Description
The case is to decide whether to continue risk management program of short-selling the NASDAQ index or switch to a hedging program utilizing put options on the index.
Pine Street Capital
Discussion and Analysis
1
PINE STREET CAPITAL – WHAT RISK TO HEDGE & WHAT TO BEAR?
2
Hedge: market related risks
1. Currently managing a market neutral fund ($32 AUM)
In the past the market risk was
hedged by shorting or short-selling
representative shares of the
market index
In the past the market risk was
hedged by shorting or short-
selling representative shares of
the market index
The alternative under
consideration was hedging the
market risk with the help of put
options on the market index
Ready to Bear: individual security related risk; leverage
1. The fund deals with technology driven companies due to the
expertise of its fund manager in that area; comfortable in
prediction of individual stock related risk/ return
2. Use leverage to maximize returns
HEDGE FUND STRATEGIES
Leverage
•By using debt
to finance a
portion of
assets, RoE is
greater
•However, if
assets lose
value, then
high leverage
works against
the investor
•Used to eliminate
general market risk
from the fund
•Expected Return =
? + ? ( Market Return)
• Removes market
return component,
leaving only alpha
return in the portfolio
• Return on hedged
portfolio = guaranteed
?, whether up or down
movement
•Extreme volatility in the
market
•Beta of portfolio dynamic,
changing rapidly in high
volatility market
•Options can better
immunize against market
fluctuations
•Instead of shorting, buy
PUT options
•Keep utilizing leverage and
protect against large
negative movements
Option Based
Short-Selling
3
BALANCE SHEET EFFECTS OF LEVERAGE
4
Assets Equity Assets Equity
50 50 100 100
Assets Debt Assets Debt
100 50 200 50
Equity Equity
50 150
Unlevered Portfolio
ROE = 100%
Levered Portfolio
ROE = 200%
SHORT SELLING STRATEGY
5
1. In normal circumstances the risk was reasonably hedged by
using short selling strategy
2. High proficiency of the fund managers in predicting the
portfolio beta; systems in place to achieve the exact amount
of short selling required
3. Expected PSC portfolio return = ? + ?*(Market Return)
4. With the help of exact prediction of market risk (?), they
were successful in mitigating the whole market related risk
to make the portfolio “market neutral”
However, due to extreme volatility in the markets, especially in technology
driven shares the prediction of beta became very difficult
SHORT SELLING STRATEGY EXAMPLE
6
As NASDAQ increases by 10%, using ? + ?*(Market Return), where ? = 1%
and ? = 1.5, we get 1 + 1.5(10) = 16% and 1 + 1.5(-10) = -14%
As NASDAQ increases by 10%, shorting it results in a 10% decrease ($15
decrease) and vice versa
Initial Value NASDAQ (+10%) NASDAQ (-10%)
Long Portfolio $100 $116 $86
Short NASDAQ $150 $135 $165
Total $250 $251 $251
1% 1%
Tomorrow
Return on Hedged Portfolio
( )
( ) ( )
b-r T
-rT
gen 1 2
C = Se N d - Ke N d
( )
( )
( )
b-r T
-rT
gen 2 1
P = Ke N -d - Se N -d
o
o
+ +
=
2
1
ln(S/K) (b /2)T
d
T
o
o
o
+ ÷
= = ÷
2
2 1
ln(S/K) (b /2)T
d d T
T
BLACK SCHOLES MERTON MODEL
7
Call Option
Put Option
OPTION GREEKS
8
The “Greeks” are sensitivities of option price to model inputs*
First Order
1. Delta
2. Theta
3. Vega
4. Rho
Second Order
1. Gamma
Each measures a different dimension to the risk in an option position
*Black Scholes Merton model
DELTA
9
Delta is the rate of change of the option price with respect to
the price of the underlying asset
Delta indicates the number of shares of stock required to
mimic the returns of the option
for Call = N(d
1
)
for Put = N(d
1
) - 1
S
C
c
c
c
= A
S
P
p
c
c
= A
Option
price
A
B
Slope = A
Stock price
PUT OPTION BASED HEDGING EXAMPLE
10
Using So = K = $100, volatility = 25%, RFR = 5%, 2m to maturity, option price
and delta for the option is calculated as shown in the table in the current
scenario
As S&P increases/ decreases, the option price decreases/ increases and
accordingly the ROE figures change
Assets Equity Assets Equity Assets Equity
(Stock) $100 $100 (Stock) $107.5 $107.5 (Stock) $92.5 $92.5
Assets Equity Assets Equity Assets Equity
(Stock) $89.09 (Stock) $95.77 (Stock) $84.21
(S&P Puts) $10.91 $100 (S&P Puts) $5.60 $101.37 (S&P Puts) $19.07 $101.48
Hedged Portfolio (PUT Options)
Today S&P (+5%) S&P (-5%)
ROE = 1.37% ROE = 1.48%
Un-hedged Portfolio
Today S&P (+5%) S&P (-5%)
ROE = 7.5% ROE = -7.5%
LINEAR v/s NON LINEAR HEDGING
11
Linear – Future Contracts – payoff function is linear
- every one-tick movement translates directly into a
specific dollar value per contract
Non Linear – Option Contracts – payoff function is non-linear
- payoff changes with time
Delta Hedging - possible to capture gains from volatility by
hedging a portion of the option's value
- if you delta hedge, make money both when price goes
up and down
- hedge consistently; make money if realized delta-
hedging profits that are greater than the premium paid
away for the option
OPTION BASED HEDGING
12
Purchasing stock index put options permits a portfolio manager
to hedge equity market risk by limiting downside risk while
retaining upside potential
1. If the NASDAQ index rises, given the assumption of a
correlation between the portfolio and the index, the value of
the portfolio increases
2. If the NASDAQ index falls, an increase in the value of the
puts may approximate the loss in the portfolio’s value. The
protective put limits the portfolio’s downside
SHORT HEDGING v/s OPTION HEDGING
13
Exhibit 10
Short Selling:
Portfolio value = $34.55m
Average beta = 1.785
Share price = 95.63
# stocks required = 0.64m
Consider Aug 95 option with price $4.125
- 1m, rfr = 5.97%
Volatility can be calculated as 40.69; calculate delta = -0.4365
# puts required = 1.47m
THETA
14
Theta of a derivative (or portfolio of derivatives) is the rate of
change of the value with respect to the passage of time –
‘Time Decay’
The theta of a call or put is usually negative. If time passes
with the price of the underlying asset and its volatility
remaining the same, the value of the option declines
) (
2 2
) (
2 2
2
) ( 5 .
2
) ( 5 .
2
1
2
1
d N rKe
t
e S
d N rKe
t
e S
rt
d
p
rt
d
c
÷
÷
÷
÷
+ = O
÷ ÷ = O
t
o
t
o
GAMMA
15
Gamma is the rate of change of delta (?) with respect to the
price of the underlying asset
• Gamma addresses Delta hedging errors caused by curvature
S S
P
S S
C
p
p
c
c
c
A c
=
c
c
= I
c
A c
=
c
c
= I
2
2
2
2
VEGA
16
Vega is the rate of change of the value of the portfolio with
respect to the volatility of the underlying asset
• All long options have positive Vegas
• Higher the volatility, higher the value of the option
o
o
c
c
=
c
c
=
P
C
p
c
vega
vega
RHO
17
Rho is the rate of change of the value of the portfolio with
respect to the interest rate
Measures the sensitivity of the value of the portfolio to change
in interest rate when all else remains same
) (
) (
2 p
2 c
d N Kte
d N Kte
rt
rt
÷ ÷ =
=
÷
÷
µ
µ
Thank You
18
doc_777214434.pdf
The case is to decide whether to continue risk management program of short-selling the NASDAQ index or switch to a hedging program utilizing put options on the index.
Pine Street Capital
Discussion and Analysis
1
PINE STREET CAPITAL – WHAT RISK TO HEDGE & WHAT TO BEAR?
2
Hedge: market related risks
1. Currently managing a market neutral fund ($32 AUM)
In the past the market risk was
hedged by shorting or short-selling
representative shares of the
market index
In the past the market risk was
hedged by shorting or short-
selling representative shares of
the market index
The alternative under
consideration was hedging the
market risk with the help of put
options on the market index
Ready to Bear: individual security related risk; leverage
1. The fund deals with technology driven companies due to the
expertise of its fund manager in that area; comfortable in
prediction of individual stock related risk/ return
2. Use leverage to maximize returns
HEDGE FUND STRATEGIES
Leverage
•By using debt
to finance a
portion of
assets, RoE is
greater
•However, if
assets lose
value, then
high leverage
works against
the investor
•Used to eliminate
general market risk
from the fund
•Expected Return =
? + ? ( Market Return)
• Removes market
return component,
leaving only alpha
return in the portfolio
• Return on hedged
portfolio = guaranteed
?, whether up or down
movement
•Extreme volatility in the
market
•Beta of portfolio dynamic,
changing rapidly in high
volatility market
•Options can better
immunize against market
fluctuations
•Instead of shorting, buy
PUT options
•Keep utilizing leverage and
protect against large
negative movements
Option Based
Short-Selling
3
BALANCE SHEET EFFECTS OF LEVERAGE
4
Assets Equity Assets Equity
50 50 100 100
Assets Debt Assets Debt
100 50 200 50
Equity Equity
50 150
Unlevered Portfolio
ROE = 100%
Levered Portfolio
ROE = 200%
SHORT SELLING STRATEGY
5
1. In normal circumstances the risk was reasonably hedged by
using short selling strategy
2. High proficiency of the fund managers in predicting the
portfolio beta; systems in place to achieve the exact amount
of short selling required
3. Expected PSC portfolio return = ? + ?*(Market Return)
4. With the help of exact prediction of market risk (?), they
were successful in mitigating the whole market related risk
to make the portfolio “market neutral”
However, due to extreme volatility in the markets, especially in technology
driven shares the prediction of beta became very difficult
SHORT SELLING STRATEGY EXAMPLE
6
As NASDAQ increases by 10%, using ? + ?*(Market Return), where ? = 1%
and ? = 1.5, we get 1 + 1.5(10) = 16% and 1 + 1.5(-10) = -14%
As NASDAQ increases by 10%, shorting it results in a 10% decrease ($15
decrease) and vice versa
Initial Value NASDAQ (+10%) NASDAQ (-10%)
Long Portfolio $100 $116 $86
Short NASDAQ $150 $135 $165
Total $250 $251 $251
1% 1%
Tomorrow
Return on Hedged Portfolio
( )
( ) ( )
b-r T
-rT
gen 1 2
C = Se N d - Ke N d
( )
( )
( )
b-r T
-rT
gen 2 1
P = Ke N -d - Se N -d
o
o
+ +
=
2
1
ln(S/K) (b /2)T
d
T
o
o
o
+ ÷
= = ÷
2
2 1
ln(S/K) (b /2)T
d d T
T
BLACK SCHOLES MERTON MODEL
7
Call Option
Put Option
OPTION GREEKS
8
The “Greeks” are sensitivities of option price to model inputs*
First Order
1. Delta
2. Theta
3. Vega
4. Rho
Second Order
1. Gamma
Each measures a different dimension to the risk in an option position
*Black Scholes Merton model
DELTA
9
Delta is the rate of change of the option price with respect to
the price of the underlying asset
Delta indicates the number of shares of stock required to
mimic the returns of the option
for Call = N(d
1
)
for Put = N(d
1
) - 1
S
C
c
c
c
= A
S
P
p
c
c
= A
Option
price
A
B
Slope = A
Stock price
PUT OPTION BASED HEDGING EXAMPLE
10
Using So = K = $100, volatility = 25%, RFR = 5%, 2m to maturity, option price
and delta for the option is calculated as shown in the table in the current
scenario
As S&P increases/ decreases, the option price decreases/ increases and
accordingly the ROE figures change
Assets Equity Assets Equity Assets Equity
(Stock) $100 $100 (Stock) $107.5 $107.5 (Stock) $92.5 $92.5
Assets Equity Assets Equity Assets Equity
(Stock) $89.09 (Stock) $95.77 (Stock) $84.21
(S&P Puts) $10.91 $100 (S&P Puts) $5.60 $101.37 (S&P Puts) $19.07 $101.48
Hedged Portfolio (PUT Options)
Today S&P (+5%) S&P (-5%)
ROE = 1.37% ROE = 1.48%
Un-hedged Portfolio
Today S&P (+5%) S&P (-5%)
ROE = 7.5% ROE = -7.5%
LINEAR v/s NON LINEAR HEDGING
11
Linear – Future Contracts – payoff function is linear
- every one-tick movement translates directly into a
specific dollar value per contract
Non Linear – Option Contracts – payoff function is non-linear
- payoff changes with time
Delta Hedging - possible to capture gains from volatility by
hedging a portion of the option's value
- if you delta hedge, make money both when price goes
up and down
- hedge consistently; make money if realized delta-
hedging profits that are greater than the premium paid
away for the option
OPTION BASED HEDGING
12
Purchasing stock index put options permits a portfolio manager
to hedge equity market risk by limiting downside risk while
retaining upside potential
1. If the NASDAQ index rises, given the assumption of a
correlation between the portfolio and the index, the value of
the portfolio increases
2. If the NASDAQ index falls, an increase in the value of the
puts may approximate the loss in the portfolio’s value. The
protective put limits the portfolio’s downside
SHORT HEDGING v/s OPTION HEDGING
13
Exhibit 10
Short Selling:
Portfolio value = $34.55m
Average beta = 1.785
Share price = 95.63
# stocks required = 0.64m
Consider Aug 95 option with price $4.125
- 1m, rfr = 5.97%
Volatility can be calculated as 40.69; calculate delta = -0.4365
# puts required = 1.47m
THETA
14
Theta of a derivative (or portfolio of derivatives) is the rate of
change of the value with respect to the passage of time –
‘Time Decay’
The theta of a call or put is usually negative. If time passes
with the price of the underlying asset and its volatility
remaining the same, the value of the option declines
) (
2 2
) (
2 2
2
) ( 5 .
2
) ( 5 .
2
1
2
1
d N rKe
t
e S
d N rKe
t
e S
rt
d
p
rt
d
c
÷
÷
÷
÷
+ = O
÷ ÷ = O
t
o
t
o
GAMMA
15
Gamma is the rate of change of delta (?) with respect to the
price of the underlying asset
• Gamma addresses Delta hedging errors caused by curvature
S S
P
S S
C
p
p
c
c
c
A c
=
c
c
= I
c
A c
=
c
c
= I
2
2
2
2
VEGA
16
Vega is the rate of change of the value of the portfolio with
respect to the volatility of the underlying asset
• All long options have positive Vegas
• Higher the volatility, higher the value of the option
o
o
c
c
=
c
c
=
P
C
p
c
vega
vega
RHO
17
Rho is the rate of change of the value of the portfolio with
respect to the interest rate
Measures the sensitivity of the value of the portfolio to change
in interest rate when all else remains same
) (
) (
2 p
2 c
d N Kte
d N Kte
rt
rt
÷ ÷ =
=
÷
÷
µ
µ
Thank You
18
doc_777214434.pdf