Understanding Returns to Short Selling Using Option-Implied Stock Borrowing Fees

1. Understanding Returns to Short Selling Using Option-Implied Stock Borrowing Fees Dmitriy Muravyev*, Neil D. Pearson#, and Joshua M. Pollet# * Boston College # University of Illinois at Urbana-Champaign March, 2019

2. Puzzle 1: Returns to shorting • Hard-to-borrow stocks have abnormally negative returns • 1.4% per month or ~20% p.a. (2006-2015 sample, EW) • Sorting on borrowing fees, short interest, utilization, days to cover, etc. • The puzzle was documented well before 2006 • Data on short selling measures are public/for sale • Hedge funds that specialize in shorting have small alphas

3. Returns to shorting –potential explanations • Hard-to-borrow stocks have abnormally negative returns • Possible explanations: • short selling is not profitable to the marginal short seller net of fees • short selling is risky and caries a risk premium

4. Puzzle 2: Option prices predict stock returns • The IV spread and skew predict future stock returns • Cremers and Weinbaum (2010), Xing, Zhang, and Zhao (2010) • … yet, option prices are public information • Option prices follow the underlying intraday as option market-makers auto-quote • Muravyev, Pearson, and Broussard (2012)

5. Summary of main findings • The returns to shorting net of stock borrowing costs are less than half of the gross returns to typical strategy, and are not significant • Our results differ from the literature because we use fees that short seller pay instead of fees that lenders get • The option-implied borrowing fees strongly predict changes in fees. • the implied fee is a forward looking measure of the expected borrowing fee during the remaining life of the option. • The borrowing fee risk premium is small • We infer the risk premium from the difference between the actual and implied borrowing fees • The premium was positive: (i) during the financial crisis and (ii) for financial stocks (relative non-financial) before and after the short-sale ban • Shorting though options is expensive after acc. for transaction costs

6. Summary of main findings (cont.) • The implied borrowing fees we compute are excellent predictors of stock returns during the next week (month): • Implied fees drive out short interest, short fee risk, and other short sale constraint measures in joint return regressions. • Implied fees drive out actual fees for net-of-fee returns • After adjusting for the cost of selling short, the IV spread and skew’s P&L declines by more than 50% and is not statistically significant. • These seemingly unrelated strategies based on option prices are not exploitable after taking into account the cost of borrowing stock • IV spread and skew no longer predict returns once we include the option-implied borrowing fee and utilization in predictive regressions. • IV spread and skew predict stock returns not because they reflect informed option market demand that has not yet been reflected in stock prices, but rather because they proxy for stock borrow costs

7. Literature on Shorting Risks • A growing literature emphasizes that borrowing stock and selling it short is risky • Duffie, Garleneau, and Pedersen (2002), D’Avolio (2002), Prado et al. (2014), Engelberg et al (2017), Drechsler and Drechsler (2014), Chuprinin and Ruf (2016) • One possibly important risk stems from the market practice that stock loans may be recalled at any time • borrowing fee for any period longer than a day is uncertain • Engelberg et al. (2017): risk of borrowing fee increases is an important impediment to short-selling and explains a large fraction of the returns to shorting • Prado et al. (2014): risk of changes in future borrowing fees is an impediment to shorting. • Chuprinin and Ruf (2016): short sale recalls force the liquidation of otherwise profitable short positions

8. Other literature • Link between options and short sales • Black (1975): buying put options is an alternative to short selling • Put-call parity violations and short sales: Figlewski and Webb (1993), Battalio and Schultz (2011), Lamont and Thaler (2003), Ofek and Richardson (2003), Ofek, Richardson, and Whitelaw (2004), and Evans, Geczy, Musto, and Reed (2009) • Short-sales constraints may cause stock overvaluation • Miller (1977), Scheinkman and Xiong (2003), Jones and Lamont (2002), Boehmer, Jones, and Zhang (2008), • Geczy, Musto, and Reed (2002), Battalioand Schultz (2006), and Drechsler and Drechsler (2014) short-sales constraints appear unable to explain anomalies because returns significantly exceed fees

9. Motivation • Short selling accounts for a third of equity trading volume • The SEC and EU Commission have recently issued numerous rules (including short-sale bans) • Shorting costs determine profitability of various trading strategies, and hence, the efficiency of stock prices • Many anomalies are concentrated in hard-to-borrow stocks • While some measures of the costs of short selling may be costly or difficult to access, our option-implied measure is directly observable on a daily basis.

10. Simplified mechanics of securities lending Shares Shares Pension Fund Prime Broker (e.g., GS) Option Market Maker “borrowing fee $$” “lending fee $” • Loan terms are negotiated between lender and borrower (OTC market). Loans have usually no specified term and can be recalled at any time. • Borrower delivers the collateral in exchange for securities. The Prime Broker invests the cash collateral to generate income. Only a portion of this income, the “short rate” or rebate, is given to the Option Market Maker • The borrowing fee is the difference between the short-term interest rate (Fed Funds Open) rate and the short rate • Hard-to-borrow securities may command a negative rebate so that the Option Market Maker pays the Prime Broker • At the end of the loan period, the borrowed securities are returned to the lender, and the cash collateral is returned to the borrower.

11. Data • Stock lending data are from the Markit Securities Finance Buy Side Analytics Data Feed • 85% of US securities loans (Markit 2012) • Main variable of interest is “Indicative Fee,” which is an estimate of the fee to be paid by borrower on a new stock loan • Sample period July 2006 to August 2015 • Daily option prices from OptionMetrics • End-of-day bid and ask option prices • We also confirm our results using intraday option data from OPRA • Stock returns are from CRSP

12. Optionable vs. all stocks • Optionable stocks are larger than CRSP stocks • Optionable stocks have lower shorting costs but higher short interest • Actual borrowing fee is often missing and biased, while indicative fee is almost always available

13. Returns net of borrowing fees • Short sellers pay a borrowing fee, which reduces abnormal returns to shorting • We find that the returns to shorting net of stock borrowing costs are less than half of the gross returns • …and not statistically significant • …and roughly match alphas for HFs specializing in shorting • Prior literature primarily used fees received by the lenders, which are much lower than fees paid the borrowers. • … prime brokers intermediate and collect the difference/spread

14. Option-implied borrowing fee • We compute the option-implied borrowing feeusing the version of the put-call parity relation with dividends: • borrowing fee risk premium is difference between option-implied fee and average actual fee over life of option:

15. Computation of option-implied fee • Filters: • drop in-the-money put options, if dividend yield is large, option bid-ask spread is wide, or stock price is low. Only options with 15 to 90 days to expiration • For each stock-date, take the median across the one-minute frequency option-implied fees. The median is our estimate of the (unadjusted) option-implied borrowing fee for the stock-date • Adjust for early exercise bias

16. Adjusting for early exercise premium • Put-call parity relation on previous page is for European options, but prices are for American options • Use only options that are near-the-money and with zero or small dividends during the options’ lives • Time to expiration between 15 and 90 days • But large borrowing fees themselves can make early exercise optimal • Use binomial model to compute option prices for grid of borrowing fees and implied volatilities • Use European put-call parity relation to compute implied borrowing fees • Discover that early exercise bias is large for large borrowing fee and low moneyness ln(K/S), and not sensitive to volatility • Early exercise bias is well described by linear function of min(h×ln(K/S),0) • Estimate the relation using OLS and use estimated relation to adjust the option-implied borrowing fees for the early exercise bias

17. Implied fee example: AIG • Put-call parity relation on previous page is for European

18. Implied fees are forward-looking • Dependent variable is average borrowing fee during next month – current fee • Option-implied borrowing fees predict changes in borrowing fees

19. Is shorting risky? Risk premium? • Shorting costs depend on borrowing fees that may change on a daily basis • Options can be used to infer a fixed borrowing fee for the remaining life of the option • This implied fee can be extracted from put-call pairs and is directly related to violations of put-call parity • Risk premium for bearing borrowing-fee risk = (the fixed option-implied fee) – (actual fees during the option life) • If changes in borrowing fees are systematic in nature, then this risk associated with selling short may be priced

20. Risk premium - subsamples • The risk premium is small for all subsamples

21. Borrowing risk premium • Implied and actual fees are close for all utilization levels • The premium is small for any utilization level

22. Risk premium for HTB stocks over time

23. Risk premium for HTB stocks over time • The risk premium is small for hard-to-borrow stocks even after option market makers’ ability to short stock and failure-to-deliver ended. The only large deviation is during the financial crisis • The risk premium for hard-to-borrow stocks is stable over time and does not seem to be impacted by the ability of option market makers to short stock and fail-to-deliver (Evans, Geczy, Musto, and Reed 2009).

24. Borrowing risk premium & short-sale ban • Shortly before and just after the 2008 short-sale ban, the risk premia reflected in the borrowing costs of financial stocks were larger than for non-financial stocks. This time period is when option market makers were plausibly worried about the possible imposition or re-imposition of ban on shorting financial stocks.

25. Implied fees and future stock returns • If option-implied fees are forward-looking estimates of actual borrowing fees then they should predict stock returns • We find that implied fees do predict stock returns for both one-week and one-month horizons • Coefficient on the option-implied borrowing fee remains highly significant even when other variables such as the actual fee, loan utilization, short interest, and short fee risk measure proposed by Engelberg et al. (2017) are included • Short fee risk measure predicts returns in a univariate regression, but becomes insignificant when any one or more of loan utilization, actual borrowing fee, or option-implied borrowing fee are included in the regression

26. Stock return predictability (weekly returns) • Implied fee predicts returns even after controls • For hard-to-borrow sample, it’s the only predictor

27. Stock return predictability (monthly returns) • Implied fee predicts returns even after controls • For hard-to-borrow sample, it’s the only predictor

28. Implied fees vs. option-based ret. predictors • We also consider the literature showing that differences between certain option implied volatilities predict underlying stock returns • E.g., Cremers and Weinbaum (2010) find that the implied volatility spread positively predicts returns and Xing et al. (2010) find that the implied volatility skew is a negative predictor of returns • When we estimate predictive regressions that include both the option-implied borrowing fee and these other option-based predictors, the option-implied borrowing fee “drives out” the other predictors • We interpret this as evidence that implied volatility spread and skew predict returns because they proxy for the option-implied borrowing fee • CW (2010) and Xing et al. (2010) use OptionMetrics implied volatilities, which are computed treating the borrowing fee as zero. The impact of the borrowing fee on option value is the same as the impact of a dividend yield.

29. Option-based return predictors • Implied volatility measures from literature predict returns • …but are driven out by option-implied fee and utilization

30. Informed trading vs. implied shorting costs • Observations with option ADV < 100 contracts • .…implied fee drives out IV spread and skew in the subsample with little informed trading

31. Returns net of borrowing fees • IV spread and skew strategies are not profitable after accounting for shorting costs

32. Validating quote midpoint for implied fees • The borrowing premium should be small for easy-to-borrow stocks, which is true if implied fees are computed from the option quotes. However, if bid & ask prices are used the implied fees become unrealistically large. • Shorting though options is costly

33. Conclusion • The returns to shorting net of stock borrowing costs are less than half of the gross returns to typical strategy and are not significant • We compute option-implied borrowing fees based on put-call pairs • Risk premium for bearing risk of borrowing fee changes during the remaining life of the option pair is small • In cross-sectional tests, • Option-implied borrowing fees predict future actual fees and changes in future fees, corroborating our claim that they reflect market’s assessment of future borrowing fees • Option-implied borrowing fees predict returns and subsume the predictability associated with most other measures of short selling activity, especially in the hard-to-borrow sample • Option-implied borrowing fees predict returns, and drive out the option-implied volatility measures in Cremers and Weinbaum (2010) and Xing et al. (2010)

34. Sorting on implied fee • After accounting for the borrowing fee, net returns are less than half of gross returns.

35. Returns adjusted for the borrowing fees • Implied fee predicts net-of-fee returns

36. Option order imbalance • Option investors buy puts and sell calls in the high utilization portfolio. I.e., they get short exposure through options. • Thus, option market-makers have to short stock to delta hedge for stocks in the high utilization portfolio.