Transcript FIN 377L – Portfolio Analysis and Management

Second Investment Course – November 2005
Topic Eight:
Currency Hedging & Using Derivatives
in Portfolio Management
8-0
Using Derivatives in Portfolio Management

Most “long only” portfolio managers (i.e., non-hedge fund managers)
do not use derivative securities as direct investments.

Instead, derivative positions are typically used in conjunction with
the underlying stock or bond holdings to accomplish two main tasks:
“Repackage” the cash flows of the original portfolio to create a more
desirable risk-return tradeoff given the manager’s view of future market
activity.
 Transfer some or all of the unwanted risk in the underlying portfolio,
either permanently or temporarily.


In this context, it is appropriate to think of the derivatives market as
an insurance market in which portfolio managers can transfer certain
risks (e.g., yield curve exposure, downside equity exposure) to a
counterparty in a cost-effective way.
8-1
The Cost of “Synthetic” Restructuring With Derivatives
Consider the relative costs of rebalancing a stock portfolio in two ways:
Cost Factor
(i)
physical rebalancing by trading the stocks themselves; or
(ii)
synthetic rebalancing using future contracts
United States
(S&P 500)
Japan
(Nikkei 225)
United Kingdom
(FT-SE 100)
France
(CAC 40)
Germany
(DAX)
Hong Kong
(Hang Seng)
A. Stocks
Commissions
Market Impact
Taxes
Total
0.12%
0.30
0.00
0.42%
0.20%
0.70
0.21
1.11%
0.20%
0.70
0.50
1.40%
0.25%
0.50
0.00
0.75%
0.25%
0.50
0.00
0.75%
0.50%
0.50
0.34
1.34%
0.01%
0.05
0.00
0.06%
0.05%
0.10
0.00
0.15%
0.02%
0.10
0.00
0.12%
0.03%
0.10
0.00
0.13%
0.02%
0.10
0.00
0.12%
0.05%
0.10
0.00
0.15%
B. Futures
Commissions
Market Impact
Taxes
Total
Source: Joanne M. Hill, “Derivatives in Equity Portfolios,” in Derivatives in Portfolio Management, edited by T. Burns, Charlottesville, VA: Association for
Investment Management and Research, 1998.
8-2
The Hedging Principle (cont.)

Consider three alternative methods for hedging the downside risk of
holding a long position in a $100 million stock portfolio over the next
three months:
1) Short a stock index futures contract expiring in three months.
Assume the current contract delivery price (i.e., F0,T) is $101 and that
there is no front-expense to enter into the futures agreement. This
combination creates a synthetic T-bill position.
2) Buy a stock index put option contract expiring in three months with an
exercise price (i.e., X) of $100. Assume the current market price of the
put option is $1.324. This is known as a protective put position.
3) (i) Buy a stock index put option with an exercise price of $97 and (ii)
sell a stock index call option with an exercise price of $108. Assume
that both options expire in three months and have a current price of
$0.560. This is known as an equity collar position.
8-3
1. Hedging Downside Risk With Futures
Expiration Date Value of a Futures-Hedged Stock Position:
Potential
Portfolio Value
Value of Short
Futures Position
60
(101-60) = 41
0
(60+41) = 101
70
(101-70) = 31
0
(70+31) = 101
80
(101-80) = 21
0
(80+21) = 101
90
(101-90) = 11
0
(90+11) = 101
0
(100+0) = 101
100
0
Cost of
Futures Contract
Net Futures
Hedge Position
110
(101-110) = -9
0
(110-9) = 101
120
(101-120) = -19
0
(120-19) = 101
130
(101-130) = -29
0
(130-29) = 101
140
(101-140) = -39
0
(140-39) = 101
Notice that this net position can be viewed as a synthetic Treasury Bill (i.e., risk-free) holding with
a face value of $101.
8-4
The Hedging Principle
Suppose a portfolio manager holds a $100 million position in U.S. equity securities and she is
concerned with the possibility that the stock market will decline over the next three months. How
can she hedge the risk that her portfolio will experience significant declines in value?
1) Hedging With Stock Index Futures:
Economic Event
Actual
Stock Exposure
Desired
Futures Exposure
Stock Prices Fall
Loss
Gain
Stock Prices Rise
Gain
Loss
2) Hedging With Stock Index Options:
Economic Event
Actual
Stock Exposure
Desired
Hedge Exposure
Stock Prices Fall
Loss
Gain
Stock Prices Rise
Gain
No Loss
8-5
1. Hedging Downside Risk With Futures (cont.)
Graphically, restructuring the long stock position using a short position in the futures contract
creates the following synthetic restructuring:
Now
Three Months
Long Stock
Short Futures
Net
Position:
Long T-Bill
(p = 0)
Long Stock
(p = 1)
8-6
2. Hedging Downside Risk With Put Options
Expiration Date Value of a Protective Put Position:
Potential
Portfolio Value
Value of
Put Option
Cost of
Put Option
Net Protective
Put Position
60
(100-60) = 40
-1.324
(60+40)-1.324 = 98.676
70
(100-70) = 30
-1.324
(70+30)-1.324 = 98.676
80
(100-80) = 20
-1.324
(80+20)-1.324 = 98.676
90
(100-90) = 10
-1.324
(90+10)-1.324 = 98.676
100
0
-1.324
(100+0)-1.324 = 98.676
110
0
-1.324
(110+0)-1.324 = 108.676
120
0
-1.324
(120+0)-1.324 = 118.676
130
0
-1.324
(130+0)-1.324 = 128.676
140
0
-1.324
(140+0)-1.324 = 138.676
8-7
2. Hedging Downside Risk With Put Options (cont.)
Long Stock Plus Long Put:
Terminal
Pos ition
Value
Equals:
Terminal
Pos ition
Value
Long Stock
Put-Protected
Stock Portfolio
98.676
98.676
100
Expiration Date
Stock Value
-1.324
100
Expiration Date
Stock Value
-1.324
Long Put
8-8
3. Hedging Downside Risk With An Equity Collar
Expiration Date Value of an Equity Collar-Protected Position:
Potential
Portfolio Value
Net Option
Expense
Value of
Put Option
Value of
Call Option
Net CollarProtected Position
60
(0.56-0.56)=0
(97-60)=37
0
60 + 37 = 97
70
(0.56-0.56)=0
(97-70)=27
0
70 + 27 = 97
80
(0.56-0.56)=0
(97-80)=17
0
80 + 17 = 97
90
(0.56-0.56)=0
(97-90)= 7
0
90 + 7 = 97
97
(0.56-0.56)=0
0
0
97 + 0 = 97
100
(0.56-0.56)=0
0
0
100 + 0 = 100
108
(0.56-0.56)=0
0
0
108 - 0 = 108
110
(0.56-0.56)=0
0
(108-110)= -2
110 - 2 = 108
120
(0.56-0.56)=0
0
(108-120)= -12
120 - 12 = 108
130
(0.56-0.56)=0
0
(108-130)= -22
130 - 22 = 108
140
(0.56-0.56)=0
0
(108-140)= -32
140 - 32 = 108
8-9
3. Hedging Downside Risk With An Equity Collar (cont.)
Terminal Position
Value
Collar-Protected
Stock Portfolio
108
97
97
108
Terminal
Stock Price
8 - 10
Zero-Cost Collar Example: IPSA Index Options
8 - 11
Zero-Cost Collar Example: IPSA Index Options (cont.)
8 - 12
Another Portfolio Restructuring

Suppose now that upon further consideration, the portfolio manager
holding $100 million in U.S. stocks is no longer concerned about her
equity holdings declining appreciably over the next three months.
However, her revised view is that they also will not increase in value
much, if at all.

As a means of increasing her return given this view, suppose she
does the following:


Sell a stock index call option contract expiring in three months with an
exercise price (i.e., X) of $100. Assume the current market price of the
at-the-money call option is $2.813.
The combination of a long stock holding and a short call option
position is known as a covered call position. It is also often referred
to as a yield enhancement strategy because the premium received
on the sale of the call option can be interpreted as an enhancement
to the cash dividends paid by the stocks in the portfolio.
8 - 13
Restructuring With A Covered Call Position
Expiration Date Value of a Covered Call Position:
Potential
Portfolio Value
Value of
Call Option
Proceeds from
Call Option
Net Covered
Call Position
60
0
2.813
(60+0)+2.813 = 62.813
70
0
2.813
(70+0)+2.813 = 72.813
80
0
2.813
(80+0)+2.813 = 82.813
90
0
2.813
(90+0)+2.813 = 92.813
100
0
2.813
(100+0)+2.813 = 102.813
110
-(110-100) = -10
2.813
(110-10)+2.813 = 102.813
120
-(120-100) = -20
2.813
(120-20)+2.813 = 102.813
130
-(130-100) = -30
2.813
(130-30)+2.813 = 102.813
140
-(140-100) = -40
2.813
(140-40)+2.813 = 102.813
8 - 14
Restructuring With A Covered Call Position (cont.)
Long Stock Plus Short Call:
Equals:
Terminal
Pos ition
Value
Terminal
Pos ition
Value
102.813
Long Stock
C overed Call
Portfolio
Expiration Date
Stock Value
2.813
100
Short
C all
2.813
100
Expiration Date
Stock Value
8 - 15
Some Thoughts on Currency Hedging and Portfolio Management
Question: How much FX exposure should a portfolio manager hedge?
Exchange Rate
C hile an P e so p er U.S . D olla r
Month ly: S ep 2 9, 20 00 - Se p 3 0, 2 00 5
High : 7 49
Lo w: 52 9
La st: 52 9
75 0
Weakening CLP
Strengthening CLP
70 0
65 0
60 0
55 0
01
02
03
04
05
8 - 16
Conceptual Thinking on Currency Hedging in Portfolio Management
There are at least three diverse schools of thought on the optimal amount of
currency exposure that a portfolio manager should hedge (see A. Golowenko,
“How Much to Hedge in a Volatile World,” State Street Global Advisors, 2003):
1. Completely Unhedged: Froot (1993) argues that over the long term, real
exchange rates will revert to their means according to the Purchasing Power
Parity Theorem, suggesting currency exposure is a zero-sum game. Further,
over shorter time frames—when exchange rates can deviate from long-term
equilibrium levels—transaction costs make involved with hedging greatly
outweigh the potential benefits. Thus, the manager should maintain an
unhedged foreign currency position.
2. Fully Hedged: Perold and Schulman (1988) believe that currency exposure
does not produce a commensurate level of return for the size of the risk; in fact,
they argue that it has a long-term expected return of zero. Thus, since the
investor cannot, on average, expect to be adequately rewarded for bearing
currency risk, it should be fully hedged out of the portfolio.
8 - 17
Currency Hedging in Portfolio Management (cont.)
3. Partially Hedged: An “optimal” hedge ratio exists, subject to the usual
caveats regarding parameter estimation. Black (1989) develops the notion of
universal hedging for equity portfolios, based on the idea that there is a net
expected benefit from some currency exposure. (This is attributed to Siegel’s
Paradox, the empirical relevance of which is questionable in this context.) He
demonstrates that this ratio can vary between 30% and 77% depending on a
variety of factors.
Gardner and Wuilloud (1995) use the concept of investor regret to argue that a
position which is 50% currency hedged is an appropriate benchmark for
investors who do not possess any particular insights and FX rate movements.
A variation of the partial hedging approach is that different asset classes should
have different hedging policies. For instance, Black (1989) also suggests that
foreign fixed-income portfolios should be fully (i.e., 100%) hedged under the
universal hedging scheme. This is partly due to the fact that currency volatility
represents a larger percentage of the volatility to a fixed-income position than
the volatility of an equity holding.
8 - 18
Hedging the FX Risk in a Global Portfolio: Some Evidence

Consider a managed portfolio consisting of five different asset
classes:



Monthly returns over two different time periods:



Chilean Stocks (IPSA), Bonds (LVAC Govt), Cash (LVAC MMkt)
US Stocks (SPX), Bonds (SBBIG)
September 2000 – September 2005
September 2002 – September 2005
Five different FX hedging strategies (assuming zero hedging
transaction costs):
#1: Hedge US positions with selected hedge ratio, monthly rebalancing
#2: Leave US positions completely unhedged
#3: Fully hedge US positions, monthly rebalancing
#4: Make monthly hedging decision (i.e., either fully hedged or completely
unhedged) on a monthly basis assuming perfect foresight about future
FX movements
#5: Make monthly hedging decision (i.e., either fully hedged or completely
unhedged) on a monthly basis assuming always wrong about future FX
movements
8 - 19
Investment Performance for Various Portfolio Strategies:
September 2000 – September 2005
8 - 20
Investment Performance for Various Portfolio Strategies:
September 2002 – September 2005
8 - 21
Sharpe Ratio Sensitivities for Various Managed Portfolio Hedge Ratios
8 - 22
Currency Hedging and Global Portfolio Management: Final Thoughts

Foreign currency fluctuations are a major source of risk that the global
portfolio manager must consider.

The decision of how much of the portfolio’s FX exposure to hedge is not
clear-cut and much has been written on all sides of the issue. It can depend
of many factors, including the period over which the investment is held.

It is also clear that tactical FX hedging decisions have potential to be a
major source of alpha generation for the portfolio manager.

Recent evidence (Jorion, 1994) suggests that the FX hedging decision
should be optimized jointly with the manager’s basic asset allocation
decision. However, this is not always possible or practical.

Currency overlay (i.e., the decision of how much to hedge made outside of
the portfolio allocation process) is rapidly developing specialty area in global
portfolio management.
8 - 23