Effects of short-sale restrictions

Effects of Short-Sale Restrictions* R. Corwin Grube, University of Kansas William L. Beedles, University of Kansas

A recently developed simplified portfolio construction scheme is used here to compare empirically the characteristics of optimal equity holdings with and without restrictions on the sale of borrowed securities. Among other results, unrestricted portfolios are found to have less overall risk, and more return per unit of portfolio risk, than positions restricted to long-only holdings.

The sale of borrowed securities plays a central role in both capital market theory and practice. For example, the original Sharpe [ 151, Lintner [ 111, Mossin [13] (hereafter SLM) development of the capital asset pricing model (hereafter CAPM) did not restrict short selling of either riskless or risky assets within the rubric of perfect markets. The modifications to the SLM version of the CAPM, offered by Brennan [3], Vasicek [ 161, and especially Black [ 11, were largely motivated by the inability of investors to freely short sell (issue) riskless securities. However, these extensions did not change the essential character of the SLM two-parameter pricing model. Recent work by Brito [4], Hutardo-Sanchez [9], Elton, Gruber, and Padburg [6], and Ross [ 141 emphasizes that substantial differences may exist in the return and risk characteristics of mean-variance efficient portfolios when the short sale of risky assets is prohibited. These results are especially noteworthy since legislation such as the Securities Act of 1933 and the Investment Company Act of 1941 severely restricts fiduciaries’ abilities to sell borrowed stock. Moreover, both the perfect market and restricted riskless asset pricing characterizations have been the subjects of extensive empirical scrutiny [2, 121. However, little attention has been given to the impacts of risky asset short-sale limitations. The present effort has thus been designed with the objectives of examining the impacts of short-sale restrictions on the characteristics of mean-variance optimal portfolios and estimating the cost to investors of the restrictions. These results may be of interest to other students of capital markets or to regulatory authorities for comparison with any perceived benefits of the restrictions. Address correspondence to: WilliamL. Beedles, School of Business, University of Kansas, Lawrence, KS 66045. JOURNAL OFBUSINESS

RESEARCH

9,231-236

0 Elsevier North Holland, Inc., 1981 52 Vanderbilt Ave., New York, NY 10017

(1981) 231 0148-2963/81/02231-06$2.50

232

K. Corwin Grube and William L. Beedles

A Review of a Simplified Selection Model Following the lead of Lintner [I 11, Elton, Gruber, and Padburg (hereafter EGP) [6] have formulated a simplified method for the selection of mean-variance optimal risky asset portfolios. EGP presume a market that has at least one asset with a return greater than the riskless rate, RF Likewise, each investor may freely borrow and lend at R, when attempting to maximize the ratio of excess portfolio return (RP - Rr) to portfolio standard deviation (up). For the paradigm to be investigated here, the presumptions are further made that investors possess heterogeneous expectations about the return and risk characteristics of individual securities but are willing to estimate all intersecurity return correlations to be equal to some constant (p). These are reasonable assumptions given the evidence presented in Elton and Gruber [5] and Elton, Gruber, and Urich [7]. Finally and importantly, EGP follow Lintner in assuming the investor earns the riskless rate on both margin deposits and the proceeds of any short sales. Within the described framework, EGP show that the optimal investment in asset i, Xi = Zi + Cj 1Zjl and the determination of Zi simply requires ranking all assets according to the ratio of excess return per unit of risk and, beginning with the asset with the largest ratio, computing

Zi =

Ri-Rf ai2(l

--PI

P 1-p

1 l-_p+kp

Ri-Rf.

_!_i

Ui

j=l

CJj

Zi may be viewed as an index of merit for security i. If Zi > 0, the asset is held long and the greater the magnitude of Zj, the larger the proportion of investor wealth committed to it. If Zi < 0, the security is sold short. Again, the greater the lZil value, the greater the proportion of investor wealth allocated to the short position in security i. Finally, for a given set of securities and p, all parameters of the equation are presumed known. Thus it is not incorrect to view excess security return (R; - Rf) and standard deviation of security return ( oi) as the determinants of the figure of merit of security i, Zi. For the case where no restrictions are placed on short sales, k is the total number of securities in the market and a long/zero/short position in a particular stock depends upon its Z being >O/= O/-CO. When short sales are not allowed, k is the number of securities already included, so that when an asset with a nonpositive Z is encountered, it and all other securities with smaller excess return to risk ratios are not held.

Short-Sale Restrictions

233

Methodologyand Results The optimal portfolio construction methodology sketched above has been employed here, using presumed pairwise correlations of 0.2 and 0.4, which bracket the values observed in Elton and Gruber [5] and Elton, Gruber, and Urich [7]. The monthly equity returns for 400 randomly selected firms with complete 1952-1976 data were drawn from the University of Chicago’s Center for Research in Security Prices (CRSP) data base. The riskless rate has been estimated with yields on 30-day-to-maturity Treasury bills. For each firm selected, the mean and standard deviation of the excess monthly returns (Ri - Rf) were used as inputs to the EGP portfolio construction scheme. The results for the 300-month data are reported in Table 1. Six characteristics of the data in Table 1 are worthy of emphasis. 1. The return of the long-only risky asset portfolio is substantially larger than that of the unrestricted portfolio. Thus, this construction scheme positions the long-only investor heavily into equities with dramatically large returns. 2. With short sales allowed, portfolio risk is much smaller than under the restricted regime. This somewhat surprising result supports a conclusion that, used in an optimal manner, the short-sale mechanism serves primarily as a diversification agent rather than a return agent. Indeed, an investigation of the underlying data revealed short positions in several high-return stocks. 3. Overall, the risk-adjusted performance [(R, - Rf)/o,] for the unconstrained position was superior to that of the long-only portfolio. In other words, the marked increase in return from the long-only position was insufficient to offset the additional portfolio risk relative to the unrestricted risky asset portfolio. 4. When no constraints are faced, the investor holds approximately the same number of securities long and short. However, only a few assets are required to reach the optimal long-only position. Moreover, this latter result is noteworthy since roughly the same conclusion was reached by Evans and Archer [8] when investigating the number of randomly selected long purchases necessary to eliminate essentially all diversifiable risk. 5. For the most part, the results are insensitive to the presumed average pairwise correlation, the exception being the number of securities held in the long-only portfolio. When assets are presumed to be “more similar” (i.e., when p is increased), fewer assets are required to obtain the available diversification benefits associated with combining long positions.

R. Corwin Grube and William L. Beedles

234

Table 1: Characteristics

of Optimal

Risky Asset Portfolios Short Sales

p = 0.2

Allowed

Disallowed

Average monthly return Standard deviation Excess return per unit risk Securities held long

.0071 .0098 .4101 219

.0167 .0440 .3096 29

p = 0.4 Average monthly return Standard deviation Excess return per unit risk Securities held long

.0068 .0099 .3781 210

.0167 .0442 .3077 14

6. The annual percentage cost to investors of restrictions on selling borrowed stock can be estimated for any specified risk level. For example, presume borrowing and lending at Rf in order to bring both optimal portfolios to the risk level of the market. (The estimated standard deviation of monthly market returns was 3.95%). At that risk level the unrestricted portfolio’s return exceeds that of the long-only holding by about 28 basis points per month [.378 1 (.0395) - .3077 (.0395)], so the cost is about 3.4% annually. Although not tabulated here in the interest of brevity, four other generalizations are supported by the results of investigations of the five contiguous 5-yr subperiods contained in the 1952-1976 study period. 7. The return and standard deviation for the unrestricted portfolio are less than the return and standard deviation for the restricted portfolio in each of the five subperiods. The risk-adjusted performance of the unrestricted portfolio exceeds that of the long-only portfolio in each of the five subperiods. 8. In both the case of the unrestricted and long-only portfolios, the numbers of securities held long and the magnitudes of standard deviations of portfolio returns remain fairly constant and approximately equal to the 25-yr results reported in Table 1. 9. Both the unrestricted and long-only portfolios exhibited subperiod risk-adjusted returns typically greater than the 25-yr results reported in Table 1. In other words, the composition of optimal risky asset portfolios changed substantially over time.

Short-Sale Restrictions

235

10. The annual percentage cost of the restriction on short sales is often more substantial during the subperiods. When the risk-free lending and borrowing mechanism is employed to bring the portfolios’ risk levels to equivalence with the market, the average subperiod cost of the short-sale restriction is nearly 25% annually, ranging from 0.6% (1957-1961) to 42.3% (1962-1966). Summary

and Conclusions

Whatever the original justification for the enabling legislation, the ability to sell borrowed stock is strictly restricted by statute for many groups of investors. The intent of this essay is to describe the comparative characteristics of unrestricted and long-only optimal portfolios and the risk-adjusted cost of the short-sale restrictions. Under the paradigm adopted here (heterogeneous expectations and unlimited borrowing and lending of riskless assets), the risky asset short-sale restriction was observed to alter substantially the return and risk characteristics of optimal risky asset portfolios. The investor who is allowed to short sell will hold a risky asset portfolio with lower measured risk and return than the restricted investor. Importantly, the latter may expect a lower return per unit of portfolio risk. Perhaps the most striking difference between the regimes is the number of securities held. The unrestricted investor positions either long or short in every asset, although many of the holdings are small in magnitude. The long-only investor, on the other hand, buys but a few securities-those with exceptional performance per unit of risk. This result is consistent in spirit both with the long-standing evidence that a few (10 to 20) randomly selected securities closely mirror the optimal (before transaction charges) naive portfolio and the recent work of Levy [lo], who focused on changes in optimal behavior when transactions charges were explicitly included in the analysis. A final and crucial observation concerns the annual percentage cost for the short-sale restriction. Over the 1952 to 1976 period, the annual return of the unrestricted optimal risky asset portfolio, adjusted to the risk level of the market, was 3.4% greater than the long-only portfolio. During 5yr subperiods, the average of this cost was nearly 25%. This research was supported in part by the University of Kansas General Research Allocation No. 3320-0038. Robert C. Klemkosky provided helpful comments on an earlier draft of this paper.

236

R. Corwin

Grube

and William L. Beedles

References Black, Fisher, Capital Market 45 (July 1972): 444-454.

2.

Black, Fisher, Jensen, Michael, and Scholes, Myron, The Capital Asset Pricing Model: Some Empirical Tests, in Michael Jensen, ed., Studies in the Theory of CapitalMarkets, Praeger, New York, pp. 79-121.

3.

Brennan, Michael J., Capital Market Equilibrium Lending Rates, J. Fin. Quant. An~ly. 6 (December

4.

Brito, Ney O., Portfolio Selection in an Economy Sale Restrictions, J. Fin. 33 (May 1978): 589602.

5.

Elton, Edwin J., and Gruber, Martin J., Estimating the Dependent Structure of Share Prices-Implications for Portfolio Selection, J. Fin. 27 (December 1973): 1203-1233.

6.

Elton, Edwin J., Gruber, Martin J., and Padburg, Optimal Portfolio Selection, J. Fin. 31 (December

1.

Elton, Edwin 33 (December

8.

Evans, John, and Archer, Stephen H., Diversification persion: An Empirical Analysis, J. Fin. 23 (December

9.

Hutardo-Sanchez, Luis, Short Interest: Its Influence as a Stabilizer turns, J. Fin. Quant. Anal. 13 (December 1978): 965-985.

J., Gruber, Martin 1978): 1375-1384.

Equilibrium

with

Restricted

J. Bus.

1.

Borrowing,

with Divergent Borrowing 1971): 1197-1205. with Marketability

and

and Short

Manfred W., Simple Criteria 1976): 1341-1357.

J., and Urich, Thomas

for

J., Are Betas Best?, J. Fin. and the Reduction 1968): 761-767.

of Dis-

of Stock

Re-

10.

Levy, Haim, Equilibrium Securities in the Portfolio,

in an Imperfect Market: A Constraint on the Number Am. &on. Rev. 68 (September 1978): 643-665.

11.

Lintner, John, Secutity Prices, Risk, and Maximal Fin. 20 (December 1965): 587-616.

12.

Miller, Merton, and Scholes, Myron, Rates of Return in Relation to Risk: A ReExamination of Some Recent Findings, in Michael Jensen, ed., Studies in the Theory of CapitalMarkets, Praeger, New York, 1972, pp. 47-78.

13.

Mossin, Jan, Equilibrium 1966): 768-783.

14.

Ross, Stephen A., The Capital Asset Pricing Model (CAPM), tions and Related Issues, J. Fin. 32 (March 1977): 177-183.

Short

15.

Sharpe, William F., Capital Asset Prices: Conditions of Risk, J. Fin. 19 (September

Equilibruim

16.

Vasicek, Oldrich A., Capital Market Equilibrium with No Riskless unpublished manuscript (March 1971), Wells Fargo Bank.

in a Capital

Gains from

Asset Market,

Diversification,

Econometrica

A Theory of Market 1964): 425-442.

of J.

34 (October

Sale Restricunder

Borrowing,