Structured Products and the Mischief of Self-Indexing
By: Geng Deng, Craig McCann and Mike Yan (Oct 2016)
Published in The Journal of Index Investing, Spring 2017, Vol. 7, No. 4, pp. 16-29.
In recent years, investment banks have issued structured products linked to indexes they create rather than just linking to standardized indexes from Standard & Poor's. In doing so, the issuers create additional difficulties for retail investors to understand these, sometimes complex, investments. We illustrate the potential conflicts of interest created with structured products linked to proprietary volatility indexes although the conflicts are present in other proprietary index based investments as well.
In the 1990s, investment banks switched from underwriting reverse convertibles and tracking securities issued by operating companies like Citicorp and Reynolds Metals linked to their own stock to issuing and underwriting structured products linked to unrelated publicly traded companies like Cisco Systems. This change in investment banks' role led to a dramatic proliferation of new issuances and ever more complicated payoff structures since the underwriters were no long limited to underwriting securities other companies wanted to issue. Investment banks could now issue notes in relatively small denominations linked to publicly traded companies that the brokerage firms could then sell through their retail sales force. The complexity of these notes made regulatory oversight more difficult and allowed issuers to sell structured products with very low issue date values.
Ex-post Structured Product Returns: Index Methodology and Analysis
By: Geng Deng, Tim Dulaney, Tim Husson, Craig McCann, and Mike Yan (Apr 2014)
Published in The Journal of Investing, Summer 2015, Vol. 24, No. 2: pp. 45-58.
The academic and practitioner literature now includes numerous studies of the substantial issue date mispricing of structured products but there is no large scale study of the ex-post
returns earned by structured product investors. This paper augments the current literature by analyzing the ex-post returns of nearly 18,000 individual structured products issued by
13 brokerage firms since 2007. We construct our structured product index and sub-indices for reverse convertibles, single-observation reverse convertibles, tracking securities, and auto-callable securities by valuing each structured product in our database each day.
The ex-post returns of US structured products are highly correlated with the returns
of large capitalization equity markets in the aggregate and individual structured products
generally underperform simple alternative allocations to stocks and bonds. The observed
underperformance of structured products is consistent with the significant issue date under-pricing documented in the literature.
Efficient Valuation of Equity-Indexed Annuities Under Lévy Processes Using Fourier-Cosine Series
By: Geng Deng, Tim Dulaney, Craig McCann, and Mike Yan (Apr 2014)
Published in The Journal of Computational Finance, Vol 21, No. 2, September 2017.
Equity-Indexed Annuities (EIAs) are deferred annuities which accumulate value over time according to crediting formulas and realized equity index returns. We propose an efficient algorithm to value two popular crediting formulas found in EIAs - Annual Point-to-Point (APP) and Monthly Point-to-Point (MPP) - under general Lévy-process based index returns. APP contracts observe returns of referenced indexes annually and credit EIA accounts, subject to
minimum and maximum returns. MPP contracts incorporate both local/monthly caps and global/annual floors on index credits. MPP contracts have payoffs of a "cliquet" option.
Our algorithm, based on the COS method (Fang and Oosterlee, 2008), expands the present value of an EIA contract using Fourier-cosine series, expresses the value of the EIA contract
as a series of terms involving simple characteristic function evaluations. We present several
examples with different Lévy processes, including the Black-Scholes model and the CGMY
model. These examples illustrate the efficiency of our algorithm as well as its versatility
in computing annuity market sensitivities, which could facilitate the hedging and pricing of
annuity contracts.
The Fall of Willow
By: Geng Deng and Craig McCann (Mar 2014)
Published in the PIABA Bar Journal, 21 (1): 71-90, 2014.
From May 8, 2000 until June 30, 2007, the UBS Willow Fund was invested in distressed obligations with offsetting but smaller cash and synthetic short debt positions through credit default swaps (CDS). After June 2007 the Fund dramatically increased its purchases of CDS and became massively short distressed debt. Investors in the Fund lost $278.4 million during this second period from June 2007 to December 2012 and the Willow Fund was liquidated in 2013.
The Willow Fund understated the risk of its CDS portfolio and did not disclose the dramatic increase in the Fund's risks. In fact, the Willow Fund stopped reporting the CDS premiums it paid as a line item expense and thereafter bundled them with realized and unrealized gains on losses on its overall securities and derivatives portfolio making it nearly impossible for investors to discern the impact of the Fund's change in strategy and dramatic increase in risk. Investors in the Willow Fund suffered losses of between $351 million and $419 million compared to diversified portfolios of junks bonds while UBS made over $100 million selling and managing the Fund.
Valuation of Structured Products
By: Geng Deng, Tim Husson, and Craig McCann (Feb 2014)
Published in The Journal of Alternative Investments, Spring 2014, Vol. 16, No. 4: pp. 71-87.
The market for structured products has grown dramatically in the past decade. Their
diversity and complexity has led to the development of many different valuation approaches,
and which approach to use to value a given product is not always clear. In this paper
we demonstrate and discuss four approaches to valuing structured products: simulation of
the linked financial instrument's future values, numerical integration, decomposition, and
partial differential equation approaches. As an example, we use all four approaches to value
a common type of structured product and discuss the virtues and pitfalls of each. These
approaches have been practically applied to value 20,000 structured products in our database.
Valuation of Reverse Convertibles in the VG Economy
By: Geng Deng, Tim Dulaney, and Craig McCann (Jan 2014)
Published in the Journal of Derivatives & Hedge Funds 19, 244-258 (November 2013).
Prior research on structured products has demonstrated that equity-linked notes sold to retail investors in initial public offerings are typically issued at above their
fair market value. A particular type of equity-linked note reverse convertibles embed down-and-in put options and other investors relatively high coupon payments
in exchange for bearing some of the downside risk of the equity underlying the note.
We analytically study the magnitude of the overpricing of reverse convertibles - one
of the most popular structured products on the market today - within a stochastic
volatility model.
We extend the current literature to include analytical valuation formulas within
a model of stochastic volatility - the Variance Gamma (VG) model. We show
that these complex notes are even more overpriced than previously estimated when
stochastic volatility is taken into account. As a result of their complex payouts and
the lack of a secondary market to correct the mispricing, reverse convertible notes
continue to be sold at prices substantially in excess of their fair market value.
Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options
By: Geng Deng, Tim Dulaney, Craig McCann, and Mike Yan (Jan 2014)
Published in the Journal of Derivatives & Hedge Funds 19, 278-294 (November 2013).
We find that leverage in exchange traded funds (ETFs) can affect the "crookedness" of
volatility smiles. This observation is consistent with the intuition that return shocks are
inversely correlated with volatility shocks - resulting in more expensive out-of-the-money
put options and less expensive out-of-the-money call options. We show that the prices of
options on leveraged and inverse ETFs can be used to better calibrate models of stochastic
volatility. In particular, we study a sextet of leveraged and inverse ETFs based on the S&P
500 index. We show that the Heston model (Heston , 1993) can reproduce the crooked smiles
observed in the market price of options on leveraged and inverse leveraged ETFs. We show
further that the model predicts a leverage dependent moneyness, consistent with empirical
data, at which options on positively and negatively leveraged ETFs have the same price.
Finally, by analyzing the asymptotic behavior for the implied variances at extreme strikes,
we observe an approximate symmetry between pairs of LETF smiles empirically consistent with the predictions of the Heston model.
Modeling a Risk-Based Criterion for a Portfolio with Options
By: Geng Deng, Tim Dulaney, and Craig McCann (Dec 2013)
Published in the Journal of Risk, Vol. 16, No. 6.
The presence of options in a portfolio fundamentally alters the portfolio's risk and return profiles when compared to an all equity portfolio. In this paper, we advocate modeling a
risk-based criterion for optioned portfolio selection and rebalancing problems. The criterion
is inspired by Chicago Mercantile Exchange's risk-based margining system which sets the
collateralization requirements on margin accounts. The margin criterion computes the losses
expected at the portfolio level using expected stock price and volatility variations, and is
itself an optimization problem. Our contribution is to remodel the criterion as a quadratic
programming subproblem of the main portfolio optimization problem using option Greeks.
We also extend the margin subproblem to a continuous domain. The quadratic programming
problems thus designed can be solved numerically or in closed-form with high efficiency,
greatly facilitating the main portfolio selection problem. We present two extended practical
examples of the application of our approach to obtain optimal portfolios with options. These
examples include a study of liquidity effects (bid/ask spreads and limited order sizes) and sensitivity to changing market conditions. Our analysis shows that the approach advocated
here is more stable and more efficient than discrete approaches to portfolio selection.
Robust Portfolio Optimization with VaR Adjusted Sharpe Ratio
By: Geng Deng, Tim Dulaney, Craig McCann, and Olivia Wang (Nov 2013)
Published in the Journal of Asset Management, 14(5):293-305, 2013.
We propose a robust portfolio optimization approach based on Value-at-Risk (VaR) adjusted Sharpe ratios. Traditional Sharpe ratio estimates using a limited series of historical returns are subject to estimation errors. Portfolio optimization based on traditional Sharpe ratios ignores this uncertainty and, as a result, is not robust. In this paper, we propose a robust portfolio optimization model that selects the portfolio with the largest worse-case-scenario Sharpe ratio within a given confidence interval. We show that this framework is equivalent to maximizing the Sharpe ratio reduced by a quantity proportional to the standard deviation in the Sharpe
ratio estimator. We highlight the relationship between the VaR-adjusted Sharpe ratios and other modified Sharpe ratios proposed in the literature. In addition, we present both numerical and empirical results comparing optimal portfolios generated by the approach advocated here with those generated by both the traditional and the alternative optimization approaches.
Structured Product Based Variable Annuities
By: Geng Deng, Tim Dulaney, Tim Husson, and Craig McCann (Sep 2013)
Published in the Journal of Retirement, Winter 2014, Vol. 1, No. 3: pp. 97-111.
Recently, a new type of variable annuity has been marketed to investors which is based on structured product-like investments instead of the mutual fund-like investments found in traditional variable annuities. Embedding a structured product into a variable annuity introduces substantial complexity into an investment typically considered conservative. In this paper, we describe structured product based variable annuity (spVA) crediting formulas and how they differ from traditional VAs, value the embedded derivative position for a range of example parameters, and calculate the fair cap levels required to fairly compensate investors for the derivative position. We also provide extensive backtests of spVA crediting formulas using our calculated cap levels and compare the results to their underlying indexes. Our findings suggest that the complexity of spVAs can be used to hide fees and reduce the comparability of variable annuities to other investments in the market.
