Tải bản đầy đủ - 0trang
2 Alpha From Realized / Implied Volatility Arbitrage
forecasting volatilities, in understanding the nuances of the market and
skill in managing the underlying exposure.
3.3 Alpha From Volatility Skew Trades
In many markets, different options on even the same underlying
instrument trade at substantially different Black-Scholes implied
volatilities. In the equity area, for example, lower strikes (out-of-themoney puts) often have implied volatilities much higher than options
that are at-the-money. To the extent that underlying price distributions
should be lognormal (as assumed in the Black-Scholes model), volatility
skews represent a source of pure profits. The trade can be constructed
by buying the cheaper implied strikes, selling the more expensive ones
(thereby creating a vega / volatility neutral position), and going delta
neutral by trading in the underlying. OEX backspreads or put ratio
spreads are case in point. These trades again rely on skill in predicting
volatilities and the likely price distributions. But rather than relying on
convergence in volatility levels to historical values (as was the case
above), volatility skew trades are based on exploiting differentials in the
shapes of the price distributions — the distribution implied from option
prices and the distribution expected to prevail.
3.4 Alpha From Cash Futures Basis Trade
The cash futures basis trade exists in almost all markets. The general
principle is to buy (or sell) the cash instrument and sell (or buy) the
futures on it, with the objective of exploiting price differences between
the two, after accounting for any hidden costs or imbedded options. In
the US government bond market, for example, the futures seller
implicitly owns various options stemming from the seller’s ability in
terms of cheapest-to-deliver — quality option, end-of-month option,
afternoon or wildcard option, timing option and new issue option. The
option to decide which of these to exercise and make the cheapest
possible delivery depends on yield levels, yield spreads between
Using Derivatives to Create Alpha
alternative cash bonds, realized bond volatility and cost of carry. The fair
price of the futures contract vis-à-vis the cash bond is determined after
stripping off these options, and can be arbitraged away by buying futures
and selling options and cash bonds, or the reverse.
3.5 Alpha From Trading the Optionality in Bonds
Callable bonds, range accrual notes, period caps and indexed amortizers
are bonds that embed negative optionality and that pay higher coupons
than the non-option counterparts. Callable bonds, for example, are
structured in a Bermuda style, where the issuer / seller can exercise the
call at different times after an initial period. These bonds often also have
derivative equivalents — the Bermuda swap is a synthetic variation on
the callable bond — and are motivated by the need for someone to hedge
their cash bond exposure, or because of transaction costs, or the need to
keep trades off-balance sheet and reduce margin requirements. In any
case, it is possible to construct relative value trades that exploit volatility
differences between different markets and that rely on superior modeling
skills to create alpha. In the callable bond example, one can buy different
European swaptions that synthetically mimic the short Bermuda option
exposure. To the extent that these swaptions can be bought cheaply
enough, and the Bermuda / European mismatch managed effectively,
there is a possibility of locking in alpha profits.
3.6 Alpha From Trading the Optionality in Convertible Bonds
The core convertible bond strategy entails purchasing convertible bonds
and shorting the underlying stocks, leaving a net long volatility position.
The hedge neutralizes equity risk but is exposed to interest rate and
volatility risk. Income is captured from the convertible coupon and the
interest on the short position in the underlying stock. This income is
reduced by the cost of borrowing the underlying stock and also the
dividends payable to the lender of the underlying stock. The non-income
return comes from the long volatility exposure. Rebalancing will add to
or subtract from the short stock position, and will be driven by
transaction costs and risk appetite. The core arbitrage comes down to the
implied volatility of the convertible bond vis-à-vis’ actual volatility over
the life of the position.
The strategy, as outlined, does not necessarily entail the use of
derivatives, since one can simply buy the converts and short stocks. But
derivatives technology still is a must — the techniques that enable the
imbedded options to be priced and risk managed properly. In addition, in
markets where shorting stocks is difficult, derivatives can play an
explicit role. One can buy puts or sell calls, synthetically creating short
equity exposure. This synthetic transaction may result in arbitrage
opportunities that depend on differences in the implied volatilities
between the options and convertible bonds, two different (though
theoretically correlated) markets. The possibility of generating alpha
returns can be significant, given that this is not a widely understood asset
3.7 Alpha From Macro Interest Rate Trades
A lot of hedge fund strategies are arbitrage-driven, seeking to exploit
perceived mispricing across different products and markets. The other
strategies are explicitly directional such as macro bets on interest rates
in different countries, directional plays on yield curve spreads, etc. The
instruments used for these trades range from both cash bonds to futures,
including U.S. T-Bond futures, U.S. T-Note futures, German Bunds,
Japanese JGBs, and British Gilts. Constant maturity swaps (CMSs) and
derivatives that pay based on differences in CMS rates between two
points on the yield curve are also instruments that can be used to
implement specific views and to trade in size. The trades are
conceptually simple, requiring someone to either go long or short these
instruments, and represent pure alpha by following an active management strategy.
Using Derivatives to Create Alpha
3.8 Alpha From Relative-Value Trades: Mortgage-Backed Securities
An example of a mortgage-backed relative-value trade is going long
(short) an MBS pass-through security or a tranche of a CMO, selling
(buying) a duration-adjusted equivalent of treasuries (notes or futures),
and buying (selling) OTC treasury options. The idea is to capture the
option-adjusted spread between the mortgage-backed security and
treasuries. Value is created based on someone’s ability to develop a good
hypothesis of how pre-payments, interest rates and cash flows interact
in these markets, and the ability to translate that hypothesis into
sophisticated pricing and risk management models. More often than
not, relative value trades come with imbedded options and basis risk.
They require taking an integrated view of different markets within a
consistent cross-product pricing framework that covers both cash and
derivatives markets. In this case, one needs to look at Eurodollar prices
and swap rates (to create the forward curve), cap and swaption prices
(to incorporate volatility and optionality into rates), and IO / PO prices
(to calibrate prepay models).
3.9 Alpha From Credit Derivatives
Credit derivatives have been pounded over the 2007–2008 period and are
not likely to get back to previous form. The risk in credit derivatives
stems from the fact that models are grossly incapable of predicting
default rates. The complexity in some of the structures also makes it hard
computationally to drill down to pool-level data and derive cash flows
that flow through the tranching waterfall. Credit default data that covers
a long history of extreme market environments, which one can use to
build reasonable models, is also hard to get, especially in the subprime
space that has been so problematical. Finally, there is a paucity of
hedging instruments that one can use. Most dealers have been caught on
the same side, and need to hedge using the same instruments.
That being said, credit derivatives should remain a useful tool in
terms of completing financial markets as well as in mitigating
counterparty risk of default. As long as trading involves two
counterparties, credit risk is not going away. In theory at least, it should
also be possible to find greater pricing dislocations in the market in
the current environment, dislocations that can be acted upon profitably.
CDO tranches that are pricing in extreme levels of defaults are potential
buys. To the extent that some of the collateral might be better than the
collateral underlying standard ABX / TABX indices, and to the extent
that one can understand and properly model those differences, one can
buy into structures that are trading lower than the indices, all else equal,
using the indices as a hedge.
3.10 Alpha From Energy Derivatives
One of the more unusual derivatives in the energy world is the swing
option — an option that allows the energy quantities delivered or used
to vary. These options have historically been embedded in the legal
contracts written by energy producers and require a good understanding
of the stochastic price dynamics that drive energy markets, including
the ability to model distinctive price spikes, volatilities and seasonal
movements. They present opportunities for alpha creation simply
because they have not always been priced using that level of
sophistication. There is also value that can be created by integrating these
financial options more closely with the physical options inherent in
operating physical plants, and by looking at both as a portfolio.
3.11 Alpha From Long / Short Strategies
Long-short trades are very common in arbitrage-oriented strategies,
relying as they do on price convergence on both legs of the trade. But
they have traditionally not been used as extensively in putting together
funds or in stock market investing. Mutual funds for the most part
are long-only, often by mandate. This limitation reduces the potential
Using Derivatives to Create Alpha
Assume the following long-only portfolio allocations which use
ETFs for broad-based market exposure: 40% US Stock (symbol SPY),
20% US Bonds (IEF), 20% Commodities (IAU), 15% Real Estate (IYR),
and 5% Money Market (VMFXX). This is an example of a diversified
portfolio for a U.S. investor.
Now, instead of 40% allocation in SPYs, an alternative would be to
employ leverage and use shares in, say, the ProFund Ultra Bull (ULPIX).
With 2 times leverage, a 20% allocation in ULPIX would provide the
same exposure as a 40% allocation to S&P500. This strategy frees up
20% capital, which can then be allocated for a long-short alpha play. A
portion of this capital could be used to target sectors that are expected
to outperform S&P500s, with the remainder invested in inverse sector
fund ETFs (such as PHPIX) that are expected to do well in a declining
market. To the extent that the long-short sectors perform as expected, the
strategy would add alpha over and above what could be generated with
the long-only portfolio.
Of course, skill is required in this example, as in other alpha trades.
But when portfolio solutions can be long-short, the strategy set is
widened, returns become potentially uncorrelated with the market,
portfolio volatility is lowered, and one can profit from not only the longs,
but also the shorts.
4. Using Derivatives to Transport Alpha
Alpha transport is the process of transferring an investment manager’s
ability to add alpha in one investment strategy to another market.
Consider the following: long a fund which excels at picking US stocks,
short S&P futures, long FTSE futures. The strategy of going long the
fund and shorting S&P futures creates essentially a US market-neutral
position. Any value that is added is due to the manager’s ability with
regard to selecting US stocks that outperform the S&P index. Overlaid
with FTSE futures, the net effect is a portfolio, which is subject to the
exceptional returns (over S&P index) offered by the US manager on top
of the returns of the core FTSE position. Alpha transport allows
participants to go beyond their traditional orientation and add value from
5. Risk Management of Derivatives Portfolios
Finding alpha-generating strategies is one side of the coin. Preserving
alpha is the other, and that is where risk management shines. Derivatives
are subject to the following investment risks:
Leverage risk. The use of derivatives can result in large losses due to
the use of leverage. Derivatives allow investors to earn large returns from
small movements in the underlying asset's price. However, investors
could lose large amounts if the price of the underlying moves against
them significantly. There have been several instances of massive losses
in derivative markets, including Long Term Capital Management
(LTCM) and Orange County.
Take the case of an arbitrage fund. A good arbitrage pricing model
can at best suggest what is rich or cheap today. But by itself, it cannot
predict whether things will not get richer or cheaper tomorrow.
Arbitrages often take time to converge, whereas leverage and mark-tomarket pressures necessitate good timing, even in the short-term. Many
funds that have destructed over the years used excess leverage and they
got their timing wrong as well.
Factor risk. The risk in equity derivatives is not only systematic
market exposure, but also exposure to various other factors: industry,
sector, country, momentum, P/E, to name a few. In fixed income,
duration bond-equivalents, convexity, option-adjusted spreads, exposure
to different points along the yield curve, are the usual yardsticks. The
optionality inherent in many derivatives portfolios also necessitates a
close look at the various Greeks- delta, vega, gamma, theta, rho etc.
Correlation risk. Correlation is a key input when it comes to multiasset class portfolios. A lot rides on realized correlations turning out the
same as the ones that are input. In times of extreme market stress, asset
correlations break down, often catastrophically. Models that assume a
constant correlation dynamic are fraught with pricing and risk
management errors; a risk that can perhaps be mitigated by the use of
sophisticated correlation Multi-Garch forecasting algorithms.
Model risk (leading to both incorrect valuation and risk numbers).
Market prices for exchange-traded derivatives are mostly transparent.
They can be viewed on trading screens the world over, and are often
Using Derivatives to Create Alpha
published in real time by the exchanges. Price discovery is a simple
matter. Model risk does not come into play for these trades. For other
derivatives, however, the arbitrage-free price for a derivatives contract
is complex, and there are many different factors to consider. Valuation
becomes model-driven, and is subjected to someone’s ability to
accurately model price, volatility and correlation dynamics. It is not
uncommon then to find that on most trades, both counterparties show
profits. Problematical as that is, it happens because each is marking their
positions to their respective models. In fact, it is this model discrepancy
that drives the two sides to trade.
There are of course other risks in derivatives — operational risk,
counter-party risk, and liquidity risk. These however are not unique to
derivatives. A more complete discussion of risk is discussed in Chapter 12.
The ability to effectively manage these risks is important. The
specific methodologies for doing so vary from market to market. In
general, given that so much of derivatives trading is model-driven,
models have to be vetted against market prices wherever available. Stress
testing the inputs, scenario analysis, and netting exposures into different
exposures, all have to be part of the risk management models. Interactive
risk management interfaces that enable users to track benchmark indices,
and quickly change trade size and determine hedges, are also key.
Derivatives are an integral part of most trading strategies. They offer the
ability to quickly put on sizeable directional bets and hedges across
different markets. For the arbitrage-oriented hedge fund, they also serve
as the building blocks for cross-product strategies. They complete the
cash markets and provide price information that is essential to the
valuation and risk management of complex strategies and portfolios. In
sophisticated hands, they can be used to systematically create alpha,
transfer alpha and preserve alpha.
Hedge Fund Alpha Tear Sheet — Chapter 7
Derivatives are financial contracts or instruments whose value is
tied to other assets.
Derivatives are the building blocks that underlie most crossproduct arbitrage trades.
Derivatives complete the markets and help expand the alpha
We briefly discussed the following alpha generating strategies
o Alpha from futures arbitrage
o Alpha from realized / implied volatility arbitrage
o Alpha from volatility skew trades
o Alpha from cash futures basis trade
o Alpha from trading the optionality in bonds
o Alpha from trading the optionality in convertible bonds
o Alpha from macro interest rate trades
o Alpha from relative-value trades: Mortgage-backed securities versus Treasuries
o Alpha from credit derivatives
o Alpha from energy derivatives
o Alpha from Long / Short strategies
Derivatives are used in alpha transport strategies, the process of
transferring an investment manager’s ability to add alpha in one
investment strategy to another market.
In sophisticated hands, derivatives may be used to systematically
create alpha, transfer alpha, and preserve alpha.
Using Derivatives to Create Alpha
If one does not use leverage, the maximum loss for an investment is
100%, while the maximum gain is unlimited (or several thousand percent
in practical terms.) Given this dynamic, the lognormal distribution
provides a better estimate of security returns than the normal distribution.
The net result is that a procedure that measures alpha, adjusted for
lognormal returns, is generally more accurate than the traditional linear
Leland, Hayne, “Beyond Mean-Variance: Risk and Performance
Measurement in a Nonsymmetrical World”, Financial Analysts Journal,
January–February 1999, pp. 27–36.
This page intentionally left blank