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Does portfolio margining make borrowing more attractive?
International Review of Financial Analysis 43 (2016) 128–134
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International Review of Financial Analysis
Does portfolio margining make borrowing more attractive? Dmytro Matsypura ⁎, Laurent L. Pauwels 1 The University of Sydney, New South Wales 2006, Australia
a r t i c l e
i n f o
Article history: Received 17 April 2015 Received in revised form 13 November 2015 Accepted 19 November 2015 Available online 27 November 2015 Keywords: Margin debt Margin requirements Portfolio margining Financial regulations Structural change U.S. securities markets
a b s t r a c t This paper investigates the effects of a change in the margin rules of the U.S. financial securities markets. These rules determine how much investors can borrow to leverage their investments. Since the 1929 stock market crash, margin loans have been tightly regulated by the Securities and Exchange Act Regulation T. Between 2005 and 2008, the Securities and Exchange Commission modified these margin rules because they were perceived as not adequately reflecting investment risk. The amended rules have made it more attractive for investors to borrow by opening new margin accounts and diversifying their investment positions. This paper tests the hypothesis that the change in the margin rules has increased margin debt across the U.S. securities markets. It provides statistical evidence that this structural change can be dated to the amendments in the rules. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Investors who purchase securities can borrow part of the purchase price from financial institutions, such as brokerage firms, by opening margin accounts. They are required to deposit a portion of the purchase price, the margin, which represents the initial equity in the accounts. The portion that must be deposited is called the initial margin requirement and is calculated by following margin rules that are regulated by the U.S. Federal Reserve Board. The margin debt held by investors with their financial institutions is secured by the purchased securities. Securities exchanges, such as the New York Stock Exchange (NYSE), the Chicago Board Options Exchange (CBOE) and the National Association of Securities Dealers (NASD), can set higher initial margin requirements at their discretion. Exchanges also establish a maintenance margin requirement that determines the amount necessary to be kept as collateral in the margin account for the duration of an investment. Whenever the margin is below the requirement, the broker issues a margin call. Investors typically use margin accounts to leverage their investments and increase their purchasing power. Since the 1929 stock market crash, the U.S. Federal Reserve Board has been given authority to regulate margin loans with the Securities and Exchange Act Regulation T of 1934. One of the objectives of this act is the “control of monetary aggregates” (Climan, 1978). The U.S. Federal Reserve Board has achieved this by establishing an initial margin requirement for margin loans. This requirement sets a minimum ⁎ Corresponding author at: The University of Sydney, Room 4089, Abercrombie Building H70, NSW 2006, Australia. Tel.: +61 2 9359 3945; fax: +61 2 9351 6409. E-mail address: [email protected] (D. Matsypura). 1 The order of the authors' names is alphabetical.
http://dx.doi.org/10.1016/j.irfa.2015.11.006 1057-5219/© 2015 Elsevier Inc. All rights reserved.
equity position on the date of a credit-financed security transaction. The initial margin requirement for listed stocks has changed 22 times between 1934 and 1974 and has been as high as 100% and as low as 40%. Since 1974, however, the initial margin requirement has been fixed at 50% of the current market value of the stock. During the 1980s and 1990s, margin requirements were often perceived as too high and not accurately representative of investment risks. To more accurately represent risk, the Option Clearing Corporation (OCC) developed a new portfolio margining methodology whereby portfolio margin requirements were calculated using the Theoretical Intermarket Margining System (TIMS).2 TIMS was first implemented in 1997 to calculate the net capital requirements for brokers' proprietary portfolios of listed options (SEC, 1997; GAO, 1998). However, this margining methodology was not used to margin customer accounts prior to 2005. After two proposals from NYSE, the Securities and Exchange Commission (SEC) approved the use of the portfolio margining methodology under a temporary pilot programme that began in 2005 and ended in 2008 (SEC, 2002; SEC, 2004; SEC, 2005b). This paper hypothesises that the amendments to the margin rules introduced between 2005 and 2008 stimulated investor borrowing due to the lower margin requirements; as a result, there was an increase in margin debt. The lower initial and maintenance margin requirements made it more attractive for new investors to open margin accounts and for existing investors to diversify their investment positions. This change should be particularly apparent during the second phase of the pilot programme, as this phase included a wider range of securities.
2 It is now known as the System for Theoretical Analysis and Numerical Simulations (STANS).
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The change in investment behaviour should be observable in the monthly margin debt series for the U.S. securities markets over time, after adjustments for market sentiments. This is a monthly series and constitutes the only data on margin debt publicly available. Fig. 1 depicts the margin debt series for the U.S. securities markets from January 1997 to February 2014. It is worth noting that prior to the change in margin rules, investors already displayed bullish borrowing behaviour, as margin debt grew by 72% over the three years between September 2002 and July 2005. Between July 2006 and its peak in July 2007, however, the upward trend in margin debt accelerated by 63% in a single year. The existing literature on margin requirements has mostly been published prior to 2005. The earliest work on the topic is by (Moore, 1966) and studies the influence of margin requirements on investors' equity ratios. Later research conducted on margin requirements has primarily focused on their impact on stock prices (Grube, Joy, & Panton, 1979; Luckett, 1982) and stock price volatility (Hardouvelis, 1990; Hardouvelis & Peristiani, 1992; Salinger, 1990; Hardouvelis & Theodossiou, 2002). It is apparent from the literature that margin requirements can have a direct influence on the size of margin loans. This theoretical finding is empirically corroborated by Hsieh and Miller (1990), who found a negative relationship between margin requirements and the amount of margin credit outstanding, i.e., margin debt. This leads to the conclusion that initial margin requirements might serve as a mild automatic stabiliser, limiting margin debt more during periods of bull markets than during bear markets (Fortune, 2000). Section 2 discusses history and practice of margin requirements. Section 3 describes the empirical model and the data. Section 4 empirically investigates whether this change in margin rules can be detected and dated in the margin debt series. A common way to test for such a change is to use structural change tests. Lastly, Section 5 provides concluding remarks.
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Regulation T applies to broker-dealers, Regulation U applies to banks and other lenders, and Regulation X applies to margin loans not explicitly covered by the other regulations. These requirements set a minimum equity position on the date of a loan-based transaction (Fortune, 2000). In 1933 NYSE established its own requirement that member firms' customers could borrow no more than 50% of the value of securities held. These requirements apply to the existing holdings of securities and therefore are maintenance margin requirements. At the moment, minimal equity standards exist at all registered exchanges: for example, they are set under Rule 431 at NYSE, Rule 12 at CBOE, and Rule 2520 at NASD. Until 2005, these rules stated that broker–dealers must require customers to have a maintenance margin equal to at least 25% of a long position in stocks and 30% of a short position. Brokers typically required a higher ratio, on the order of 30 to 35% for long positions (Fortune, 2000). The rules also set requirements for more complex transactions, such as options, option spreads, straddles, and boxes. For a good summary of margin requirements under Regulation T and NYSE Rule 431 the reader is referred to Table 1 in Fortune (2000). On May 13, 2002, NYSE proposed to amend its rules to allow member organisations to use a portfolio margin methodology for certain customer accounts. In 2005, SEC approved the proposal as a pilot programme available to member organisations on a voluntary basis (SEC, 2005a). The pilot programme was implemented in three phases. Phase I began on July 14, 2005 and permitted the use of the portfolio margining methodology only for a limited number of portfolios of listed broad-based securities index options, warrants, futures, futures options and related exchange-traded funds. Phase II began on July 11, 2006 and included listed stock options and securities futures (SEC, 2006a). Phase III began on April 2, 2007 and included equities, equity options, unlisted derivatives and narrow-based index futures. Unlike Phase I, the changes in margin requirements in Phases II and III were more significant because they targeted a much wider array of securities. Furthermore, Phase III was widely advertised in the media after its approval on December 12, 2006 (SEC, 2006b), more than 3 months before it would become effective. By July 2008, SEC ended the pilot programme, thus making portfolio margining permanent and leading to the amendment of the margin rules of the Financial Industry Regulatory Authority (FINRA), CBOE and NYSE.
2. History and practice of margin requirement After the 1929 stock market crash, the U.S. Federal Reserve Board established initial margin requirements under Regulations T, U and X. 550
2,400 2,200
450
2,000
400
1,800
350
1,600 1,400
300
1,200 250 1,000
S&P 500 index
Margin debt in billions of $US
500
200 800 150 600 100
400
50
200
01-2014
07-2008
07-2006 03-2007
07-2005
01-1997
0
I II III pilot programme
0
Fig. 1. Aggregate margin debt in billions of dollars (—) and S&P 500 index (− −) in the period from January 1997 through February 2014. Data from www.finra.org and finance.yahoo.com.
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options, i.e., the securities that were part of Phases II and III of the pilot programme.
Table 1 Augmented Dickey–Fuller Tests — p-values. t-statistics Margin debt series|models
Constant
Aggregate U.S. securities market 0.6372 NYSE 0.9332
Lags
Constant & trend Lags
12 12
0.0649 0.0394
12 12
F-statistics Margin debt series|hypotheses No constant & unit root No trend & unit root Aggregate U.S. securities market 0.2204 0.0070 NYSE 0.2420 0.0025 Notes: This table reports the Dickey and Fuller (1979) tests for the null of a unit root against the stationary alternative. There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. When the model tested includes a constant (μ) and a trend (t), it is written 12
3. Data The data used in this paper are as follows. The size of the margin loan qt is measured by the aggregate margin debt collected from FINRA website for the entire U.S. securities market.4 The data are available monthly from January 1997 until February 2014. There is also data for NYSE, which represents a large portion of the aggregate U.S. securities market margin debt.5 The amount borrowed depends on the investor's preferences, attitude towards risk and other considerations. However, the investor is likely to change the amount borrowed depending on the market expectations. Hence, the variable of interest becomes
as yt ¼ μ þ βt þ α yt−1 þ ∑c j yt−i þ εt . The p-values are computed from the ordinary j¼1
Dickey–Fuller distribution.
The original margin requirements under Regulation T are termed strategy-based whilst margin requirements produced by the portfolio margin methodology are termed portfolio margin requirements by SEC. The portfolio margin requirements are substantially lower than their strategy-based counterparts. Under the strategy-based methodology the daily margin calculation initially requires the determination of an allowable decomposition of the account into hedging strategies (or offsets). It then requires the calculation of the margin requirements for each offset in the decomposition as a current (or maximum, in some cases) loss associated with that offset. The sum of these losses constitutes the required margin. Under the portfolio methodology, implemented as STANS by OCC, the daily margin calculation for each account is based on full portfolio Monte Carlo simulations. OCC utilises a proprietary derivation of the Cox–Ross–Rubinstein binomial option pricing model to calculate projected liquidating prices. Projected prices are calculated based upon the closing underlying asset price for each day plus and minus price moves at ten equidistant data points over a broad range of market movement. The percentages of the daily price move for an underlying price are + 6 to − 8% for high capitalisation broad-based securities indexes, +/ − 10% for non-high capitalisation broad-based securities indexes, and +/ − 15% for equity products and sector indexes. Prices for all instruments are projected, and the resulting profits and losses of the portfolio are summed to estimate the aggregate gain or loss at each of the ten underlying price points. Within a class group (all products with the same underlying instrument), 100% of a position's gain at any one valuation point is allowed to offset another position's loss at the same valuation point. The largest aggregated projected loss over the range of the ten potential market moves for each class and product group, in the case of the offset-eligible classes, is the margin requirement for the portfolio (OCC, 2008). It should be noted that under the amended rules, margining can be performed with either methodology. In summary, while strategy-based margining generally limits leverage on equity to 2:1, with portfolio margining, leverage of 6:1 or more is possible.3 In a 2006 promotional communication to its clients, CBOE provided several numerical examples that demonstrated the potential benefits of the new approach to margining. Two of these examples are reproduced in Fig. 2. In all of the examples provided by CBOE, including the two reproduced in this paper, portfolio margining produced lower margin requirements; in some cases, more than 40 times lower. The difference is particularly noticeable for portfolios containing
yt ¼ logðqt =pt Þ where the asset price pt is measured with the S&P 500 price index, which is collected from Yahoo! Finance.6 The S&P 500 price index captures the overall market trend, accounting for market sentiments and potential market exuberances such as the 2000 dot com bubble and the 2008 global financial crisis. This is an important consideration when testing whether the margin debt changed as a result of the new margin rules. The fluctuations of yt shown in Figs. 3 and 4. For example, during the dot com bubble, the amount borrowed by investors rose and fell back to its trend. In contrast, the change in margin rules seems to have caused a shift in the level of yt and a possible change in the slope of the trend of yt, as suggested in Figs. 3 and 4. These observations are tested formally in the next section. Consider the following empirical model for yt: yt ¼ μ þ βt þ α yt−1 þ
Coffman, Matsypura, and Timkovsky (2010), Matsypura and Timkovsky (2012), and Matsypura and Timkovsky (2013) show that strategy-based margining, when coupled with complex option spreads (SEC, 2003) produces much lower margin requirements and a more accurate estimation of risk.
εt i:i:d 0; σ 2
ð1Þ
i¼1
for the sample t ∈ [1, T ], where α is the AR(1) parameter, μ is the constant (or drift) and t is the trend. As a starting point, the unit root hypothesis is tested: H 0 : α ¼ 1 and H 1 : α b 1 for all t; as it is often a practice in empirical work involving financial time series. Testing this hypothesis is also necessary to determine the appropriate structural change tests. The unit root hypothesis is tested using two different specifications of model (1) using Augmented Dickey and Fuller (1979) tests (ADF). In the first ADF test, yt is a random walk under the null hypothesis, while under the alternative it is a stationary autoregressive process. In the second ADF test, yt is a random walk with a drift under the null and a trend-stationary process under the alternative. The lag length in each model under scrutiny is chosen to be 12, as is often done with monthly data series in empirical studies. Note that in order to confirm the correctness of the chosen lag length, a data-dependent general to specific recursive method proposed by Ng and Perron (2001) is also applied. The results are presented in the Appendix A. The results and conclusion from this data-dependent approach confirm those presented below. The results of the ADF tests are shown in Table 1.7 When including a constant term in the estimated equation, the ADF tests do not reject the 4
3
k X ci Δyt−i þ εt ;
www.finra.org. www.nyxdata.com. http://finance.yahoo.com. 7 The ADF tests have been computed with R using the CADFtests package constructed by Lupi (2009). 5 6
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Fig. 2. Numerical examples provided by the Chicago Board Options Exchange to its clients in 2006.
null hypothesis, which provides evidence that both the aggregate and NYSE margin debt series are random walks. However, when including both a constant and a deterministic trend, the results indicate that both adjusted margin debt series are stationary around a trend. The statistical evidence appears to be stronger for NYSE than for the aggregate series. It is worth pointing out that the estimates of the autoregressive coefficient in the model with a constant and a trend are 0.87 and 0.84 for the aggregate and NYSE series, respectively. Similarly, the F-statistics clearly reject the joint hypothesis of a random walk with a drift in favour of trend-stationary processes for both series at the 1% level of significance. These F-test results do not hold when only including a constant term in the estimated model. In that case, the evidence supports the hypothesis of a random walk. This ambiguity in the ADF t- and F-test results could originate from the presence of a structural change due to the amendments in the margin rules, as conjectured in this paper. This conjecture can be incorporated
in the ADF tests by re-specifying the alternative hypothesis. On the other hand, if the series are indeed stationary around a trend, then the change in the margin rules can be tested with the QLR test of Andrews (1993). These possibilities are investigated in turn. 4. Evidence It is well known from the seminal work of Perron (1989) that the standard unit root tests such as the ADF tests cannot reject the null hypothesis if the data-generating process of the series under scrutiny is stationary around a trend with a break point. Zivot and Andrews (1992) proposes to test for a unit root against the alternative hypothesis of a trend-stationary process with one break point in the level and/or in the slope of the trend. Zivot and Andrews (1992) is essentially an extension of Perron (1989) with the added benefit that the null of a unit root is tested over all possible break dates. In contrast, Perron (1989)
5.7 5.6 5.5 5.4 5.3 5.2 5.1 5 4.9
06-2013
01-2012
09-2010
04-2009
12-2007
08-2006
03-2005
11-2003
06-2002
02-2001
09-1999
05-1998
01-1997
4.8
Fig. 3. Log-transform of the aggregate margin debt adjusted by the S&P 500 index in the period from January 1997 through February 2014. Data from www.finra.org and finance.yahoo. com.
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5.6 5.5 5.4 5.3 5.2 5.1 5 4.9 4.8
06-2013
01-2012
09-2010
04-2009
12-2007
08-2006
03-2005
11-2003
06-2002
02-2001
09-1999
05-1998
01-1997
4.7
Fig. 4. Log-transform of NYSE margin debt adjusted by the S&P 500 index in the period from January 1997 through February 2014. Data from www.nyxdata.com and finance.yahoo.com.
requires the assumption of a known break point. The reason for using tests that estimate the position of the break is twofold. First, the potential location of the break corresponding to the change in the rules is within a 3-year interval, from July 2005 to July 2008, and second, these tests tend to have higher power. Zivot and Andrews (1992) considers the Innovational Outlier (IO) model in which the more general regression equation to test the null of a unit root is yt ¼ μ þ θDU t ðλÞ þ βt þ γDT t ðλÞ þ α yt−1 þ
k X ci Δyt−i þ εt
ð2Þ
i¼1
for t = 1 , … , T, λ ∈ [0, 1] where DUt(λ) = 1 if t N λT and 0 otherwise; DTt(λ) = t − λT if t N λT and 0 otherwise.8 This is often named model C, using the nomenclature established in Perron (1989). The two other IO types of regression equations are model A, where it is assumed that γ = 0, and model B, where θ = 0. The IO models are relevant in the context of this paper because they model structural change as a gradual process. The test is the minimal value of the t-statistic testing α =1 over all possible break dates in a given sample. This minimal value is denoted as t α⁎ =infλ∈[0,1]tα(λ) with tα(λ) is the t-statistic when the break date is ⌊ λT⌋, and ⌊⋅⌋ denotes the largest integer that is smaller than the argument. The estimated λ determines the break date (i.e. T break ¼ λT ) which coincides with the minimal value of the t-statistic, t α⁎. The unit root hypothesis is rejected for both the aggregate and NYSE series in favour of trend stationarity with a one-time break in both the intercept and the trend. Although all models (A, B and C) are reported for completeness in Table 2, model C is the most appropriate model using a general-to-specific approach.9,10 8 Note that the results of Zivot and Andrews (1992) are valid without trimming at the end points, as shown in Perron (1997). 9 The lag length k is chosen to be 12, as with the ADF tests. It turns out that when the lag length is selected using Ng and Perron (2001), the selected lag length is also 12. 10 Zivot and Andrews (1992) tests have been computed with R using the urca package.
Model C implies that there are two significant changes taking place in both margin debt series. The positive signs of θ (.072 and .067) indicate that there is an increase in the level of margin debt at the time of the break. This change is statistically significant as shown by the t-statistic of the constant break dummy. Moreover, the negative signs of γ (− . 0008 and − . 0006) imply a decrease in the rate of growth of margin debt. This is again statistically significant. The estimates of the autoregressive coefficient, α, are .686 and .672 for the aggregate and NYSE series, respectively, which is lower than in their earlier ADF specification. Interestingly, in both cases, the constant break dummy is more significant than the slope break dummy, especially for NYSE, where the slope break dummy is significant at the 5% level whereas the constant break dummy is significant at the 0.1% level. As a side remark, when conducting the tests with regression model B, the null of a random walk cannot be rejected against a stationary process with a break in trend, whereas the null is rejected against a stationary process with a break in the intercept. This is consistent with the paper's hypothesis that the change in margin rules increased margin debt in the U.S. securities market. The estimated date of the structural change in margin debt corresponds to Phase II of the pilot programme. For both measures of margin debt, the break date is estimated to be in October 2006. It is interesting to notice that none of the estimated dates point to Phase I. This is consistent with expectations, as very few market instruments (only broadbased indices and exchange-traded funds derivatives) were included in that early Phase, and it was not anticipated to have much impact. Both the statistical test results and the estimated dates of structural change in the margin debt support this paper's hypothesis. Next, let us return to the possibility that both adjusted margin debt series are indeed trend-stationary processes, as discussed earlier. If this is the case, then the change in margin rules can be tested using “conventional” tests for structural change, such as with the well-known Chow (1960) test. However, because the exact timing of the break induced by the change in margin rules is unknown, the Quandt Likelihood
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Table 2 Zivot and Andrews (1992) — t-statistics. Margin debt series
t-stat.
T^ break
k
μ^
^θ
^ β
^ γ
^ α
Model A (break in intercept) Agg. U.S. market
−4.62
Oct-2006
12
−4.88
Oct-2006
12
.052 (3.16) .052 (3.30)
.0005 (3.06) .0006 (3.39)
–
NYSE
1.20 (4.65) 1.34 (4.90)
.757 (14.4) .726 (12.9)
Model B (break in trend) Agg. U.S. market
−3.97
–
12
–
NYSE
−3.91
–
12
.971 (3.99) .934 (3.93)
.0009 (3.67) .0008 (3.57)
−.0008 (−2.11) −.0005 (−1.66)
.798 (15.7) .804 (16.1)
Model C (break in intercept & trend) Agg. U.S. market −5.53
Oct-2006
12
−5.53
Oct-2006
12
1.53 (5.54) 1.59 (5.53)
.072 (4.14) .067 (4.02)
.001 (4.30) .0009 (4.24)
−.0008 (−2.95) −.0006 (−2.50)
0.686 (12.1) .672 (11.3)
NYSE
–
–
Asymptotic critical values Significance level
Model A
Model B
Model C
1% 5% 10%
−5.34 −4.80 −4.58
−4.93 −4.42 −4.11
−5.57 −5.08 −4.82
Notes: t-statistics are in brackets. There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. The tests reported are the Zivot and Andrews (1992) tests for a unit root (α = 1) unit root against the alternative hypothesis of trend-stationary with one break point in the level and/or in the slope of the trend. The most general model corresponds to the Innovational Outlier model C following the nomenclature in Perron (1989), which is written k
as yt ¼ μ þ θDU t ðλÞ þ βt þ γDT t ðλÞ þ α yt−1 þ ∑c j Δyt−i þ εt . The Innovational Outlier model A is obtained by setting γ = 0 and model B by setting θ = 0. The lag length is found j¼1
by applying the strategy proposed by Ng and Perron (2001).
Ratio (QLR) statistic proposed by Andrews (1993) is employed. It generalises the Chow (1960) test to the case of an unknown break date. The QLR statistic, denoted as Fn(λ), tests the null of no structural change for a given break point (⌊λT⌋) as such: SupF n ¼ supλ1 ≤ λ ≤ ð1−λ1 Þ F n ðλÞ; where the usual choice for λ1 is 0.15. The approximate asymptotic p-values reported in Table 3 are computed based on Hansen (1997).11 The model used to test for a structural change is the trend-stationary model found in Table 1, which includes a constant, a trend and 12 lags of the dependent variable to account for potential serial correlation.12 The test statistics provide evidence that there is a structural change in both the aggregate and NYSE models. The p-values indicate that the null hypothesis is rejected at higher level than the 1% significance level. As recommended, the ends of the data are trimmed for estimation consistency, but the results appear to be insensitive to trimming, which are set at 15% and 10%. Note that the maximum trimming allowable is approximately 10%, as the model is required to estimate 15 parameters. The timing of the break is estimated to be October 2006, which corresponds to Phase II of the pilot programme, again confirming the results found in Table 2 with the Zivot and Andrews (1992) test. Overall, these results support this paper's hypothesis. 5. Concluding remarks This paper presents statistical evidence of a structural change in margin debt, which can be dated to the time of the change in margin
11
The structural break tests have been computed with R using the strucchange package constructed by Zeileis, Leisch, Hornik, and Kleiber (2002) and also discussed by Zeileis (2006). 12 The results using Ng and Perron (2001) methodology are presented in the Appendix.
rules between 2005 and 2008. Specifically, there is a statistically significant increase in the level of margin debt. The timing of this increase is estimated to be in Phase II of the pilot programme, as anticipated. Indeed, Phase II of the pilot programme gave investors additional incentives to enter the financial market. Both tests by Zivot and Andrews (1992) and Andrews (1993) agree on the presence and timing of a break in margin debt. The empirical evidence presented in this paper supports the premise that margin requirements affect margin loans. A number of researchers have considered how interactions between financial regulations, institutions and markets impacted the 2008 financial crisis and how these interactions could or should change (see Carey, Kashyap, Rajan, & Stulz, 2012). Because margin requirements are monetary policy tools of the U.S. Federal Reserve Board, it is important to further investigate the efficacy of strengthening and loosening these requirements to prevent high risks of defaulting on margin loans, particularly in times of financial crisis.
Table 3 QLR test — p-values. Margin debt series
p-Value
Break date
Lags
Trimming
Aggregate U.S. securities market
0.0010 0.0011 0.0065 0.0078
Oct-2006 Oct-2006 Oct-2006 Oct-2006
12 12 12 12
15% 10% 15% 10%
NYSE
Notes: The results in this table are for the Quandt Likelihood Ratio (QLR) statistic proposed by Andrews (1993). The p-values are computed based on Hansen (1997). There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. The model of log-adjusted margin debt includes a constant, a trend and 12 lags of the dependent variable to account for potential serial correlation as in the ADF specification.
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Appendix A.
Table 4 Augmented Dickey–Fuller Tests — p-values. t-statistics Margin debt series|models
Constant
Lags
Constant & trend
Lags
Aggregate U.S. securities market NYSE
0.6415 0.9217
2 8
0.1290 0.0407
8 8
Margin debt series|hypotheses
No const. & unit root
No trend & unit root
Aggregate U.S. securities market NYSE
0.2365 0.2622
0.0089 0.0002
F-statistics
Notes: This table reports the Dickey and Fuller (1979) tests for the null of a unit root against the stationary alternative. There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. When the model tested includes a constant (μ) and a trend k
(t), it is written as yt ¼ μ þ βt þ α yt−1 þ ∑c j Δyt−i þ ε t . The p-values are computed j¼1
from the ordinary Dickey–Fuller distribution. The lag length is found by applying the strategy proposed by Ng and Perron (2001). Table 5 QLR test — p-values. Margin debt series
p-Value
Break date
Lags
Trimming
Aggregate U.S. securities market
0.0131 0.0165 0.0447 0.0553
Oct-2006 Oct-2006 Oct-2006 Oct-2006
8 8 8 8
15% 10% 15% 10%
NYSE
Notes: The results in this table are for the Quandt Likelihood Ratio (QLR) statistic proposed by Andrews (1993). The p-values are computed based on Hansen (1997). There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. The model of log-adjusted margin debt includes a constant, a trend and 8 lags of the dependent variable to account for potential serial correlation as in the ADF specification. The lag length is found by applying the strategy proposed by Ng and Perron (2001).
References Andrews, D. W. K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica, 61(4), 821–856. Carey, M., Kashyap, A. K., Rajan, R., & Stulz, R. M. (2012). Market institutions, financial market risks, and the financial crisis. Journal of Financial Economics, 104(3), 421–424. Chow, G. C. (1960). Tests of equality between sets of coefficient in two linear regressions. Econometrica, 28, 591–605. Climan, R. E. (1978). Civil liability under the credit-regulation provisions of the Securities Exchange Act of 1934. Cornell Law Review, 63(1), 206–270.
Coffman, E. G., Jr., Matsypura, D., & Timkovsky, V. G. (2010). Strategy vs risk in margining portfolios of options. 4OR, 8(4), 375–386. Dickey, D. A., & Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431. Fortune, P. (2000). Margin requirements, margin loans, and margin rates: Practice and principles. New England Economic Review September/October (pp. 19–44). GAO (1998). Regulatory and industry approaches to capital risk. Grube, R. C., Joy, O. M., & Panton, D. B. (1979). Market responses to federal reserve changes in the initial margin requirement. The Journal of Finance, 34(3), 659–674. Hansen, B. (1997). Approximate asymptotic p values for structural-change tests. Journal of Business and Economics Statistics, 15, 60–67. Hardouvelis, G. A. (1990). Margin requirements, volatility, and the transitory components of stock prices. American Economic Review, 80(4), 736–762. Hardouvelis, G. A., & Peristiani, S. (1992). Margin requirements, speculative trading, and stock price fluctuations: The case of Japan. The Quarterly Journal of Economics, 107(4), 1333–1370. Hardouvelis, G. A., & Theodossiou, P. (2002). The asymmetric relation between initial margin requirements and stock market volatility across bull and bear markets. Review of Financial Studies, 15(5), 1525–1560. Hsieh, D. A., & Miller, M. H. (1990). Margin regulation and stock market volatility. The Journal of Finance, 45(1), 3–29. Luckett, D. G. (1982). On the effectiveness of the federal reserve's margin requirements. Journal of Finance, 37(3), 783–795. Lupi, C. (2009). Unit root CADF testing with R. Journal of Statistical Software, 32(2), 1–19. Matsypura, D., & Timkovsky, V. G. (2013). Integer programs for margining option portfolios by option spreads with more than four legs. Computational Management Science, 10(1), 51–76. Matsypura, D., & Timkovsky, V. G. (2012). Margining option portfolios by network flows. Networks, 60(2), 120–131. Moore, T. G. (1966). Stock market margin requirements. Journal of Political Economy, 74(2), 158–167. Ng, S., & Perron, P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69(6), 1519–1554. OCC (2008). Customer portfolio margin User Guide. The Options Clearing Corporation (‘OCC’). Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57(6), 1361–1401. Perron, P. (1997). Further evidence from breaking trend functions in macroeconomic variables. Journal of Econometrics, 2(80), 355–385. Salinger, M. (1990). Stock market margin requirements and volatility: Implications for regulation of stock index futures. In F. Edwards (Ed.), Regulatory reform of stock and futures markets (pp. 23–40). Netherlands: Springer. SEC, 1997, February 6. release 34–38248. URL http://www.sec.gov/rules/final.shtml SEC, 2002, October 1. release 34–46576. URL http://www.sec.gov/rules/final.shtml SEC, 2003, July 1. release 34–48115. URL http://www.sec.gov/rules/final.shtml SEC, 2004, December 20. release 34–50885. URL http://www.sec.gov/rules/final.shtml SEC, 2005a, July 14. release 34–52031. URL http://www.sec.gov/rules/final.shtml SEC, 2005b, December 14. release 34–52738. URL http://www.sec.gov/rules/final.shtml SEC, 2006a, July 11. release 34–54125. URL http://www.sec.gov/rules/final.shtml SEC, 2006b, December 12. release 34–54918. URL http://www.sec.gov/rules/final.shtml Zeileis, A. (2006). Implementing a class of structural change tests: An econometric computing approach. Computational Statistics and Data Analysis, 50, 2987–3008. Zeileis, A., Leisch, F., Hornik, K., & Kleiber, C. (2002). strucchange: An R package for testing for structural change in linear regression models. Journal of Statistical Software, 7(2), 1–38. Zivot, E., & Andrews, D. W. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business and Economics Statistics, 10(3), 251–270.
Contents lists available at ScienceDirect
International Review of Financial Analysis
Does portfolio margining make borrowing more attractive? Dmytro Matsypura ⁎, Laurent L. Pauwels 1 The University of Sydney, New South Wales 2006, Australia
a r t i c l e
i n f o
Article history: Received 17 April 2015 Received in revised form 13 November 2015 Accepted 19 November 2015 Available online 27 November 2015 Keywords: Margin debt Margin requirements Portfolio margining Financial regulations Structural change U.S. securities markets
a b s t r a c t This paper investigates the effects of a change in the margin rules of the U.S. financial securities markets. These rules determine how much investors can borrow to leverage their investments. Since the 1929 stock market crash, margin loans have been tightly regulated by the Securities and Exchange Act Regulation T. Between 2005 and 2008, the Securities and Exchange Commission modified these margin rules because they were perceived as not adequately reflecting investment risk. The amended rules have made it more attractive for investors to borrow by opening new margin accounts and diversifying their investment positions. This paper tests the hypothesis that the change in the margin rules has increased margin debt across the U.S. securities markets. It provides statistical evidence that this structural change can be dated to the amendments in the rules. © 2015 Elsevier Inc. All rights reserved.
1. Introduction Investors who purchase securities can borrow part of the purchase price from financial institutions, such as brokerage firms, by opening margin accounts. They are required to deposit a portion of the purchase price, the margin, which represents the initial equity in the accounts. The portion that must be deposited is called the initial margin requirement and is calculated by following margin rules that are regulated by the U.S. Federal Reserve Board. The margin debt held by investors with their financial institutions is secured by the purchased securities. Securities exchanges, such as the New York Stock Exchange (NYSE), the Chicago Board Options Exchange (CBOE) and the National Association of Securities Dealers (NASD), can set higher initial margin requirements at their discretion. Exchanges also establish a maintenance margin requirement that determines the amount necessary to be kept as collateral in the margin account for the duration of an investment. Whenever the margin is below the requirement, the broker issues a margin call. Investors typically use margin accounts to leverage their investments and increase their purchasing power. Since the 1929 stock market crash, the U.S. Federal Reserve Board has been given authority to regulate margin loans with the Securities and Exchange Act Regulation T of 1934. One of the objectives of this act is the “control of monetary aggregates” (Climan, 1978). The U.S. Federal Reserve Board has achieved this by establishing an initial margin requirement for margin loans. This requirement sets a minimum ⁎ Corresponding author at: The University of Sydney, Room 4089, Abercrombie Building H70, NSW 2006, Australia. Tel.: +61 2 9359 3945; fax: +61 2 9351 6409. E-mail address: [email protected] (D. Matsypura). 1 The order of the authors' names is alphabetical.
http://dx.doi.org/10.1016/j.irfa.2015.11.006 1057-5219/© 2015 Elsevier Inc. All rights reserved.
equity position on the date of a credit-financed security transaction. The initial margin requirement for listed stocks has changed 22 times between 1934 and 1974 and has been as high as 100% and as low as 40%. Since 1974, however, the initial margin requirement has been fixed at 50% of the current market value of the stock. During the 1980s and 1990s, margin requirements were often perceived as too high and not accurately representative of investment risks. To more accurately represent risk, the Option Clearing Corporation (OCC) developed a new portfolio margining methodology whereby portfolio margin requirements were calculated using the Theoretical Intermarket Margining System (TIMS).2 TIMS was first implemented in 1997 to calculate the net capital requirements for brokers' proprietary portfolios of listed options (SEC, 1997; GAO, 1998). However, this margining methodology was not used to margin customer accounts prior to 2005. After two proposals from NYSE, the Securities and Exchange Commission (SEC) approved the use of the portfolio margining methodology under a temporary pilot programme that began in 2005 and ended in 2008 (SEC, 2002; SEC, 2004; SEC, 2005b). This paper hypothesises that the amendments to the margin rules introduced between 2005 and 2008 stimulated investor borrowing due to the lower margin requirements; as a result, there was an increase in margin debt. The lower initial and maintenance margin requirements made it more attractive for new investors to open margin accounts and for existing investors to diversify their investment positions. This change should be particularly apparent during the second phase of the pilot programme, as this phase included a wider range of securities.
2 It is now known as the System for Theoretical Analysis and Numerical Simulations (STANS).
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The change in investment behaviour should be observable in the monthly margin debt series for the U.S. securities markets over time, after adjustments for market sentiments. This is a monthly series and constitutes the only data on margin debt publicly available. Fig. 1 depicts the margin debt series for the U.S. securities markets from January 1997 to February 2014. It is worth noting that prior to the change in margin rules, investors already displayed bullish borrowing behaviour, as margin debt grew by 72% over the three years between September 2002 and July 2005. Between July 2006 and its peak in July 2007, however, the upward trend in margin debt accelerated by 63% in a single year. The existing literature on margin requirements has mostly been published prior to 2005. The earliest work on the topic is by (Moore, 1966) and studies the influence of margin requirements on investors' equity ratios. Later research conducted on margin requirements has primarily focused on their impact on stock prices (Grube, Joy, & Panton, 1979; Luckett, 1982) and stock price volatility (Hardouvelis, 1990; Hardouvelis & Peristiani, 1992; Salinger, 1990; Hardouvelis & Theodossiou, 2002). It is apparent from the literature that margin requirements can have a direct influence on the size of margin loans. This theoretical finding is empirically corroborated by Hsieh and Miller (1990), who found a negative relationship between margin requirements and the amount of margin credit outstanding, i.e., margin debt. This leads to the conclusion that initial margin requirements might serve as a mild automatic stabiliser, limiting margin debt more during periods of bull markets than during bear markets (Fortune, 2000). Section 2 discusses history and practice of margin requirements. Section 3 describes the empirical model and the data. Section 4 empirically investigates whether this change in margin rules can be detected and dated in the margin debt series. A common way to test for such a change is to use structural change tests. Lastly, Section 5 provides concluding remarks.
129
Regulation T applies to broker-dealers, Regulation U applies to banks and other lenders, and Regulation X applies to margin loans not explicitly covered by the other regulations. These requirements set a minimum equity position on the date of a loan-based transaction (Fortune, 2000). In 1933 NYSE established its own requirement that member firms' customers could borrow no more than 50% of the value of securities held. These requirements apply to the existing holdings of securities and therefore are maintenance margin requirements. At the moment, minimal equity standards exist at all registered exchanges: for example, they are set under Rule 431 at NYSE, Rule 12 at CBOE, and Rule 2520 at NASD. Until 2005, these rules stated that broker–dealers must require customers to have a maintenance margin equal to at least 25% of a long position in stocks and 30% of a short position. Brokers typically required a higher ratio, on the order of 30 to 35% for long positions (Fortune, 2000). The rules also set requirements for more complex transactions, such as options, option spreads, straddles, and boxes. For a good summary of margin requirements under Regulation T and NYSE Rule 431 the reader is referred to Table 1 in Fortune (2000). On May 13, 2002, NYSE proposed to amend its rules to allow member organisations to use a portfolio margin methodology for certain customer accounts. In 2005, SEC approved the proposal as a pilot programme available to member organisations on a voluntary basis (SEC, 2005a). The pilot programme was implemented in three phases. Phase I began on July 14, 2005 and permitted the use of the portfolio margining methodology only for a limited number of portfolios of listed broad-based securities index options, warrants, futures, futures options and related exchange-traded funds. Phase II began on July 11, 2006 and included listed stock options and securities futures (SEC, 2006a). Phase III began on April 2, 2007 and included equities, equity options, unlisted derivatives and narrow-based index futures. Unlike Phase I, the changes in margin requirements in Phases II and III were more significant because they targeted a much wider array of securities. Furthermore, Phase III was widely advertised in the media after its approval on December 12, 2006 (SEC, 2006b), more than 3 months before it would become effective. By July 2008, SEC ended the pilot programme, thus making portfolio margining permanent and leading to the amendment of the margin rules of the Financial Industry Regulatory Authority (FINRA), CBOE and NYSE.
2. History and practice of margin requirement After the 1929 stock market crash, the U.S. Federal Reserve Board established initial margin requirements under Regulations T, U and X. 550
2,400 2,200
450
2,000
400
1,800
350
1,600 1,400
300
1,200 250 1,000
S&P 500 index
Margin debt in billions of $US
500
200 800 150 600 100
400
50
200
01-2014
07-2008
07-2006 03-2007
07-2005
01-1997
0
I II III pilot programme
0
Fig. 1. Aggregate margin debt in billions of dollars (—) and S&P 500 index (− −) in the period from January 1997 through February 2014. Data from www.finra.org and finance.yahoo.com.
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options, i.e., the securities that were part of Phases II and III of the pilot programme.
Table 1 Augmented Dickey–Fuller Tests — p-values. t-statistics Margin debt series|models
Constant
Aggregate U.S. securities market 0.6372 NYSE 0.9332
Lags
Constant & trend Lags
12 12
0.0649 0.0394
12 12
F-statistics Margin debt series|hypotheses No constant & unit root No trend & unit root Aggregate U.S. securities market 0.2204 0.0070 NYSE 0.2420 0.0025 Notes: This table reports the Dickey and Fuller (1979) tests for the null of a unit root against the stationary alternative. There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. When the model tested includes a constant (μ) and a trend (t), it is written 12
3. Data The data used in this paper are as follows. The size of the margin loan qt is measured by the aggregate margin debt collected from FINRA website for the entire U.S. securities market.4 The data are available monthly from January 1997 until February 2014. There is also data for NYSE, which represents a large portion of the aggregate U.S. securities market margin debt.5 The amount borrowed depends on the investor's preferences, attitude towards risk and other considerations. However, the investor is likely to change the amount borrowed depending on the market expectations. Hence, the variable of interest becomes
as yt ¼ μ þ βt þ α yt−1 þ ∑c j yt−i þ εt . The p-values are computed from the ordinary j¼1
Dickey–Fuller distribution.
The original margin requirements under Regulation T are termed strategy-based whilst margin requirements produced by the portfolio margin methodology are termed portfolio margin requirements by SEC. The portfolio margin requirements are substantially lower than their strategy-based counterparts. Under the strategy-based methodology the daily margin calculation initially requires the determination of an allowable decomposition of the account into hedging strategies (or offsets). It then requires the calculation of the margin requirements for each offset in the decomposition as a current (or maximum, in some cases) loss associated with that offset. The sum of these losses constitutes the required margin. Under the portfolio methodology, implemented as STANS by OCC, the daily margin calculation for each account is based on full portfolio Monte Carlo simulations. OCC utilises a proprietary derivation of the Cox–Ross–Rubinstein binomial option pricing model to calculate projected liquidating prices. Projected prices are calculated based upon the closing underlying asset price for each day plus and minus price moves at ten equidistant data points over a broad range of market movement. The percentages of the daily price move for an underlying price are + 6 to − 8% for high capitalisation broad-based securities indexes, +/ − 10% for non-high capitalisation broad-based securities indexes, and +/ − 15% for equity products and sector indexes. Prices for all instruments are projected, and the resulting profits and losses of the portfolio are summed to estimate the aggregate gain or loss at each of the ten underlying price points. Within a class group (all products with the same underlying instrument), 100% of a position's gain at any one valuation point is allowed to offset another position's loss at the same valuation point. The largest aggregated projected loss over the range of the ten potential market moves for each class and product group, in the case of the offset-eligible classes, is the margin requirement for the portfolio (OCC, 2008). It should be noted that under the amended rules, margining can be performed with either methodology. In summary, while strategy-based margining generally limits leverage on equity to 2:1, with portfolio margining, leverage of 6:1 or more is possible.3 In a 2006 promotional communication to its clients, CBOE provided several numerical examples that demonstrated the potential benefits of the new approach to margining. Two of these examples are reproduced in Fig. 2. In all of the examples provided by CBOE, including the two reproduced in this paper, portfolio margining produced lower margin requirements; in some cases, more than 40 times lower. The difference is particularly noticeable for portfolios containing
yt ¼ logðqt =pt Þ where the asset price pt is measured with the S&P 500 price index, which is collected from Yahoo! Finance.6 The S&P 500 price index captures the overall market trend, accounting for market sentiments and potential market exuberances such as the 2000 dot com bubble and the 2008 global financial crisis. This is an important consideration when testing whether the margin debt changed as a result of the new margin rules. The fluctuations of yt shown in Figs. 3 and 4. For example, during the dot com bubble, the amount borrowed by investors rose and fell back to its trend. In contrast, the change in margin rules seems to have caused a shift in the level of yt and a possible change in the slope of the trend of yt, as suggested in Figs. 3 and 4. These observations are tested formally in the next section. Consider the following empirical model for yt: yt ¼ μ þ βt þ α yt−1 þ
Coffman, Matsypura, and Timkovsky (2010), Matsypura and Timkovsky (2012), and Matsypura and Timkovsky (2013) show that strategy-based margining, when coupled with complex option spreads (SEC, 2003) produces much lower margin requirements and a more accurate estimation of risk.
εt i:i:d 0; σ 2
ð1Þ
i¼1
for the sample t ∈ [1, T ], where α is the AR(1) parameter, μ is the constant (or drift) and t is the trend. As a starting point, the unit root hypothesis is tested: H 0 : α ¼ 1 and H 1 : α b 1 for all t; as it is often a practice in empirical work involving financial time series. Testing this hypothesis is also necessary to determine the appropriate structural change tests. The unit root hypothesis is tested using two different specifications of model (1) using Augmented Dickey and Fuller (1979) tests (ADF). In the first ADF test, yt is a random walk under the null hypothesis, while under the alternative it is a stationary autoregressive process. In the second ADF test, yt is a random walk with a drift under the null and a trend-stationary process under the alternative. The lag length in each model under scrutiny is chosen to be 12, as is often done with monthly data series in empirical studies. Note that in order to confirm the correctness of the chosen lag length, a data-dependent general to specific recursive method proposed by Ng and Perron (2001) is also applied. The results are presented in the Appendix A. The results and conclusion from this data-dependent approach confirm those presented below. The results of the ADF tests are shown in Table 1.7 When including a constant term in the estimated equation, the ADF tests do not reject the 4
3
k X ci Δyt−i þ εt ;
www.finra.org. www.nyxdata.com. http://finance.yahoo.com. 7 The ADF tests have been computed with R using the CADFtests package constructed by Lupi (2009). 5 6
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131
Fig. 2. Numerical examples provided by the Chicago Board Options Exchange to its clients in 2006.
null hypothesis, which provides evidence that both the aggregate and NYSE margin debt series are random walks. However, when including both a constant and a deterministic trend, the results indicate that both adjusted margin debt series are stationary around a trend. The statistical evidence appears to be stronger for NYSE than for the aggregate series. It is worth pointing out that the estimates of the autoregressive coefficient in the model with a constant and a trend are 0.87 and 0.84 for the aggregate and NYSE series, respectively. Similarly, the F-statistics clearly reject the joint hypothesis of a random walk with a drift in favour of trend-stationary processes for both series at the 1% level of significance. These F-test results do not hold when only including a constant term in the estimated model. In that case, the evidence supports the hypothesis of a random walk. This ambiguity in the ADF t- and F-test results could originate from the presence of a structural change due to the amendments in the margin rules, as conjectured in this paper. This conjecture can be incorporated
in the ADF tests by re-specifying the alternative hypothesis. On the other hand, if the series are indeed stationary around a trend, then the change in the margin rules can be tested with the QLR test of Andrews (1993). These possibilities are investigated in turn. 4. Evidence It is well known from the seminal work of Perron (1989) that the standard unit root tests such as the ADF tests cannot reject the null hypothesis if the data-generating process of the series under scrutiny is stationary around a trend with a break point. Zivot and Andrews (1992) proposes to test for a unit root against the alternative hypothesis of a trend-stationary process with one break point in the level and/or in the slope of the trend. Zivot and Andrews (1992) is essentially an extension of Perron (1989) with the added benefit that the null of a unit root is tested over all possible break dates. In contrast, Perron (1989)
5.7 5.6 5.5 5.4 5.3 5.2 5.1 5 4.9
06-2013
01-2012
09-2010
04-2009
12-2007
08-2006
03-2005
11-2003
06-2002
02-2001
09-1999
05-1998
01-1997
4.8
Fig. 3. Log-transform of the aggregate margin debt adjusted by the S&P 500 index in the period from January 1997 through February 2014. Data from www.finra.org and finance.yahoo. com.
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5.6 5.5 5.4 5.3 5.2 5.1 5 4.9 4.8
06-2013
01-2012
09-2010
04-2009
12-2007
08-2006
03-2005
11-2003
06-2002
02-2001
09-1999
05-1998
01-1997
4.7
Fig. 4. Log-transform of NYSE margin debt adjusted by the S&P 500 index in the period from January 1997 through February 2014. Data from www.nyxdata.com and finance.yahoo.com.
requires the assumption of a known break point. The reason for using tests that estimate the position of the break is twofold. First, the potential location of the break corresponding to the change in the rules is within a 3-year interval, from July 2005 to July 2008, and second, these tests tend to have higher power. Zivot and Andrews (1992) considers the Innovational Outlier (IO) model in which the more general regression equation to test the null of a unit root is yt ¼ μ þ θDU t ðλÞ þ βt þ γDT t ðλÞ þ α yt−1 þ
k X ci Δyt−i þ εt
ð2Þ
i¼1
for t = 1 , … , T, λ ∈ [0, 1] where DUt(λ) = 1 if t N λT and 0 otherwise; DTt(λ) = t − λT if t N λT and 0 otherwise.8 This is often named model C, using the nomenclature established in Perron (1989). The two other IO types of regression equations are model A, where it is assumed that γ = 0, and model B, where θ = 0. The IO models are relevant in the context of this paper because they model structural change as a gradual process. The test is the minimal value of the t-statistic testing α =1 over all possible break dates in a given sample. This minimal value is denoted as t α⁎ =infλ∈[0,1]tα(λ) with tα(λ) is the t-statistic when the break date is ⌊ λT⌋, and ⌊⋅⌋ denotes the largest integer that is smaller than the argument. The estimated λ determines the break date (i.e. T break ¼ λT ) which coincides with the minimal value of the t-statistic, t α⁎. The unit root hypothesis is rejected for both the aggregate and NYSE series in favour of trend stationarity with a one-time break in both the intercept and the trend. Although all models (A, B and C) are reported for completeness in Table 2, model C is the most appropriate model using a general-to-specific approach.9,10 8 Note that the results of Zivot and Andrews (1992) are valid without trimming at the end points, as shown in Perron (1997). 9 The lag length k is chosen to be 12, as with the ADF tests. It turns out that when the lag length is selected using Ng and Perron (2001), the selected lag length is also 12. 10 Zivot and Andrews (1992) tests have been computed with R using the urca package.
Model C implies that there are two significant changes taking place in both margin debt series. The positive signs of θ (.072 and .067) indicate that there is an increase in the level of margin debt at the time of the break. This change is statistically significant as shown by the t-statistic of the constant break dummy. Moreover, the negative signs of γ (− . 0008 and − . 0006) imply a decrease in the rate of growth of margin debt. This is again statistically significant. The estimates of the autoregressive coefficient, α, are .686 and .672 for the aggregate and NYSE series, respectively, which is lower than in their earlier ADF specification. Interestingly, in both cases, the constant break dummy is more significant than the slope break dummy, especially for NYSE, where the slope break dummy is significant at the 5% level whereas the constant break dummy is significant at the 0.1% level. As a side remark, when conducting the tests with regression model B, the null of a random walk cannot be rejected against a stationary process with a break in trend, whereas the null is rejected against a stationary process with a break in the intercept. This is consistent with the paper's hypothesis that the change in margin rules increased margin debt in the U.S. securities market. The estimated date of the structural change in margin debt corresponds to Phase II of the pilot programme. For both measures of margin debt, the break date is estimated to be in October 2006. It is interesting to notice that none of the estimated dates point to Phase I. This is consistent with expectations, as very few market instruments (only broadbased indices and exchange-traded funds derivatives) were included in that early Phase, and it was not anticipated to have much impact. Both the statistical test results and the estimated dates of structural change in the margin debt support this paper's hypothesis. Next, let us return to the possibility that both adjusted margin debt series are indeed trend-stationary processes, as discussed earlier. If this is the case, then the change in margin rules can be tested using “conventional” tests for structural change, such as with the well-known Chow (1960) test. However, because the exact timing of the break induced by the change in margin rules is unknown, the Quandt Likelihood
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Table 2 Zivot and Andrews (1992) — t-statistics. Margin debt series
t-stat.
T^ break
k
μ^
^θ
^ β
^ γ
^ α
Model A (break in intercept) Agg. U.S. market
−4.62
Oct-2006
12
−4.88
Oct-2006
12
.052 (3.16) .052 (3.30)
.0005 (3.06) .0006 (3.39)
–
NYSE
1.20 (4.65) 1.34 (4.90)
.757 (14.4) .726 (12.9)
Model B (break in trend) Agg. U.S. market
−3.97
–
12
–
NYSE
−3.91
–
12
.971 (3.99) .934 (3.93)
.0009 (3.67) .0008 (3.57)
−.0008 (−2.11) −.0005 (−1.66)
.798 (15.7) .804 (16.1)
Model C (break in intercept & trend) Agg. U.S. market −5.53
Oct-2006
12
−5.53
Oct-2006
12
1.53 (5.54) 1.59 (5.53)
.072 (4.14) .067 (4.02)
.001 (4.30) .0009 (4.24)
−.0008 (−2.95) −.0006 (−2.50)
0.686 (12.1) .672 (11.3)
NYSE
–
–
Asymptotic critical values Significance level
Model A
Model B
Model C
1% 5% 10%
−5.34 −4.80 −4.58
−4.93 −4.42 −4.11
−5.57 −5.08 −4.82
Notes: t-statistics are in brackets. There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. The tests reported are the Zivot and Andrews (1992) tests for a unit root (α = 1) unit root against the alternative hypothesis of trend-stationary with one break point in the level and/or in the slope of the trend. The most general model corresponds to the Innovational Outlier model C following the nomenclature in Perron (1989), which is written k
as yt ¼ μ þ θDU t ðλÞ þ βt þ γDT t ðλÞ þ α yt−1 þ ∑c j Δyt−i þ εt . The Innovational Outlier model A is obtained by setting γ = 0 and model B by setting θ = 0. The lag length is found j¼1
by applying the strategy proposed by Ng and Perron (2001).
Ratio (QLR) statistic proposed by Andrews (1993) is employed. It generalises the Chow (1960) test to the case of an unknown break date. The QLR statistic, denoted as Fn(λ), tests the null of no structural change for a given break point (⌊λT⌋) as such: SupF n ¼ supλ1 ≤ λ ≤ ð1−λ1 Þ F n ðλÞ; where the usual choice for λ1 is 0.15. The approximate asymptotic p-values reported in Table 3 are computed based on Hansen (1997).11 The model used to test for a structural change is the trend-stationary model found in Table 1, which includes a constant, a trend and 12 lags of the dependent variable to account for potential serial correlation.12 The test statistics provide evidence that there is a structural change in both the aggregate and NYSE models. The p-values indicate that the null hypothesis is rejected at higher level than the 1% significance level. As recommended, the ends of the data are trimmed for estimation consistency, but the results appear to be insensitive to trimming, which are set at 15% and 10%. Note that the maximum trimming allowable is approximately 10%, as the model is required to estimate 15 parameters. The timing of the break is estimated to be October 2006, which corresponds to Phase II of the pilot programme, again confirming the results found in Table 2 with the Zivot and Andrews (1992) test. Overall, these results support this paper's hypothesis. 5. Concluding remarks This paper presents statistical evidence of a structural change in margin debt, which can be dated to the time of the change in margin
11
The structural break tests have been computed with R using the strucchange package constructed by Zeileis, Leisch, Hornik, and Kleiber (2002) and also discussed by Zeileis (2006). 12 The results using Ng and Perron (2001) methodology are presented in the Appendix.
rules between 2005 and 2008. Specifically, there is a statistically significant increase in the level of margin debt. The timing of this increase is estimated to be in Phase II of the pilot programme, as anticipated. Indeed, Phase II of the pilot programme gave investors additional incentives to enter the financial market. Both tests by Zivot and Andrews (1992) and Andrews (1993) agree on the presence and timing of a break in margin debt. The empirical evidence presented in this paper supports the premise that margin requirements affect margin loans. A number of researchers have considered how interactions between financial regulations, institutions and markets impacted the 2008 financial crisis and how these interactions could or should change (see Carey, Kashyap, Rajan, & Stulz, 2012). Because margin requirements are monetary policy tools of the U.S. Federal Reserve Board, it is important to further investigate the efficacy of strengthening and loosening these requirements to prevent high risks of defaulting on margin loans, particularly in times of financial crisis.
Table 3 QLR test — p-values. Margin debt series
p-Value
Break date
Lags
Trimming
Aggregate U.S. securities market
0.0010 0.0011 0.0065 0.0078
Oct-2006 Oct-2006 Oct-2006 Oct-2006
12 12 12 12
15% 10% 15% 10%
NYSE
Notes: The results in this table are for the Quandt Likelihood Ratio (QLR) statistic proposed by Andrews (1993). The p-values are computed based on Hansen (1997). There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. The model of log-adjusted margin debt includes a constant, a trend and 12 lags of the dependent variable to account for potential serial correlation as in the ADF specification.
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Appendix A.
Table 4 Augmented Dickey–Fuller Tests — p-values. t-statistics Margin debt series|models
Constant
Lags
Constant & trend
Lags
Aggregate U.S. securities market NYSE
0.6415 0.9217
2 8
0.1290 0.0407
8 8
Margin debt series|hypotheses
No const. & unit root
No trend & unit root
Aggregate U.S. securities market NYSE
0.2365 0.2622
0.0089 0.0002
F-statistics
Notes: This table reports the Dickey and Fuller (1979) tests for the null of a unit root against the stationary alternative. There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. When the model tested includes a constant (μ) and a trend k
(t), it is written as yt ¼ μ þ βt þ α yt−1 þ ∑c j Δyt−i þ ε t . The p-values are computed j¼1
from the ordinary Dickey–Fuller distribution. The lag length is found by applying the strategy proposed by Ng and Perron (2001). Table 5 QLR test — p-values. Margin debt series
p-Value
Break date
Lags
Trimming
Aggregate U.S. securities market
0.0131 0.0165 0.0447 0.0553
Oct-2006 Oct-2006 Oct-2006 Oct-2006
8 8 8 8
15% 10% 15% 10%
NYSE
Notes: The results in this table are for the Quandt Likelihood Ratio (QLR) statistic proposed by Andrews (1993). The p-values are computed based on Hansen (1997). There are two margin debt series: the aggregate U.S. securities market and NYSE. Both are log-transformed and adjusted for the S&P500 market price. The model of log-adjusted margin debt includes a constant, a trend and 8 lags of the dependent variable to account for potential serial correlation as in the ADF specification. The lag length is found by applying the strategy proposed by Ng and Perron (2001).
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