When using futures based on broad stock market indices, they provide the best way to manage the risk of diversified equity portfolios.. Given that there are no futures contracts on the t
Trang 1Reading 28 Risk Management Applications of Forward and Futures Strategies
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The preferred approach regarding risk management is
that companies should take risk in those areas in which
business has expertise and comparative advantage and
avoid risks in areas which are not related to their primary
lines of business i.e exchange rate risk, interest rate risk
Hedging: Hedging refers to a risk management approach in which a market position is taken to protect against undesirable outcomes
However, risk management is not only hedging risk;
rather, it involves managing risk i.e reducing or
increasing risk exposures, i.e changing risk exposures to the desired level
MARKET RISK
Stock market is more volatile compared to bond market
However, stock market has higher liquidity relative to the
bond market (i.e long-term and corporate bonds and
municipal bonds)
Risks associated with stock market volatility can be
managed by using futures contracts which are generally
based on stock market indices (not individual stocks)
When using futures based on broad stock market
indices, they provide the best way to manage the risk of
diversified equity portfolios Beta measures the risk of a
diversified stock portfolio i.e it measures the relative
riskiness of a stock portfolio compared to a benchmark
(market) portfolio e.g S&P 500
Beta is a relative risk measure It is used to measure only
the risk that cannot be eliminated by diversifying a
portfolio i.e systematic, non-diversifiable or market risk A
portfolio that is not well diversified could contain
additional risk known as nonsystematic, diversifiable or
asset-specific risk
•Risk associated with broad market movements is
known as Systematic risk e.g changes in interest
rates by the Federal Reserve
•Risk associated with a specific company is known
as nonsystematic risk e.g labor strike on a
particular company This risk can be managed by
diversification and by using options
Given that there are no futures contracts on the true
market portfolio, beta of a stock portfolio should be
measured relative to the index on which the futures
contract is based
Beta is similar to duration
Beta plays a critical role in risk management
Limitation of Beta: Beta measures only systematic risk not
non-systematic risk; therefore, it represents a limited
measure of risk
Example:
Consider a stock with beta of 1.20 (ignoring any asset-specific risk) and beta of benchmark index is 1.0 It represents that the stock is 20% more volatile than the index
If a stock has beta of 0.85 (ignoring any asset-specific risk), it represents that the stock is 15% less volatile than the index
NOTE:
S&P 500 Index is used as a proxy to represent the market portfolio; however, it does not truly represent the true market portfolio
Formula to compute Beta:
β = CovSI / σ2I
where,
index
σ2 I = variance of the index
Covariance measures the extent to which two assets (i.e portfolio and the index) move together
• If the covariance is positive, the portfolio and the index tend to move in the same direction
• If the covariance is negative, the portfolio and the index tend to move in the opposite direction
Dollar beta of the stock portfolio = beta of stock portfolio
× market value of the stock portfolio
= βs S Futures dollar beta = beta × futures price
= βf f
where,
βf = Futures contract beta
• Beta of Futures contract is often assumed to be 1.0 However, it is not necessarily equal to 1.0 Thus,
Trang 2it is preferably specified as βf
•Value of the futures is zero at start of each day
because it is marked to market at the end of each
day; therefore, combination of stock and futures, if
the target beta is achieved, is BTS
To achieve desired/target level of beta exposure The
following relationship holds:
βT S = βs S + Nfβf f
where,
βT = Desired beta or a target beta
ΒS = Current portfolio beta
S = stock portfolio value
f = futures price*
βf = Futures contract beta
N f = Number of futures contracts i.e
N=B− B
B SF
*Actual futures price = Quoted futures price × Multiplier
Example:
Quoted futures price = 1225 and Multiplier
= $250 Then, Actual futures price = 1225 × $250 = $306,250
•When futures price is simply stated, multiplier is
taken as 1
Observe that:
•When the goal is to increase the beta, βT>βs and
the sign of Nf will be positive which indicates that
futures should be bought in order to increase the
portfolio beta
•When the goal is to decrease the beta, βT<βs and
the sign of Nf will be negative which indicates that
futures should be sold in order to lower the
portfolio beta
When Goal is to reduce Beta to zero: When the objective
is to completely eliminate the risk, βT would be zero and
Nf would be:
N=−B
B Sf
•To hedge away all of the risk, Nf number of futures
should be sold
Example:
Value of portfolio = $9,300,000
Manager wants to decrease beta from 1.3 to 1.0
Beta of futures contract = 1.05
Futures price = $220,000
Number of futures contracts =..
. × $ , ,
= –12.08 ≈ –12
• Manager must sell 12 futures contracts to decrease the beta to the desired level
= 0
Number of futures contracts = .
. × $ , ,
=–52.3377 ≈ –52
• Manager must sell 52 futures contracts to completely hedge away the equity risk
Effectiveness of Futures Contract to hedge risk:
Futures contract can be used to hedge the risk only associated with the relationship between the stock portfolio and the index on which the futures contract is based
• This implies that to hedge the risk of the portfolio consisting of small-cap stocks, futures contract based on large-cap index (i.e S&P 500) should not
be used The appropriate approach is to use futures contract based on small-cap index
In addition, index futures typically are based only on price indices and they do not reflect payment and reinvestment of dividends This implies that dividends will accrue on the stocks but the index used to hedge risk does not reflect any dividends However, it does not adversely affect the effectiveness of the futures
The portfolio manager can manage the risk of an equity position as follows:
• Increasing beta when the market is expected to move up
o But increasing the beta increases the risk i.e if the market falls, the loss on the portfolio will be greater than if beta had not been increased
• Decreasing beta when the market is expected to move down
o But decreasing the beta decreases the risk i.e if the market rises, the portfolio value will rise but the rise will be smaller than if beta had not been decreased
• Adjusting beta from its actual level to the desired level when beta of portfolio changes due to the change in market value of portfolio over time
It is important to note that Betas are difficult to measure
Example:
Dollar value of portfolio = $38,500,000
Price of futures contract (S&P 500) = $275,000 Portfolio beta = 0.90
Target beta = 1.10 Futures beta = 0.95
Trang 3Nf* =..
. $ ", ,
= 29.47 ≈ 29 contracts
1)Assume the S&P 500 index increases by 4.4% portfolio
value increases to $40,103,000 Stock index futures
rises to $286,687.50 (i.e increase of 4.25%)
If you bought 29 contracts at $275,000, profit on the
futures contract will be:
($286,687.50 - $275,000) × 29= $338,937.50
Rate of return on stock portfolio = ($40,103,000 /
$38,500,000) – 1
= 00416 = 4.16%
The combined positions (stock and futures contracts)
result in portfolio value= $40,103,000 + $338,937.50
= $40,441,937.50
Rate of return on combined position = ($40,441,937.50 /
$38,500,000) –1
= 5.04%
Effective beta = Combined position return in % / Market
return in %
= 5.04% / 4.4% = 1.15
Thus, effective beta is close to target beta of 1.10 but
not equal to target beta due to:
1)The number of futures contracts is rounded off
2)The expected value of betas may not be equal to the
observed actual value of beta
Stock index futures can be used to create synthetic
positions in equity
Synthetic Cash:
Long Stock + Short Futures = Long risk-free bond
Synthetic Stock:
Long Stock = Long risk-free bond + Long Futures
• In synthetic equity exposure, investors hold cash
and obtain equity market exposure by using futures contracts
Advantages of Stock index futures to create synthetic positions in equity:
1 Provide significant transaction cost savings
2 Highly liquid
3.3.1) Creating a Synthetic Index Fund
A synthetic index fund is a combination of risk-free bonds and futures on the desired index i.e
Long Stock = Long risk-free bond + Long Futures
Steps to create Synthetic Index Fund:
Step 1: Calculate the number of futures contracts that
corresponds to the amount of cash investor will have at the end of the time period
Number of futures contract = Nf*
={V ×(1 + r) T}/ (q×f)
where,
N f * = number of futures contracts
q = multiplier
V = Portfolio value
r = risk-free rate
T = time period
f = futures price
Step 2: We cannot use fractional contracts; therefore,
we need to round the number of contracts to the nearest whole number By using this number
of contracts, we can estimate the amount of cash that needs to be invested or equitized Amount need to invest in bonds = V*
= (Nf*× q× f) / (1 + r)T
Step 3: The amount of Treasuries equitized will grow at
the risk-free rate Thus, amount of equity (stocks) that will be effectively purchased at the start of the contract will be:
Equity purchased = (Nf* ×q) / (1 + δ) T
where,
δ = dividend yield
• This implies that investing V* in bonds and buying
Nf* futures contracts at a price of f is equivalent to buying (Nf* q) / (1 + δ) T units of stock
of equity, then after reinvestment of dividends, value of equity at the end of time period wiould be:
Equity purchased × (1 + dividend yield)T = Nf*×q
Step 4: Futures position pay-off at the end of investment
horizon:
Practice: Example 3,
Volume 5, Reading 28
Practice: Exhibit 3,
Volume 5, Reading 28
Trang 4The pay-off of Nf* futures contracts = Nf*× q ×(ST –f)
where,
S T = Index value at time T
Equitized cash amount grows enough to settle futures
position and investor is left with exactly the amount of
equity exposure as desired at the beginning of period
i.e
Nf* × q × ST
NOTE:
It is important to note that all of these transactions are
synthetic
Issues:
1 The index is a price index only and does not include
dividends Hence, creating synthetic equity position
by using index futures can capture only the index
performance without the dividends
2 The expiration date of Futures contract can be
different from the desired date However, strategy
using futures contract will still be effective if the futures
contract is correctly priced both when the position is
opened and when the strategy is completed
Example:
Manager has $70 million investment in T-bills with a yield
of 2%
He wants to create synthetic equity position equal to the
amount invested in cash/ T-bills
S&P 500 Index level = 1065
Multiplier = $250
T = 3 months
Step 1:
Number of futures contracts = $70,000,000 (1.02) 0.25 /
(1065 × $250)
= 264.22
contracts
Step 2:
Amount of cash actually invested = (264 × $250 × 1065) /
(1.02) 0.25
= $69,942, 878 Step 3:
After three months, this amount will grow to:
$69,942, 878 (1.02)0.25 = $70,289,999
At expiration, this cash is used to settle futures contract and achieve the equity exposure desired at the beginning of the investment horizon
• It should be noted that rounding down reduced the exposure i.e Actual exposure = $69,942,878 (1.02)0.25 ≠ Target exposure = $70,000,000 (1.02)0.25
3.3.2) Equitizing Cash Equitizing cash is a transaction in which a given amount
of cash is converted into equity position using futures contract while maintaining the liquidity provided by the cash
Issues:
Investor does not have control over the pricing of the futures
• If the futures contract is overpriced, the investor will pay too much for the futures and the risk-free bonds will not be enough to offset the excessively high price effectively paid for the stock
• Opposite results when the futures contract is underpriced
Synthetic cash position: synthetic position in cash can be created by selling futures against a long stock position Long stock + Short futures = Long risk-free bonds Step 1:
Number of contracts = Nf*= –10,000,000 (1.03) 0.5 / (1425 ×
$250)
=–28.49 ≈ –28
• Manager need to sell 28 contracts
Step 2:
Actual amount of synthetic cash created = V*=(28 × 1425 × $250) / (1.03) 0.5 = $9,828,659
• After 6 months, this amount of synthetic cash will grow to $9,828,659 (1.03) 0.5 = $9,975,000
• 28 contracts are equivalent to Nf* × q = 28 × 250 =
7000 units of stocks
Step 3:
Futures pay-off at maturity = – 28 ($250) (ST – 1425) =
$9,975,000 – 7000ST
Practice: Example 4, Volume 5, Reading 28
Practice: Exhibit 4,
Volume 5, Reading 28
Trang 5• The manager can settle the short futures position
by selling the equity position Thus the manager is
left with the synthetic cash (i.e $9,975,000)
• It should be noted that due to rounding, synthetic
cash is ≠ manager’s original “real” position
NOTE:
When portfolio is identical to the index on which the
futures contracts is based, both the formulas (i.e formula
given in section 3.1 and formula given in Exhibit 5) will
provide the same result i.e same number of futures
contracts to sell
Example:
Portfolio value invested in S&P 500 index = $10,000,000
Manager wants to covert equity exposure to cash over
6-month time period
Risk-free rate = 3%
S&P 500 index level = 1,425
Multiplier = $250
Formula given in section 3.1 is a general formula and
can be used to eliminate systematic risk of any portfolio
Alternative ways to manage risk:
• Beta can be increased (decreased) by selling (buying) low-beta stocks and buying (selling) high-beta stocks
• Beta can be reduced to zero by selling the entire portfolio and investing that money in the risk-free asset
• Beta can be increased by reducing any position in the risk-free asset or even by issuing a risk-free asset (i.e borrowing)
Advantages of using derivatives i.e stock index futures
to manage risk:
1)Derivatives are less costly because they involve lower transaction costs
2)Derivatives have greater liquidity
3)Derivatives provide better timing and allocation strategies
4)Derivatives provide a quicker way to execute a transaction and/or to acquire the portfolio or to dispose a position
5)Derivatives are less disruptive in nature
6)Derivatives provide ease of altering risk exposures without disturbing the asset allocation
7)Derivatives require less capital to trade than the underlying securities
Limitation:
Derivatives do not solve liquidity problems For example, the greatest liquidity in the futures market is in the shortest expirations However, generally, derivatives are more liquid than the underlying securities
The performance of an asset portfolio significantly
depends on the allocation of the portfolio among asset
classes Portfolio manager can effectively alter the asset
allocation through the use of futures contract
Example:
Manager wants to change $7 million of a large cap
position with a current beta of 0.90 to a mid cap position
with a beta of 1.20
Large-cap futures price = $95,000
Large-cap futures beta = 0.84
Mid-cap futures price = $36,000
Mid-cap futures beta = 1.5
To achieve the desired asset allocation:
Number of Large cap futures contract required to sell =
.
."% $$,,
Number of Mid cap futures contract required to buy =
. $$,,
Important:
Reducing duration of a portfolio through futures contract does not increase the liquidity of the position For
example, when duration is reduced, it only converts the volatility of the long-term instrument to that of a short-term instrument i.e long-short-term instrument will have interest rate sensitivity of the short-term instrument Reasons why hedge is not perfect: A hedge will usually not be perfect because:
1)It is not possible to hedge exactly
2)The number of futures contracts is rounded off 3)Both beta and duration are difficult to measure due
to their unstable nature The expected value of betas and duration may not be equal to the observed
Practice: Example 6, Volume 5, Reading 28
Practice: Exhibit 6, Volume 5, Reading 28
Practice: Exhibit 5,
Volume 5, Reading 28
Trang 6actual values i.e they may not truly reflect the
sensitivities of stocks and bonds to the underlying
sources of risk
• Stock portfolios do not always respond in the exact
manner as predicted by their betas
• Bond portfolios do not always respond in the exact
manner as predicted by their durations
4) The futures contract is subject to basis risk i.e
change in futures price is different from the change
in underlying index
5) Futures contracts are based on price index and do
not include dividends
Pre-investing: It is a strategy in which futures contracts
are used to create or add exposure that converts a
yet-to-received cash into a desired synthetic equity or bond
exposure
This strategy is useful to use when the investor might not
have the cash to invest at a time when the investment
opportunities are attractive
We know:
Long underlying + Short futures = Long risk-free bond
Long Underlying = Long risk-free bond + Long futures
Long underlying + Loan = Long Futures
• It implies that an outright long position in futures is
similar to a fully leveraged position in the
underlying
• So, by taking long position in futures, investor
effectively borrows against the cash that he/she
expects to receive in the future
• When cash is eventually received, the investor will
close out the futures position and invest the cash in
the underlying
• Risks: Taking a leveraged long position in the
market is similar to speculating that the market will
perform well and the gain from outperformance of the market will be > the cost of borrowing But when gain < cost of borrowing, leveraged position magnifies the losses
Example:
Manager will receive $10 million after 3 months The manager wants to invest 60% in equity and 40% in debt Equity beta = 1.5
Bond duration = 4 Stock index futures price = $200,000 with beta = 1.05 Bond futures price = $98,000 with duration = 5 and yield beta = 1
Objective:
To create
• Equity position = $10 million × 60% = $6 million
and
• Bonds position = $10 million × 40% = $4 million number of Equity contracts = .
. $&,,
= 42.86 ≈ long 43 contracts number of Bonds contracts = 1 %
$%,,
$ ",
= 32.65 ≈ long 33 contracts
CURRENCY RISK
Companies are affected both by the exchange rate
uncertainty itself and also by its effects on their ability to
plan for the future e.g a parent company not only
needs to predict its foreign subsidiary’s sales but also
needs to predict the exchange rate at which it will
convert its foreign cash flows into domestic cash flows
Predicting foreign exchange rates with much certainty is
extremely difficult; therefore, companies prefer to
manage exchange rate risk with the use of derivatives
Types of Foreign Exchange Rate Risk:
1) Transaction Exposure: It is a foreign exchange risk
when foreign transactions are made For example,
• Risk that contracted future cash flows i.e foreign currency receipts become less valuable in terms of domestic currency when foreign currency
depreciates or
• When planned purchases i.e foreign currency payments become more expensive when foreign currency appreciates
2) Translation Exposure: It is a risk that multi-national corporations face due to decline in the value of their assets denominated in foreign currencies as a result of foreign currency depreciation when they are converted into their domestic currency at an appropriate
Practice: Example 7, Volume 5, Reading 28
Practice: Exhibit 7, 8 & 9, Volume 5, Reading 28
Trang 7exchange rate Managing translation exposure requires
a focus on accounting
3) Economic Exposure: It is a risk faced by a domestic
exporter when domestic currency appreciates relative
to foreign currency and negatively affects its
competitiveness Similarly, a domestic importer faces
economic exposure when domestic currency
depreciates relative to foreign currency To manage
economic exposure, investors need to forecast demand
in the light of competitive products and exchange rates
Receipt
Currency
Exposure
Position in Foreign Currency
Action taken to hedge Currency Risk Receiving
Foreign
Currency
Contract Paying Foreign
Buy Forward Contract
Example:
A firm expects to receive a payment in British pounds
worth ₤10 million
Payment will be received in 60 days
Current spot exchange rate = $1.45/ ₤
60-days forward exchange rate = $1.47/ ₤
A firm is long foreign currency because it expects to
receive foreign currency Therefore, a firm should take
short position in a forward contract i.e using forward
contract a firm will receive (after 60 days):
₤10,000,000 × $1.47/₤ = $14,700,000
• This amount will be received by the firm
irrespective of exchange rate at that time
Hedging Exchange rate risk:
An equity investment in the foreign market is subject to
both equity (market) risk and foreign exchange risk
• To manage equity/market risk i.e risk of decrease
in foreign market investment, we need to sell
futures contracts on foreign market index
• To reduce foreign exchange risk i.e volatility
resulting from uncertainty of exchange rate e.g risk of depreciation of foreign currency when we have long position in foreign currency, we need to sell forward contracts on the foreign currency
Portfolio Investor has following choices available:
1)Hedge local/foreign equity market return and leave the currency risk unhedged
2)Hedge both local/foreign equity market return and the currency risk
i Use futures contract on the foreign equity portfolio to lock in the future value of the portfolio (ignoring any currency risk)
ii By hedging foreign equity portfolio, investor will
be able to know the number of units of the foreign currency that he/she will need to convert
to his/her domestic currency at the hedge termination date Investors can use forward contract to hedge the exchange rate/currency risk
3)Hedge neither the local/foreign equity market return nor the currency risk
NOTE:
It is not possible to leave the local equity market return unhedged and hedge the currency risk i.e to hedge
currency risk, investor must hedge local equity market
return
• Hedging only the market risk generates return equal to foreign risk-free rate
• Hedging both the market risk and exchange rate risk generates return equal to domestic risk-free rate
This implies that neither strategy is feasible to use in the long-run These strategies can be used only in the short-run by investors who have foreign market investments and want to temporarily alter a position without liquidating the portfolio and converting it to cash
Practice: Example 9, Volume 5, Reading 28
Practice: Exhibit 12, Volume 5, Reading 28
Practice: Example 8,
Volume 5, Reading 28
Practice: Exhibit 10 & 11,
Volume 5, Reading 28
Trang 86 FUTURES OR FORWARDS?
• Standardized
contracts
• All terms (except
price) are set by
futures exchange
clearinghouse against
default
• Requires margin
deposits and daily
settlement of gains
and losses
• Regulated by federal
authorities
• Conducted in a
public arena i.e
futures exchange
• Futures trade on
active secondary
markets
• Reported to the
exchanges and
regulatory authority
• They represent fully
leveraged positions
• Both futures and
forwards have initial
value of zero and
offer linear pay-offs
• Customized contracts
• Terms are set by the parties according to their needs
• Subject to default risk
• Pay the full value of the contract at contract expiration
• Forward contracts are not cleared through an exchange and are not marked to market
However, parties may decide to use margin deposits and
occasional settlements
to reduce default risk
• Unregulated
• Conducted privately
• Forward contracts do not trade in secondary markets
• Not reported to the public or regulators
• Hedging a specific portfolio using Forwards contracts is a more costly approach relative to futures but provides a better hedge
• They represent fully leveraged positions
• Both futures and forwards have initial value of zero and offer linear pay-offs
Preferred instruments to use in different situations:
A.When risks are associated with very specific dates e.g
a loan in which interest rates are reset, Forward
contracts should be preferred Because futures
contract has specific expirations
B When investors do not require a perfect hedge and
transaction costs are a concern, risk of bond portfolios
can be managed using Treasury Bond Futures
C.When investors have the flexibility with respect to the
horizon date, Treasury bond futures can be used to
manage risk of bond portfolios
D.Generally, risk of equity portfolios is managed by using
stock index Futures because equity investors usually
require only satisfactory protection against market
declines rather than a perfect hedge
E Generally, investors prefer to use less costly standardized futures contracts instead of relatively costly customized forwards contract in spite of better hedge provided by forwards
F Foreign currency should be hedged using Forward contracts because foreign currency forward contracts have greater liquidity relative to foreign currency Futures market
Forward contracts are preferred by investors when they are exposed to specific currency transactions
G.When investors want to maintain privacy of the transaction, forward contracts are preferred to use
H.Some investors use different hedging instruments to meet requirements of regulatory bodies i.e when regulation prevents use of credit risky instruments i.e forward contracts and OTC options, investors should use Futures or exchange-listed options
Futures and Forwards versus Options:
• Many organizations are not permitted to use futures or forwards because they represent fully leveraged positions These firms can use options, which are not fully leveraged
• Futures or forwards are exposed to greater loss potential whereas the maximum loss borne by an investor in options is limited to the option premium paid
• Both futures and forwards have initial value of zero and offer linear pay-offs whereas, options require cash investment at the start (i.e option premium) and offer non-linear pay-offs i.e investor can gain from favorable movements and avoid
unfavorable movements
Practice: End of Chapter Practice Problems for Reading 28 &FinQuiz Item-set ID# 8812, 8805 & 8798