Valuation of Reverse Convertibles in the VG Economy
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
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
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
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
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.
Large Sample Valuations of Tenancies-in-Common
Published in the Journal of Real Estate Portfolio Management, Vol. 20, No 2, 2014.
In this paper, we value a large sample of tenant-in-common (TIC) investments based on cash flow projections found in 194 private placement memoranda. Our sample of TIC offering documents covers approximately 20% of the TIC industry from 2004 to 2009. Based on the sponsor's projections, we find that the TICs on average were worth 83.6 cents per $1 paid by TIC equity investors. However, we have found that sponsors' cash flow projections overstate likely returns to investors by assuming unrealistically high rental growth rates and unrealistically low vacancy and caps rates.
Adjusting only the sponsors' cap rates alone to rates reflecting market conditions lowers the average valuations by 9.5 cents to 74.1 cents per $1. Adjusting the sponsors' unrealistic rental growth rate and vacancy assumptions lowers the average value further. These low valuations are consistent with average upfront fees and reserves equal to 28% and 12% of equity. Our results suggest that private placement sponsors have considerable latitude in their projections, and that investors should view projected returns with skepticism.
The Priority Senior Secured Income Fund
Published in the PIABA Bar Journal, 20 (2): 191-206, 2013.
Retail investors are being sold increasingly obscure non-conventional investments. With the Priority Senior Secured Income Fund (PSSI), issuers may have finally gone too far. PSSI is the first registered investment company that invests primarily in leveraged loans and CLOs. Unlike the mutual funds with which most retail investors are familiar, PSSI investors are not able to redeem shares daily at PSSI's net asset value. PSSI is not listed on an exchange and traded like a closed-end fund and so investors will have neither an observable market price nor any opportunity to sell shares in the secondary market.
PSSI, like other non-traded investments, is an extremely high cost offering. Its upfront fees of at least 9% and annual fees of over 8%, in addition to the high cost of its underlying structured finance investments, require persistently high returns on its portfolio to generate a positive internal rate of return for fund investors. The increased risks borne by investors to generate that return are complex and are not likely to be appreciated by brokers or retail investors.
Structured Product Based Variable Annuities
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.
Private Placement Real Estate Valuation
Published in the Journal of Business Valuation and Economic Loss Analysis Volume 9, Issue 1, January 2014.
As a result of the Securities and Exchange Commission's relaxation of its prohibition against the marketing of private placements, investors will soon be exposed to a broad array of syndicated commercial real estate investments. Private placement commercial real estate investments are illiquid and so cannot be easily valued by reference to frequent transactions in the same asset in active markets.
We have reviewed over 200 syndicated commercial real estate private placement memorandums and find that virtually all include projected cash flows. This study explains how investors and their advisors can use these projections to develop estimates of investment value. We determine a lower bound for discount rates applicable to the cash flows derived from commercial real estate and apply the methodology to an actual commercial real estate private placement investment. Our findings suggest significant overvaluation by commercial real estate private placement investment sponsors even when using conservative estimates of discount rates.
Structured Certificates of Deposit: Introduction and Valuation
Published in the Financial Services Review, Volume 23, Number 3, 2014.
This paper examines the properties and valuation of market-linked certificates of deposit (structured CDs). Structured CDs are similar to structured products -- debt securities with payoffs linked to market indexes -- but while structured products have garnered significant interest in both the financial media and in the academic literature, structured CDs have received relatively little attention. We review the market for structured CDs in the United States and provide valuations for several common product types. Using our methodology, we find significant mispricing of several common types of structured CDs across multiple issuers, which is similar in magnitude to the well-documented mispricing in the structured products market. In particular, we estimate that structured CDs are typically worth approximately 93% of the value of a contemporaneously issued fixed-rate CD. These results suggest that unsophisticated investors may not understand the value, risks, and subtleties of these ostensibly conservative investments.
Using EMMA to Assess Municipal Bond Markups
Published in the PIABA Bar Journal, 20 (1): 99-122, 2013.
In the past, assessment of the reasonableness of municipal bond markups depended on anecdotal recollection of markups and subjective judgment about what was customary. Interested parties including regulators can now use the MSRB's EMMA service to determine the markups charged on a set of transactions and can make precise and accurate statements about how unusual such markups were, controlling for many factors thought to effect the reasonableness of markups.
We analyze over 13.7 million customer trades, totaling $3.9 trillion in par amount traded in fixed-coupon, long-term municipal bonds. We estimate that investors were charged $10.65 billion in municipal bond markups between 2005 and 2013 in our sample - $6.45 billion in trades on which excessive markups appear to have been charged.
Our sample includes about 30 percent of the fixed-coupon municipal bond trades and so the total markups charged from 2005 to 2013 is likely to be at least $20 billion. $10 billion of this $20 billion in markups were charged on trades on which excessive markups appear to have been charged. These markups are a transfer from taxpayers and investors to the brokerage industry and could be largely eliminated with simple, low-cost improvements in disclosure.