FINANCIAL ENGINEERING eJOURNAL
"Securities Lending Strategies, Exclusive Auction Bids"
RAVI KASHYAP, Gain Knowledge Group, City University of Hong Kong (CityUHK) - Department of Economics & Finance
This is the first of many papers on models that can improve profitability in the securities lending business. We consider how these methodologies can be applied to both buy side and sell side institutions. We look at different models to manage spreads on daily securities loans and aid the price discovery process, improve the efficiency of the locate mechanism and optimize the allocation of inventory, develop strategies for placing bids on exclusive auctions, price long term loans as a contract with optionality embedded in it and also look at ways to benchmark which securities can be considered to be more in demand or highly shorted and use this approach to estimate which securities are potentially going to become â€œhotâ€? or â€œspecialâ€?, that is securities on which the loan rates can go up drastically and supply can get constrained.
In this paper, the objective is either to design an appropriate securities lending auction mechanism or to come up with a strategy for placing bids, depending on which side of the fence a participant sits.
There are two pieces to this puzzle. One is the valuation of the portfolio being auctioned subject to the information set available to the bidder or the auction designer. This information set would include among other things, the demand for the securities, any additional demand from the locates received, the loan rates applicable to those securities, the duration of the loans, the frequency of loan turnover and the internal inventory pool available to the bidder. These variables are modeled as geometric brownian motions with uncertainty introduced via suitable lognormal distributions and a symmetric normal distribution. We derive heuristics to arrive at a set of valuations, with a pecking order that can help decide the aggresiveness of the valuation.
The other piece would be to come up with the best strategy from an auction perspective once a valuation has been obtained. We start with the benchmark scenario where the buyers, placing bids are assumed to have perfect and complete information regarding their valuation of the portfolio that is being auctioned, that is private only to them. We consider the uniform distribution as the simplest scenario and extend that to a more realistic setting that considers the valuations to be log normally distributed. We further extend this by introducing uncertainty into the estimation of bidder valuations and their bidding strategy. The possibility of number of bidders being unknown, the valuations from various bidders being correlated or the interdependent valuation framework and, a reserve price set by the auction seller are more complex extensions. We show that the strategies of the bidders constitute a Nash equilibrium, under suitable conditions.
Lastly, we run simulations to establish numerical examples for the set of valuations and for various bidding strategies corresponding to the different auction settings. It is tempting to call this one of the more (most) challenging problems in finance, and even though this is debatable and perhaps even labelled as due to ignorance on the author's part, what stands true is that this is certaintly one of the least explored yet profit laden areas of modern investment management. The models developed here could be potentially useful for inventory estimation and for wholesale procurement of financial instruments and also non-financial commodities.
"Diffusing Explosive Portfolio Performance Evaluation of High Frequency Traders"
G. CHARLES-CADOGAN, UCT - School of Economics, Ryerson University - Ted Rogers School of Management, Institute for Innovation and Technology Management
Several analysts report explosive annualized Sharpe Ratios (ASRs) for investment portfolio performance evaluation of high frequency traders (HFTers) ranging from 4.3 to 5,000. This suggests that the profitability of HFT is much higher than that of other actively managed portfolios. In highly competitive financial markets where ASRs for experienced traders are often much less than 2, those numbers imply that the ASR for HFT is misspecified. Thus, HFT performance is incomparable to the performance of experienced traders, hedge funds, and other actively managed portfolios. This paper addresses the misspecification problem by introducing an efficient Sharpe Ratio (ESR) that diffuses explosive ASRs for HFT so that they are comparable to SRs for other actively managed funds. We derive a subordinate stochastic process for HFT strategy which jumps positively only when the trader executes a successful trade or stays flat otherwise. We apply the ESR formula to a sample of risk and return data on HFT strategy, and find that the ESR for aggressive HFT is 1.15, medium HFT is 2.88, and passive HFT is 1.43. For the HFT industry as a whole the ESR is between 1.07 and 1.87. Those ESRs for HFT are equivalent to SRs reported for experienced traders, hedge funds multistrategy, convertible option arbitrage, and fund of fund strategies. Thus, contrary to reports, the profitability of HFT is in line with industry norms for active portfolio management.
"Dynamics of Debt Capacity"
ANDREEA MINCA, Cornell University
JOHANNES WISSEL, Cornell University - School of Operations Research and Industrial Engineering
We propose a model that explains the build-up of short term debt when the creditors are strategic and have different beliefs about the prospects of the borrowers' fundamentals. We define a dynamic game among creditors, whose outcome is the short term debt process as a function of the borrower's fundamentals. As common in the literature, this game has multiple Nash equilibria. We give a refinement of the Nash equilibrium concept that leads to a unique equilibrium. For the resulting debt-to-asset process of the borrower we define a notion of stability.
Bank runs are predictable: a bank run begins when the debt-to-asset process leaves the stability region and becomes a mean-fleeing sub-martingale with tendency to reach the debt ceiling, which is the point when the borrower becomes illiquid.
The debt ceiling and the stability region are computed explicitly. A critical ingredient in our model is the distribution of capital across the beliefs of the creditors and we allow for a wide variety of specifications for this distribution.
About this eJournal
This eJournal distributes working and accepted paper abstracts related to development and employment of quantitative techniques to further our understanding of financial markets, instruments, and strategies. The eJournal welcomes research with a focus on advancing the theory or practice of financial engineering in endowments, hedge funds, insurance firms, investment and commercial banks, pension funds, and personal financial and retirement planning. Topics of interest include, but are not limited to, econometric analysis of financial data, enterprise risk management, investment and consumption models, optimal portfolio, pricing and hedging of financial instruments, as well as innovative empirical studies, analytical models, and mathematical algorithms in credit, energy, fixed-income and other markets.
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