CHAPTER 6: DATA ANALYSIS AND DISCUSSION
6.3 Construction of the MLMI
6.3.1 Composition of the BLMI and the ALMI
The composition as previously discussed in the methodology chapter (see Chapter 6) depends on the value of assets, liabilities and the weight for both assets and liabilities. The present study adopted the original measure of LMI at bank level.
' ' ' , , k ti k k t k i t k k t i t A x A L xL LMI
(6.1)The definitions of the components of the LMI remains the same where assets (xtiAk) and liabilities ( '
k i tL
x ) are balance sheet items that vary over time depending on their asset or liability class (k,k'). The liquidity weights, tAk 0 and tLk' 0, are key components that are computed, and in this study, they were time-varying.
However, this study, the liquidity weights were modified and were different from weights reported by other scholars like Brunnermeier et al. (2013), Bai et al. (2014) and Krishnamurthy et al. (2016). These scholars utilised the haircuts on assets as a measure of asset weights. These weights were originally proposed by Bai et al. (2014) who argue that haircuts are natural measures of asset liquidity sensitivity as they are said to vary with measures of asset price volatility and tail risk (Kelly & Jiang, 2014) for a given asset class. For empirical analysis, the haircut is computed as 𝑚 = [1 −𝐷𝑃], where m is the
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haircut measure, P is the fair value of collateral and D, the notional amount. The haircut rates have been found to be lower for high-quality collateral and higher for riskier assets (Krishnamurthy et al., 2016).
Although the haircut measure seems to be accurate measure of assets sensitivity to liquidity shocks, however, their use is problematic since they are not uniform to all the dealers in the money market, even in a situation where different counterparties use the same type of collateral (Corrigan and De Terán, 2007). Moreover, the repo haircut data (Gorton, & Metrick, 2009) for each bank is inaccessible in an ideal world as banks are not keen to publish it (Krishnamurthy et al., 2016).
Therefore, using the JSE All Share Index over the period under investigation, the asset liquidity weight was computed using a combination of spread and volume. The measure uses the absolute spread which is the difference between the bid and the ask prices (Holden, 2009). This absolute bid–ask spread is scaled by the volume traded on a particular day. Many studies already investigated and recommended the use of spread as measure of market liquidity. See for example in this regard, Roll (1984), Glosten and Milgrom (1985), Chordia (2001), and Huberman and Halka (2001). The equity trading volume measures the market depth, i.e. how easy it is to buy or sell a significant volume without affecting the market price. According to Danyliv, Bland, and Nicholass (2014), the average daily volume and Amihud’s (2002) illiquidity ratio (ILLIQ) are the widely used liquidity measures in the industry. Scholars such as Benston and Hagerman (1974) and Stoll (1978b) argue that stock trading volume, volatility and price are influential determinants of liquidity. The measure used in this study was Danyliv et al.’s (2014) inverted liquidity index (LIX). The LIX takes the following form:
Low High ice Volume Liquidity Pr (6.2)
Since this ratio can be very big, it is reduced to manageable values by using logarithms: T Low T High Close t t P P P V LIX , , 10 log (6.3)
Danyliv et al. (2014) argue that the LIX liquidity measure captures the most important aspects of market liquidity as the calculation includes components that pertain to breadth,
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depth, resilience and immediacy of the market. According to Shin (2012), if one is to have a long-run view, spreads are found to have increased significantly with the onset of the crisis. The asset liquidity weight is then determined from equation 6.4.
𝑚 = [1 −𝐿𝐼𝑋1
𝑡] 𝜋, (6.4)
where 𝐿𝐼𝑋1
𝑡 is the inverse of LIX. The calculated weight is adjusted by 𝜋, the coefficient allocated to the assets depending on the level of liquidity. In the present study, the coefficients were adapted from previous studies by Krishnamurthy et al. (2016) and Bai et al. (2014) and following guidelines originally given by Brunnermeier et al. (2013). The asset weights were computed in the similar way as Krishnamurthy et al. (2016) and the assets took the weights between 0 and 1, implying that asset liquidity weights for these assets were also set to 0 < 𝜆𝑡𝐴𝑘< 1. Table 6.3 shows the balance sheet information of the selected banks collected from the South African banks’ BA900 returns filed at the SARB. The assigned coefficient for each category is indicated in the same table. Graph 6.1 shows the calculated 1 −𝐿𝐼𝑋1
𝑡.
Figure 6.1: The calculated asset weight coefficient
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Figure 6.1 shows the huge increase of asset weight coefficient in 2004 relative to the value in 2003. This is preceded by periods of high volatility until 2008. There was another significant increase in assets weight coefficient in 2009 and 2011. The coefficient has been stable since 2012.
Table 6.3: Assets category and the allocated coefficient.
Source: Author’s computation (Data from DA900 returns)
Category
CENTRAL BANK MONEY AND GOLD South African bank notes and subsidiary coin 1.00 Gold coin and bullion 1.00 Domestic currency deposits with SA Reserve Bank 1.00 Cash reserve deposits: Interest bearing 1.00 Cash reserve deposits: Non-interest bearing 1.00 Other deposits 1.00 DEPOSITS, LOANS AND ADVANCES SA banks 1.00
NCDs/PNsc issued by banks, with an unexpired maturity of
Up to 1 month 0.80 More than 1 month to 6 months 0.70 More than 6 months 0.50 Other deposits with and loans and advances to SA banksb 0.50 INVESTMENTS AND BILLS, including
trading portfolio assets Own bankers' acceptances 0.85 Other bankers' acceptances 0.85 Treasury bills 1.00 SA Reserve Bank bills 1.00 Promissory notes 0.85 Commercial paper 0.85 Land Bank bills 0.90 Liquid 0.70 Non-liquid 0.70 Other 0.50
NON-FINANCIAL ASSETS Tangible assets - Premises of the bank 0.20 Other fixed property - Computer equipment, including peripherals - Other tangible assets, including vehicles, equipment, furniture and fittings - Intangible assets - Computer software - Other intangible assets including purchased goodwill - OTHER ASSETS Clients' liabilities per contra -
Remittances in transit 0.20 Current income tax receivables and deferred income tax assets 0.50 Retirement benefit assets - Assets acquired or bought in to protect an advance or investment
Fixed property - Shares - Vehicles and other assets - Other - 𝜋 k i tA x
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To compute the liability side weight of the LMI, one needs to capture the feedback between LMI and liquidity stress. Bai et al. (2014) define the endogenous funding liquidity factor as a combination of its market price proxy and the aggregate LMI resulting in 6.5:
) ( ) 1 ( t t t TOIS LMI FL , (6.5)
where
is a scaling parameter that scales down the magnitude of aggregate LMI to a similar level of spread between Treasury bills and the SABOR. Instead of using OIS–T- Bill spread like Bai et al. (2014), we used the spread between the treasury bill rate and the SABOR. This measure, according to Nagel (2014), accurately measures the time variation of a money market instrument. Since the liquidity condition is assumed to be accurately depicted by the SABOR–Treasury bill spread (STBS), we dropped the) (LMIt
from our empirical analysis. The STBS is sufficient to capture the liquidity condition in a particular market. Inclusion of aggregate LMI in computing the weights could also require one to estimate the LMI at global level and determine its influence as well. Thus, in this study, we captured the liability weights empirically through the modification of the state-dependent funding factor and came up with the funding factor in equation 6.6.
𝐹𝐿𝑡= [ 1 − 𝑆𝑇𝐵𝑆 ]𝜋′ , (6.6)
where 𝑆𝑇𝐵𝑆𝑡 is the spread between Treasury bills and the SABOR. Likewise, the calculated weight was adjusted by 𝜋′, the coefficient allocated to the liabilities depending their period to maturity. Unlike Krishnamurthy et al. (2016), the time to maturity of a liability is captured in the assigned 𝜋′. Table 6.4 presents the liability categories and assigned coefficients while Graph 6.2 shows the STBS.
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Figure 6.2: The SABOR–Treasury bill spread (STBS) Source: Author’s computation
Data source: SARB: online down load facility
https://www.resbank.co.za/Research/Statistics/Pages/OnlineDownloadFacility.aspx Figure 6.2 shows that the SABOR–Treasury bill spread significantly increased over the period 2003–2005. There was a steep decrease the STBS from 2006 to 2007 mainly because the TBill rate increased at a faster rate than the SABOR that remained relatively stable. There was a slight increase in 2007, which was followed by a decrease in 2008. Contrary to expectation, there was a sharp decrease in SABOR and TBill rates during the period of 2008 to 2010. Since the end of the global financial crisis of 2007–2009, the STBS remained relatively stable with a slight increase after 2013. Since the spread is sometimes used to measure liquidity risk (Sarr and Lybek, 2002; Nagel, 2014), the graph shows that spreads increased in 2007 to 2008 signifying and increase in liquidity risk. This coincided with the begging of 2007-2009 global financial crisis.
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Table 6.4 Liability category and the allocated coefficient
Source: Author’s computation (Data from DA900 returns)
DEPOSITS DENOMINATED IN RAND Cheque 1.00
Savings 1.00
Up to 1 day 1.00
More than 1 day to 1 month 1.00 More than 1 month to 6 months 0.95
More than 6 months 0.90
DEPOSITS DENOMINATED IN FOREIGN
CURRENCY Cheque 1.00
Savings 1.00
Up to 1 day 1.00
More than 1 day to 1 month 1.00 More than 1 month to 6 months 0.95
More than 6 months 0.90
OTHER BORROWED FUNDS Short-term 1.00
Medium-term 0.95
Long-term 0.90
FOREIGN CURRENCY FUNDING Short-term 1.00
Medium-term 0.95
Long-term 0.90
OTHER LIABILITIES TO THE PUBLIC Short-term 1.00
Medium-term 0.95
Long-term 0.90
OTHER LIABILITIES Short-term 1.00
Medium-term 0.95 Long-term 0.90 Category 𝜋 ′ ' k i t L x
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