Margin Requirements and the Security Market Line

• Author: PETRI JYLHÄ
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/jofi.12616
• Published date: 01 June 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 3 •JUNE 2018

Margin Requirements and the Security

Market Line

PETRI JYLH ¨

A∗

ABSTRACT

Between 1934 and 1974, the Federal Reserve changed the initial margin requirement

for the U.S. stock market 22 times. I use this variation to show that investors’ leverage

constraints affect the pricing of risk. Consistent with earlier theoretical predictions,

I find that tighter leverage constraints result in a flatter relation between betas and

expected returns. My results provide strong empirical support for the idea that the

constraints investors face may help explain the empirical failure of the capital asset

pricing model.

ONE OF THE FIRST AND MOST persistent anomalous findings in finance is that

the return difference between high-beta and low-beta stocks is significantly

smaller than predicted by the capital asset pricing model (CAPM) of Sharpe

(1964), Lintner (1965), and Mossin (1966). An early explanation for the em-

pirical flatness of the security market line, originally documented by Black,

Jensen, and Scholes (1972), is given by Black (1972), who shows that investors’

inability to borrow at the risk-free rate results in a lower cross-sectional price

of risk than in the unconstrained CAPM. Black’s version of the CAPM is un-

realistic, however, as in the real world investors are able to borrow, just not in

infinite amounts as assumed in the CAPM. This idea is further developed by

Frazzini and Pedersen (2014), who present a model in which investors face a

limit on their leverage. In their model, the slope of the security market line,

that is, the return difference between high-beta and low-beta stocks, depends

on the tightness of investors’ leverage constraints: a tighter leverage constraint

results in a flatter security market line.

Despite the theoretical and intuitive appeal, convincing empirical evidence

of leverage constraints affecting the security market line is lacking. This is due

in part to the difficulty of identifying an appropriate measure of the tightness

∗Petri Jylh¨

a is with Aalto University School of Business. I thank Kenneth Singleton (the Ed-

itor), two anonymous referees, St´

ephane Chr´

etien, Stefanos Delikouras, Darrell Duffie, Samuli

Kn¨

upfer, Ralph Koijen, ˇ

Luboˇ

sP

´

astor, Lasse Pedersen, Joshua Pollet, Oleg Rytchkov, Mungo Wil-

son, and participants at the American Economic Association 2015, European Summer Symposium

in Financial Markets 2016, Financial Intermediation Research Society 2014, the Western Finance

Association 2016 meetings, and seminar participants at Aalto University, Copenhagen Business

School, Imperial College London, Luxembourg School of Finance, and Manchester Business School

for helpful comments. I have read the Journal of Finance’s disclosure policy and have no conflicts

of interest to disclose.

DOI: 10.1111/jofi.12616

1281

1282 The Journal of Finance R

of these constraints. A commonly used measure in the funding constraints

literature is the spread between Eurodollar and Treasury bill rates, also known

as the TED spread. However, such an interest rate spread is endogenous to

investors’ portfolio choice problem and does not directly measure the constraint

on maximum leverage, but rather can be seen as a proxy for the cost of that

leverage. Also, the empirical evidence in Cohen, Polk, and Vuolteenaho (2005)

and Frazzini and Pedersen (2014) shows that a higher interest rate spread—

typically used in the literature to indicate a tighter funding constraint—does

not result in a flatter security market line as the theory would predict.

In this paper,I use a direct measure of investors’ leverage constraints and find

strong and robust empirical evidence in support of the theoretical prediction

that tighter leverage constraints result in a flatter security market line. My

measure of leverage constraints is based on the active management of the

minimum initial margin requirement by the Federal Reserve. Pursuant to the

Securities Exchange Act of 1934, the Federal Reserve, in its Regulation T, sets

the minimum level of initial margin required when purchasing common stock

on credit on U.S. stock exchanges.1Between October 1934 and January 1974,

this margin requirement was changed 22 times and ranged between 40% and

100%. This frequent and sizable variation in a federally mandated leverage

constraint provides an excellent setting for testing whether such constraints

affect asset prices.

The main results of this paper are as follows. First, I show that the margin

requirement significantly affects investors’ leverage but is largely uncorrelated

with other prevailing and future financial market and macroeconomic condi-

tions. These findings establish that the federally set margin requirement is a

useful measure of investors’ leverage constraints and not merely a proxy for

the overall state of the economy.

Second, and more importantly, I find that the slope of the security mar-

ket line is negatively related to the prevailing margin requirement. Simi-

larly, the intercept of the beta-return relation is positively related to the

margin requirement. These findings are in line with the theoretical predic-

tion of Black (1972) and Frazzini and Pedersen (2014). Figure 1provides a

simple illustration of these main results. Specifically, it separately plots the

security market lines for periods of low, medium, and high initial margin re-

quirements. The difference between the security market lines for low- and

high-margin requirements is striking. When the margin requirement is low

(between 40% and 55%), the empirical security market line runs very near its

CAPM prediction. In contrast, during periods of a high (75% to 100%) initial

margin requirement, the empirical security market line differs significantly

from that predicted by the CAPM, and actually has a negative slope. This

figure thus provides a simple but powerful summary of the main result of this

paper.

1The initial margin requirement dictates the minimum value of collateral needed when pur-

chasing stock. For example, a 40% initial margin requirement means that an investor can borrow

up to 60% of the cost of a new stock purchase.

Margin Requirements and the Security Market Line 1283

●

●●

●

●

●●

●

●●

●

0.6 0.8 1.0 1.2 1.4 1.6

−5 0 5 10 15 20

40% ≤initial margin < 55%

Post−formation beta

Average return

ri

e=3.3+12βi

rM

e=15.4

●

●

●

●

●

●

●

●

●●

0.6 0.8 1.0 1.2 1.4 1.6

−5 0510 15 20

55% ≤initial margin < 75%

Post−formation beta

Average return

ri

e=5.9−0.9βi

rM

e=4.7

●

●

●

●

●●

●

●

●

●

0.6 0.8 1.0 1.2 1.4 1.6

−5 0 5 10 15 20

75% ≤initial margin ≤100%

Post−formation beta

Average return

ri

e=14.8−11βi

rM

e=3.3

●

●●●

●

●

●

●

●●

0.6 0.8 1.0 1.2 1.4 1.6

−5 0 5 10 15 20

Full sample

Post−formation beta

Average return

ri

e=6.8+2.2βi

rM

e=8.7

Figure 1. Initial marginrequirement and securitymarket line. This graph plots the empir-

ical relation between beta and average excess return in subsamples with different initial margin

requirements. The test assets are 10 beta-sorted value-weighted portfolios. The solid line gives the

theoretical security market line predicted by the CAPM, and the dashed line gives the empirical

security market line. The top left panel includes the 197 months for which the initial margin re-

quirement is between 40% and 55%, the top right panel includes months for which the requirement

is between 55% and 75% (183 months), and the bottom left panel includes months for which the

requirement is above 75% (112 months). The bottom right panel presents the security market lines

for the full sample of 492 months from 10/1934 to 9/1975.

Third, I show that the main result above is highly robust to using different

test assets, control variables, and estimation techniques. In all specifications,

the effects of leverage constraints on the security market line take the pre-

dicted sign and are statistically significant. In the most interesting specifica-

tion, which is closely related to the analysis of Frazzini and Pedersen (2014),

I include the difference between investors’ borrowing and lending rates—a