Endogenous Short-Selling Constraints: Who Is Buying When Shorts Are Selling?

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Endogenous Short-Selling Constraints: Who Is Buying When Shorts Are Selling?

Jesse Blocher
Vanderbilt University – Finance

Chi Zhang
Temple University – Department of Finance

November 16, 2015


When short sellers are selling and a stock becomes expensive to borrow, the marginal stock buyer becomes the marginal stock lender. We show that the marginal buyer’s lending rate is vastly smaller than the average lending rate, thus dynamically restricting stock loan supply and endogenously contributing to short- sale constraints. Investors buy and do not lend due to a preference for positive skewness: short-sales constrained stocks also exhibit increased lottery-like return distributions and idiosyncratic skewness. On average, however, we show that long investors buy and do not lend in a defensive move supporting existing stock prices rather than speculatively so as to generate short-term overpricing.

Endogenous Short-Selling Constraints: Who Is Buying When Shorts Are Selling? – Introduction

“Investor 1: [Charles Schwab] want[s] me to lend my FRPT shares to them…I’M NOT GOING TO DO THIS BECAUSE I KNOW THEY WANT TO BORROW MY SHARES SO THEY CAN BE SHORTED…My advice is DO NOT LEND YOUR SHARES. It’s apparent that someone desperately wants to short FRPT, and is willing to pay for borrowing the shares he’ll need to short against. If we all resolve not to lend our shares, then the short(s) will run out of legitimate avenues for shorting.

Investor 2: This is a slap in the face…you are very smart to tell them what to do with their offer.”

Message board on www.investorvillage.com on Force Protection, Inc (FRPT), posted 3/28/2007 (capitalization in original)

Why does a stock become special – i.e. become expensive to borrow and thus hard to sell short? The laws of supply and demand dictate that if the price to borrow stock goes up then either the demand to borrow shares has risen, the supply of lendable shares has declined, or both. However, the market to borrow stock is intrinsically linked to the stock market (Blocher, Reed, and Van Wesep (2013)). This linkage creates a circularity: those who buy stock from short sellers become potential suppliers of stock loans in the equity lending market. If, for instance, as short sellers sell, each buyer repeatedly lends all of his shares, then the supply of lendable shares expands infinitely and the price to borrow (also called the ‘lending fee’ or ‘specialness’) will remain unchanged or perhaps fall. Thus, the simple answer to ‘why does a stock become special’ is that ultimately, enough buyers do not lend their shares. Why, then, do buyers not lend their shares?

Duffie (1996) studies this question in a static model of the treasury bill market. He models lending fees as a convenience yield that accrues to the holder of the security, such that not lending stock is akin to declining to accept a dividend. Since security loans are overnight, marked-to-market daily, and collateralized at 102% of their market value, they are virtually riskfree. Thus, he assumes that unlent shares are a result of ‘institutional constraints’ on a buyer — they would like to lend but are constrained from doing so. Since then, this ‘convenience yield plus institutional constraints’ metaphor has been the dominant paradigm in the understanding of stock loan supply (e.g. Duffie, Garleanu, and Pedersen (2002)).

However, the ‘convenience yield plus institutional constraints’ paradigm, while plausible, has never been documented empirically. And while it is reasonable to assume that lending fees for treasury bills represent a convenience yield, it is not obvious that the same metaphor applies to risky equity securities. Blocher, Reed, and Van Wesep (2013) show that linkages between the stock market and equity lending market mean that higher lending fees are informative about future stock returns. Higher lending fees are the result of demand by informed short sellers who believe that the stock is overpriced, thus higher lending fees predict lower expected returns. Evans, Ferreira, and Prado (2015) provide evidence from mutual funds that a strategy of selling high lending fee stock holdings dominates holding and lending them. This result challenges the ‘convenience yield plus institutional constraints’ paradigm. Why would anyone choose to hold and lend a stock on special? Even more puzzling is this question: who is buying when shorts are selling?


We address this question in two parts. First, we show that there is a significant reduction in marginal stock loan lending rate as a stock goes on special. This reduction manifests itself as a supply shortfall: supply fails to expand at the rate expected assuming constant equilibrium stock lending rates. Stated differently, as a stock becomes special, the marginal buyers of stock become the marginal lenders of stock in the equity lending market. Subsequently, these marginal buyers of special stock lend that stock at a significantly lower rate than the average owner. This reduced lending by the marginal buyer/lender acts as a restriction on supply, thus contributing to the rise in lending fees. Since basic economics dictates that the marginal buyer and marginal seller set prices, this result is intuitive.


Second, we investigate these marginal buyers of special stocks. We show that as stocks go on special, these same stocks become more ‘lottery-like’ in that they have higher positive skewness along with a negative expected return. This finding seemingly implicates retail investors, since Kumar (2009) shows that retail investors have a preference for lottery-like stocks. However, when we investigate net order flow between retail and institutional investors when a stock goes on special, we find mixed results. Shorter horizons show no net change in order flow, indicating that the retail/institutional split remains unchanged, though longer horizon results indicate a significant increase in net buying by retail investors. Thus, while it is likely that retail investors play an important role as marginal buyers of special stocks, we cannot rule out institutional investor participation as well, especially at shorter horizons.


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