Banikanta Mishra, XIMB
34
20 May
5 Aug
Gets the
News
$3.3 mill
to be rec’d
and put in
180-day TB
Go long in
TB Futures
@973,600
offset
cum MTM
1 Sep
1 Dec
interest-rate = r6m
7 Feb
$3.3 mill
x (1 + r6m)
Money
Withdrawn
and invested
in a project
To buy 90-d
TB @ S1-Sep
Close long
TB Futures
@ f5-Aug
To sell 90-d
TB @ S1-Sep
f5-Aug - 973,600 invest @ r6m till 7 Feb f5-Aug - 973,600
x (1 + r6m)
Hull: Options, Futures and other Deriv.
35
Possible r6m (unannualized) on 5 Aug
f5-Aug
cum MTM
Lower
4.90%
Unchanged*
5.70%
Higher
6.50%
976,400
973,600
971,000
2,800
0
-2,600
x 7 (contracts) 19,600
0
-18,200
Cash Flows on 7 Feb & (unannualized) Return
FV of this amt 20,560
0
-19,383
Interest Rec’d
on $3.3 mill 161,700
TO TAL
182,260
Return (6-mth) 5.52%
188,100
188,100
5.70%
214,500
195,117
5.91%
[* Stays at the level of the forward-rate (expectation on 20 May about r6m on 5 Aug)]
Hull: Options, Futures and other Deriv.
36
Consider a 3-month TB and a 6-month TB
D6-m = 0.5
D3-m = 0.25
If D r = 1%
D%P6-m = 0.50 x 1% = 0.50%
D%P3-m = 0.25 x 1% = 0.25%
If current annual-interest-rate is 12%, then
P6-m = 94.34
P3-m = 97.09
So that
b = (D6-m / D3-m) x (P6-m / P3-m ) = (D6-m x P6-m ) / (D3-m x P3-m )
= (0.50 / 0.25) x (94.34 / 97.09) = (0.50 x 94.34) / (0.25 x 97.09)
= 1.94
So, hedge a long (short) position in ONE 6-m TB by
a short (long) position in 1.94 3-m TBs
Professor Banikanta Mishra, XIMB
37
Basis Risk
t=t
t=0
t=T
Long Futures @f0
Close Futures @ft
Buy in the open @St
-------------------------------------------------------
Net CF
- St + (ft – f0) = - f0 unless t = T
Professor Banikanta Mishra, XIMB
38
Basis Risk: Example
t=t
t=0
t=T
Long Futures @120
Close Futures @125
Buy in the open @128
-------------------------------------------------------
Net CF
- 128
+
(125–
120)
=
-123
=
-120
Prof. Banikanta Mishra, XIMB
39
Fabricator’s Hedge
S0 = 140
f = 120 Need = 100,000 lbs Copper
Suppose go long in futures @120. Then:
If ST= 125, then futures MTM= (125-120) = 5
=> Total Cost = 125 – 5 = 120
If ST= 105, then futures MTM= (105-120) = -15
=> Total Cost = 105 – (-15) = 120
Hull: Options, Futures and Other Deriv
40
Hedging Equity PF: Basics
DP
 RF  b
P
 DM

- RF  

 M

 P
DP  P * RF 1 - b    b  DM 
 M
P
HR ( ( Hedge Ratio )  b
M
Professor Banikanta Mishra, XIMB
41
Hedging Equity PF
Value of Equity PF = $5,000,000
Value of S&P 500 = 1,000
RF = 4% (1% per quarter)
DYindex = 1% (0.25% per quarter)
F4-m= 1,010 (Delivers $250 times the index)
b = 1.5 => HR = 1.5 x (5,000,000 / 250,000) = 30
Hull: Options, Futures and other Deriv.
42
What Happens When …?
At t, let St = 900 and ft = 902
(Cumulative) MTM from Futures
= (1010 – 902) x 250 x 30 = $810,000
Since Index falls by 10%
=> DM = Div + Change in Index = 2.5 + (-100)
(DM /M)= DY+CGY= 0.25%+(-10%)= -9.75%
PF Value falls by 15.125% = 756,250
Net Gain = 810,000 – 756,250 = 53,750
Professor Banikanta Mishra, XIMB
43
To Change the PF Beta to b*?
Number of contracts required to be shorted is
(b - b*)
x
[Value of Portfolio / Value of Futures Contract]
Professor Banikanta Mishra, XIMB
44
To Change b to 2.3
N = Short (1.5 – 2.3) x (5000000/250000) = -16
Or Long 16 contracts
Professor Banikanta Mishra, XIMB
45
1% or 100 bp
Fixed: 10.0%
Floating: LIBOR + 70 bp
Well
50 bp
Fixed: 11.0%
Floating: LIBOR + 120 bp
LIBOR + 120 on Notional
NSF
Known
NET
COST
L + 40b
10.8% on Notional Amount
10%
on Fixed
LIBOR + 120
on Floating
NET
COST
10.8%
CAPITAL
MARKET
CAPITAL
MARKET
Professor Banikanta Mishra, XIMB
46
+ 1% or 100 bp
Fixed: 10.0%
Floating: LIBOR + 70 bp
Well
Known
NET
COST
L + 45b
10%
on Fixed
LIBOR
9.55%
+ 50 bp
S
W
A
P
F
I
Fixed: 11.0%
Floating: LIBOR + 120 bp
LIBOR
NSF
9.65%
LIBOR + 120
on Floating
NET
COST
10.85%
CAPITAL
MARKET
CAPITAL
MARKET
Professor Banikanta Mishra, XIMB
47
t=0
t=1
t=2
t=3
t=4
t=5
Firm A *
Payments
#80
#80
#80
#80
#80
#1,000
Firm B**
Payments
$116
$116
$116
$116
$116
$1,600
(* US Company: Loan of #1,000 @8.00%; **UK Company: Loan of $1,600 @7.25%)
$116 (t=1 to 5), $1,600 (t=5)
SWAP
Firm A
Firm B
Current
Exch Rate:
#1 = $1.60
#80 (t=1 to 5), #1,000 (t=5)
Firm A’s
Outflows
$116
$116
$116
$116
$116
$1,600
After Swap
Professor Banikanta Mishra, XIMB
48
+ 1% or 100 bp
Re Loan: 15.0%
$ Loan: 6.0%
Well
-50 bp
Re Loan: 16.0%
$ Loan: 5.5%
5.3% in $ on Notional
NSF
Known
NET
COST
5.3% $
15% in Re on Re Notional
15% on
Re Loan
5.5 % on
$ Loan
NET
COST
15.2% Re
CAPITAL
MARKET
CAPITAL
MARKET
Professor Banikanta Mishra, XIMB
49
Current Data: # = $1.60, r# = 5.5%, r$ = 6.0%
# LIBOR + 20 bp in $ on $ Notional
SWAP
BANK
FIRM A
$ LIBOR on $ Notional
$ LIBOR
on $ Notional
Capital
Market
Net
Cost
# LIBOR
in $
Professor Banikanta Mishra, XIMB
50
FIXED PRICE
Producer
SPOT PRICE
SPOT
PRICE
R/M SPOT
MARKET
SWAP
Counterparty
ON THE NET PRODUCER BUYS
HER RAW-MATERIAL INPUT
AT A PRE-FIXED PRICE
Professor Banikanta Mishra, XIMB
51
FIXED PRICE
Producer
SPOT PRICE
SWAP
Counterparty
SPOT
PRICE
OUTPUT
SPOT
MARKET
ON THE NET, PRODUCER SELLS
HIS OUTPUT AT A PRE-FIXED PRICE.
Professor Banikanta Mishra, XIMB
52
INPUT
SPOT
MARKET
INPUT
PRODUCER
SPOT PR
SPOT PR
OUTPUT SPOT
- INPUT SPOT
OUTPUT
OUTPUT
SPOT
MARKET
PRESPECIFIED
SPREAD
SWAP
DEALER
Professor Banikanta Mishra, XIMB
53
ALM for a Leasing Company
Liabs: Interest Pmt of Rs.1,790 for next 3 years
+ Principal repayment of Rs.20,337 at t=3
Assets: Lease Payment Receivable of Rs.5000 for
next five years
Machine worth Rs.699.68 to be leased
out at zero NPV for N (?) years
Cash = Rs.83.26
Professor Banikanta Mishra, XIMB
54