Deposit Insurance Paper Afr Dev

African Development Review, Vol. XXX, No. XXX, 2014, 1–12

1 2 3 4 Valuation of Deposit Insurance in South Africa Using an 5 ‐ 6 Option Based Model 7 8 9 Mark Ellyne and Richard Cheng 10 11 12 13 Abstract: Discussions on introducing a deposit insurance scheme in South Africa have been floating around since 2000, 14 without any official proposal being published or brought to Parliament. Globally, countries have increasingly adopted deposit 15 insurance schemes with the understanding that they provide a public benefit of increasing confidence in the financial system. It is 16 likely that South African banks and government have resisted introduction of any scheme owing to costing issues. This paper 17 estimates the cost of deposit insurance premiums for seven large South African banks for the first time, annually over the period 18 2000 to 2009 using an option‐based model. The premiums exhibit high volatility over time and across banks but yield an average 19 value that is internationally comparable. The authors also propose a risk‐weighted, multi‐tier premium structure to encourage 20 appropriate pricing for different categories of risk. 21 22 23 1. Introduction 24 25 Determining a ‘fair’ premium rate for deposit insurance is particularly troublesome. Even in the United States, where there are a 26 large number of banks and a long history of deposit insurance premiums and bank failures, there is still a lot of debate about the 27 appropriate premium rate. As a result, a number of papers have emerged that attempt to determine whether the premium rates set 28 by the deposit insurer are fair. Examples include Marcus and Shaked (1984), Ronn and Verma (1986), Giammarino et al. (1989); 29 and more recently Duan and Simonato (2002) and Chuang et al. (2009). 30 There are two broad approaches to the pricing problem. The first, which is implemented by this paper, is based on the work by 31 Merton (1977) and uses the relationship between deposit insurance and put options to value the premiums. The second is to use 32 historical data of bank failures to determine an actuarial estimate of expected losses and set premiums accordingly 33 (Humphrey, 1976; Scott and Mayer, 1971). 34 For South Africa, using the second approach is particularly difficult because there have been so few bank failures. Consider 35 that since 1990, South Africa has experienced 13 bank failures (Ngaujake, 2004) compared to the United States that 36 has experienced close to 320 bank failures since 2000 (FDIC, 2010). The political, economic and regulatory framework of 37 South Africa has also changed fundamentally since 1994, and we argue that it is unreasonable to assume that the riskiness 38 of banks prior to this period is any indication of current risks. Additionally, the South African banking sector is very 39 concentrated, with the ‘big 4 banks’ holding approximately 85 per cent of the assets in the sector (IMF, 2008). The small number 40 of South African banks raises the question of how reliable any historical estimates would be. Therefore, the long observation 41 periods which are required for historical actuarial estimates are not meaningful for determining a ‘fair’ premium 42 (Humphrey, 1976). 43 The approach in this paperUNCORRECTED is thus to value deposit insurance premiums using anPROOFS option‐based model based on Ronn and Verma 44 (1986) and Duan (1994). This method provides a theoretical basis to value the premium that the South African Reserve Bank 45 (SARB) could charge for deposit insurance. Secondly, the method creates annual estimates of deposit insurance premiums for 46 individual banks, which allows us to investigate the merits of a flat‐rate versus risk‐adjusted premiums. 47 48 49 50 Dr Mark Ellyne is Adjunct Associate Professor at the School of Economics, University of Cape Town (e‐mail: [email protected]), and Richard 51 Cheng was a postgraduate student in the UCT Commerce Department (e‐mail: [email protected]). © 2014 The Authors. African Development Review © 2014 African Development Bank. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. 1

Journal MSP No. Dispatch: March 11, 2014 CE: Freelance AFDR 12071 No. of Pages: 12 PE: Jeanette Tan 2 M. Ellyne and R. Cheng

1 The research objectives of this paper are to first estimate deposit insurance rates for South African banks, across banks and over 2 time, using a modified method from Duan (1994). Given these estimates, further questions are considered: 3 fi ‐ 4 What is the risk distribution among banks, and what would be the implication of a xed rate premium on cross subsidization? 5 6 How variable is the calculated premium over time; and how frequently should premium rates be adjusted? How does a conservatively assumed, historical‐based insurance premium rate compare with the option‐based approach? 7 8 Do the estimated premiums support any particular insurance structure for South Africa? 9 Based on a decade of data, we find that seven South African banks cluster into three risk categories, with the smaller banks 10 (African Bank and Capitec Bank) appearing less risky than the ‘big 4 banks’ (Standard Bank, Nedbank, ABSA Bank and First 11 Rand), and one bank (Investec) consistently showing a higher risk level. A flat‐rate premium would result in smaller banks cross‐ 12 subsidizing the ‘big 4 banks’ and would discourage competition. The estimated premiums also show a high level of volatility over 13 time, which may simply reflect business cycle conditions. Based on these results, we propose a 3‐tier premium model that captures 14 relative risk and produces internationally comparable premiums. 15 16 17 2. Background 18 19 A well‐functioning financial system is important for the economic growth of a country. It allows for the efficient transfer of 20 resources from those that have an excess (investors) to those that have a shortage (entrepreneurs). Banks are particularly important 21 in this regard, acting as an intermediary between borrowers and savers — taking the deposits from savers, which are liquid short‐ 22 term liabilities, and transforming them into loans to borrowers, which are illiquid medium to long‐term assets; therefore there is a 23 mismatch between the bank’s assets and liabilities. The risk is that if all depositors at a bank decide to withdraw their deposits at 24 once, the bank would be unable to meet its short‐term liabilities and be forced to liquidate its assets and close. In fact, there could 25 even be a contagion effect, where the closure of one bank sparks panic at other banks causing other mass withdrawals of deposits — 26 a run on the banks (Ngaujake, 2004). 27 If it is perceived as generally risky to deposit money in banks, it would reduce the ability of banks to fulfil their function of 28 transferring resources between savers and borrowers. One reason for bank runs is that depositors fear that the bank will fail, 29 regardless of the underlying financial condition of the institution. The motivation to introduce deposit insurance is to address this 30 concern. If deposits at a bank could be fully guaranteed, and the guarantee was credible, then from the depositor’s point of view, 31 the deposits are essentially risk‐free (Merton, 1977). 32 South African banks do not currently have an explicit deposit insurance system in place. Nevertheless, should banks become 33 unable to meet their short‐term liabilities to depositors, depositors may believe that they will be reimbursed by the government — 34 an implied deposit insurance system. This is a reasonable assumption on the part of borrowers, based on the SARB’s previous 35 reimbursement of depositors of failed banks (Ngaujake, 2004; Okeahalam, 1998). The commercial banking industry in South 36 Africa has assets representing about 120 per cent of GDP; with the ‘big 4 banks’ accounting for almost 85 per cent of these assets 37 (IMF, 2008). Are these banks too big to fail? An explicit deposit insurance scheme allow the ‘rules of the game’ to be transparent. 38 It is also debatable whether the cost of insurance should be borne by the public or private sector. The goal of deposit insurance, 39 unlike traditional insurance, is not to compensate the customer for losses; rather, it is to prevent the loss from occurring in the first 40 place. Therefore, there are desirable positive externalities that result from the increased financial stability provided by a deposit 41 insurance scheme. We therefore argue that the government may legitimately subsidise a deposit insurance scheme as it may be 42 partially viewed as a public good.1 43 According to the 2005 BankUNCORRECTED Supervision Annual Report, serious discussions PROOFS about a deposit insurance scheme (DIS) started in 44 2000 as ‘there was a need to establish a DIS in SA’. The report further states that ‘the Department is of the opinion that it should be 45 possible to finalise a proposal, for submission to the Minister, during 2006’. One of the major unresolved issues is the legal nature 46 of the DIS. This affects how members contribute to the fund, and how the fund will pay out to members. Another issue is how the 47 DIS would be funded — initially, and operationally. 48 Interestingly, since this report there has been no mention of a DIS in any of the Bank Supervision Annual Reports from 2006 to 49 2010. Furthermore, there is no public information on any of the analysis that has been completed. News reports over the last 50 decade have mentioned a DIS every few years, but once again, there is no official documentation about the issue that has been 51 released.

1 Correspondence with the SARB reveals that a lot of preliminary work has been done on proposals on how such a scheme could 2 be funded, operated etc., but all these proposals are with the National Treasury for consideration. These documents are currently 3 still not publically available. The National Treasury has the final decisions as to the implementation of a deposit insurance scheme. 4 The pricing model under consideration is being modelled by a private company and is not the structural option‐based model used 5 in this paper (Hattingh, email correspondence, 2010). 6 Why is the government willing to hold a large uninsured risk? What are the reasons that the analysis is not open for public 7 debate and discussion? Or is government ignoring the issue, as it is preoccupied with other problems? What are the repercussions 8 for South Africa? 9 International schemes for pricing deposit insurance exhibit a wide range of parameters concerning not only rates, but coverage 10 limits, funding sources, and various administrative controls (Demirgüç‐Kunt and Sobaci, 2001). In the small sample of 11 comparator countries and factors shown in Table 1, we observe that risk‐adjusted schemes are common, and premiums are often in 12 the range of 0.3 to 0.7 per cent of deposits. 13 In June 2009, 49 per cent of countries worldwide (93 countries) had a deposit insurance system in place, and another 12 per cent 14 of countries were considering introducing a deposit insurance system (IADI, 2010). South Africa is considered to be one of the 15 countries considering introducing a deposit insurance scheme; yet, to date, no official public documents detailing any proposed 16 deposit insurance scheme have been published. 17 In 2002, after the failures of Regal Bank and Saambou Bank, there was renewed interest and pressure for the introduction of a 18 deposit insurance scheme. Government spent the next three years researching and discussing such a policy. However, the idea 19 disappeared around 2004/2005, apparently due to strong opposition from the ‘big 4 banks’. After the financial crisis of 2008, there 20 was once again renewed public interest in financial stability and hence deposit insurance, but banks and the government have let 21 the idea languish, which raises the question of ‘why’. 22 23 3. Methodology 24 25 In Merton’s (1977) seminal paper, he showed that value of deposit insurance to a bank could be described as a put option on the 26 assets of the bank, with a strike price equal to the value of the bank’s deposits. Using the Black‐Scholes formula, it is then possible 27 to calculate the value of this option, and thus the fair price that should be charged for insuring the deposits. This model is presented 28 below. 29 30 31 3.1 Theory of Deposit Insurance as a Put Option 32 33 A bank has a total asset value of V0 at time 0, consisting of equity and debt. Suppose the bank’s debt consists of deposits (B1) and 34 all other debt (B2), then the value of the bank’s total debt is B ¼ B1 þ B2. Deposits as a proportion of total debt is then B1/B. 35 Assuming that all debt is issued at the risk‐free rate of interest, at time T > 0 the bank’s total debt will be BerT. Suppose that T is the 36 37 38 Table 1: Comparison of deposit insurance premiums 39 ‐ 40 Country Annual premium cost, per cent of deposit Risk adjusted Funding (public/private) 41 Argentina 0.36–0.72 Yes Private 42 Brazil 0.3 No Private 43 Finland UNCORRECTED0.05–0.3 PROOFS Yes Joint 44 Greece 0.25–1.25 No Private 45 India 0.05 No Joint 46 Mexico 0.3–1.0 No Joint 47 Nigeria 0.9375 No Joint – 48 Turkey 1.0 1.2 Yes Joint 49 Uganda 0.2 No Joint USA 0.0–0.27 Yes Joint 50 51 Source: Demirgüç‐Kunt and Sobaci (2001).

1 length of time until the bank’s next audit, at which time a decision is made on closure: if the bank is unable to pay back its debt at 2 the time of audit, it would be forced to close and repay its debt by selling off its assets. If the further assumption is made that all 3 debt is of equal seniority, then the payoffs to the various stakeholders at time T are as follows: 4 > rT ’ ‐ rT rT 5 1. Should VT Be , then the bank s liability to debt holders would be Be and depositors would be entitled to receive B1e of ‐ – rT 6 this amount. The value of the bank to equity holders would be VT Be . < rT ‐ 7 2. If instead VT Be , then the bank would be unable to meet its liabilities and debt holders would receive a maximum amount rT – 8 of VT; incurring a loss equal to Be VT. Depositors would be entitled to receive (VTB1)/B, the proportion of the salvageable ‐ 9 asset value owed to them. The value of the bank to equity holders in this case would be 0. rT ‐ – rT 10 The payoff to depositors is therefore min{B1e ,(VTB1)/B} and the payoff to equity holders is max{VT Be , 0}. fi ’ 11 Ronn and Verma (1986) argue that the value of a rm s assets is different depending on whether its deposits are insured or ‘ ’ fi ’ 12 not. They argue that there is an accretion value on account of the insurance , so that the value of the rm s assets after fi ’ 0 — > 0 13 insurance (V) is larger than the value of the rm s assets before insurance (V ) i.e. that V V . This accretion value is ¼ 0 þ – 14 however diminished by the effect of competition (C). Let PV be the accretion value as a result of insurance, then V V PV C. Ronn and Verma (1986) point out that if the fair price for deposit insurance is charged, then no accretion occurs and V¼ 15 0 16 V , so there is no distortion due to the introduction of deposit insurance. 17 The bank now enters into an insurance contract. The terms of this contract are that if the bank is unable to repay the ’ ’ 18 depositor s portion of its total debt, B1, then the insurer would pay this debt obligation; and in exchange obtain the bank s 19 assets. In this case, payoff (1) remains the same as above, but payoff (2) becomes: < rT ‐ 20 3. If instead VT Be , then the bank would be unable to meet its liabilities and debt holders would receive a maximum amount rT – 21 of VT; incurring a loss equal to Be VT. Without the insurance contract, depositors would be entitled to receive (VTB1)/B, rT – 22 incurring a loss equal to B1e (VTB1)/B. However, because the deposits are insured, the insurer would pay out the full rT – ‐ 23 amount that is owed to depositors and incur a loss of B1e (VTB1)/B. The value of the bank to equity holders in this case 24 would be 0, as before. 25 rT rT The payoff to depositors is therefore B1e , the payoff to equity‐holders ismax{VT – Be , 0}, and the payoff to the insurer is –max 26 rT {0, B1e – (VTB1)/B}. 27 28 3.2 Value of Insurance 29 30 ’ 31 The effect of entering into this insurance contract, from the bank s point of view, is that it is now entitled to receive an additional fl rT – ¼ rT – 32 cash ow equal to max{0, B1e (VTB1)/B} at time T. In other words, at time T the insurance contract is worth IT max{0, B1e fi rT 33 (VTB1)/B}. This is identical to the payoff pro le of an European put option with a strike price of B1e and a stock price of (VTB1)/B; ‐ rT 34 effectively giving the bank the right, but not the obligation to sell the pro rated assets due to depositors for a price of B1e . Using ‐ 35 the Black Scholes formula, we can then calculate the value of I0 as 36 pffiffiffiffi B1 37 I 0 ¼ B1F y þ s T V 0 FðÞy ð1Þ 38 B 39 where F(.) is the cumulative standard normal distribution, s is the instantaneous standard deviation of the rate of return on the 40 bank’s assets, V is the unobserved post‐insurance value of the bank’s assets, and y ¼ [ln(B/V ) – (s2T)/2]/(s√T). Therefore d, the 41 0 0 value of insurance per rand of deposits, is 42 43 pffiffiffiffi UNCORRECTEDI 0 V 0 PROOFS 44 d ¼ ¼ F y þ s T FðyÞð2Þ B B 45 1 46 47 48 3.3 Empirical Application of the Model 49 50 The post‐insurance value of the bank’s assets, V, is unobservable ex ante; and hence the instantaneous standard deviation of return ’ s 51 on the bank s assets, V, is also unobservable. Ronn and Verma (1986) estimate these variables by using the relationship between

1 the volatility of assets and the volatility of equity. If we describe the equity (E) of a bank as a call option on the assets (V) of the 2 bank, with a strike price equal to the total of the debt (D), then using the Black‐Scholes formula: 3 pffiffiffiffi 4 E0 ¼ V 0FðÞx BF x sV T ð3Þ 5 6 where 7 8 ÀÁ ln V 0 þ 1 s2 T 9 x B pffiffiffiffi2 V s 10 V T 11 12 Duan (1994, 2000), however, points out that the shortcoming in the Ronn and Verma (1986) method is that they incorrectly 13 treat the equity volatility as constant. Under the theoretical model of Merton (1977), equity volatility is stochastic. Duan (2000) s 14 shows that it is possible to estimate theoretically correct values for V and V using maximum likelihood estimates from a sample of ’ ‐ 15 a bank s equity values. The log likelihood function for a sample of unobserved Vt is 16 ÀÁXn Xn 2 17 n 1 2 1 V t LV ðÞ¼Vt; t ¼ 1; …; n; m; s ln 2ps lnVt ln m ð4Þ s2 18 2 t¼2 2 t¼2 Vt 1 19 20 Equation 4 defines an element‐by‐element transformation from a sample of unobserved Vt to a sample of observed sample of 21 equity values, Et. Using the results derived in Duan (1994, 2000), the log‐likelihood function for the sample of equity values is 22 therefore 23 hi 24 ÀÁXn ðÞ¼; ¼ ; …; ; m; s n 1 ps2 b ðsÞFðb Þ 25 LEt t 1 n ln 2 ln Vt dt 2 ¼ 26 t 2 "# ! 27 2 1 Xn Vb ðsÞ 28 ln t m ð5Þ s2 b ðsÞ 29 2 t¼2 Vt1 30 b b b 31 where VtðsÞ is a solution to Equation 3 for any s, and dt corresponds to dt with VtðsÞ in place of Vt. The log‐likelihood function 32 in Equation 5 can then be optimized to compute the maximum likelihood estimates for mb and sb (Duan, 1994, 2000). These values 33 can then be substituted into Equation 2 to solve for d. 34 35 36 4. Data 37 38 Daily market capitalization data were collected from Thompson Reuters Datastream (2010). Monthly data on bank liabilities were 39 collected from the DI900 and BA900 databases on the SARB (2011a, 2011b) website. Most of the banks that were examined were 40 part of a larger holding company whose operations did not only include commercial banking. Similar to Ronn and Verma (1986), 41 we assumed that the capital structure of the bank is similar to that of its holding company because market capitalization data are 42 generally only available for the banking group. For most banking groups the large majority of assets are those of the bank. 43 Deposit insurance valuationUNCORRECTED is performed on seven banks. The choice ofPROOFS banks was restricted to those listed on the 44 Johannesburg Stock Exchange (JSE): ABSA Group Limited, African Bank Investments Limited, Capitec Bank Holdings 45 Limited, Firstrand Limited, Investec, Nedbank Limited and Standard Bank Group. 46 Data for the ten‐year period from 2000 to 2009 was collected per bank. Market capitalization and liability data were combined 47 to produce daily equity and debt values for the period — a total of 2,556 observations per bank. The total debt series was updated 48 monthly, owing to its availability. We use the GAUSS code provided by Duan (1994, 2000) to estimate the maximum likelihood 49 estimates for mb and sb. b b 50 The continuous daily returns on bank assets are calculated as ln½VtðsÞ=Vt 1ðsÞ; from this the daily standard deviation can 51 be calculated and annualized based on the number of trading days — between 248 and 262.

1 Table 2: Estimates for deposit insurance premiums per million rand of deposits 2 Absa Bank African Bank Capitec Bank Firstrand Investec Nedbank Standard Bank Weighted Averagea 3 4 2000 6,491 5,023 N/A 293 32 45 46 1,955 5 2001 3,022 197 N/A 171 5,468 355 325 1,437 6 2002 7,159 4,494 3,388 22,796 157,231 357 4,243 19,025 7 2003 5,245 0 0 1,935 54,737 7,346 935 7,008 8 2004 198 0 0 574 12,493 12,136 50 3,732 9 2005 353 0 0 15 36,219 3,637 88 3,072 10 2006 371 0 0 173 5,759 6,648 629 1,999 11 2007 5,992 0 1 1,015 15,208 494 940 3,002 2008 56,039 6,528 3,888 17,867 37,567 8,836 33,412 31,375 12 2009 338 93 81 118 7,582 84 92 645 13 Avg. 8,520 1,633 735 4,495 33,229 3,993 4,076 7,325 14 15 aWeighted by liabilities. 16 17 18 5. Results 19 20 Based on the above methodology, the estimated insurance premiums, per million rand, are reported in Table 2. Complete results 21 for all banks, including estimates of m, s and their standard deviations can be provided on request. 22 The large variation in deposit insurance premiums coupled with the tight confidence bounds, implying a small margin of 23 error, raises the question as to whether the method of Duan (1994, 2000) is inappropriate for determining an actual premium 24 rate as opposed to simply defining risk levels, as some have argued (Ron and Verma, 1986). Clearly it is impractical to 25 change premiums so dramatically from year to year, although any risk‐based scheme must allow for periodic changes in the 26 premium. 27 The model, by taking market information as an input, has advantages and disadvantages. The market is forward looking, which 28 means that the model may be able to pre‐empt periods of high bank risk. However, it is also exposed to the whims of the short‐term 29 stock exchange investor. Since bank runs are linked to market sentiment, this model may in fact be very suitable for modelling this 30 risk. The spike in deposit insurance premiums in 2008 can be explained by the increase in equity volatility over the period of the 31 financial crisis. We model the assets of banks as an element‐to‐element transformation of equity, which results in volatile asset 32 estimates over the period. The model is sensitive to estimates of asset volatility — a result of the Black‐Scholes model, and the 33 effect is that during periods of uncertainty in the stock market, the model will produce extremely high deposit insurance premiums. 34 To better identify two notable characteristics of the data, we plot ln(premium) in Figure 1. The logarithm function 35 rescales the premiums so that the trends are more pronounced. First, we note that the fairly consistent behaviour among 36 the relative bank premiums: the two smaller banks tend to be significantly below the other banks; and Investec tends to be the 37 highest. 38 Secondly, there seems to be some cyclical behaviour, or at least common annual movement for all of the banks, which might be 39 more apparent in Table 2. This is logical, as the premiums reflect JSE valuation, which is subject to common trends for the banking 40 sector. 41 To investigate how closely the series for each bank move together, we calculated the correlations between the banks. The 42 results showed that the deposit insurance premiums of banks are highly correlated, with an average correlation of 0.81. This can be 43 explained by arguing thatUNCORRECTED banks belong to the same industry and are largely exposed PROOFS to the same risks. Nevertheless, the variation 44 among banks is still disturbing and requires further examination. 45 46 6. Conclusion 47 48 Option‐based valuation models provide a ‘first jab’ at what deposit insurance premiums could look like for South African banks. 49 We conclude by discussing several issues that are of relevant to any pricing policy and then propose a hypothetical historical 50 pricing example. 51

1 Figure 1: Variation of ln(premium) over time 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 6.1 The Value of Market‐Based Risk Assessment 26 27 Our model, which utilizes market information as an input, has the advantage of distinguishing theoretically consistent estimates of 28 bank risk. We believe that substantially different categories of bank risk merit different treatment in terms of insurance premiums, 29 as is common internationally (Table 1). Recognizing that the market is also subject to the machinations of short‐term investor 30 sentiment, we would propose using long‐term average premiums, which would tend to smooth out cyclical risk. 31 The first implication of our result is to allow for bank specific premiums. If we assume that the value of deposit insurance is an 32 indicator of the riskiness of a bank, then the argument is that insurance is worth more to a risky bank than a cautious bank. 33 However, given the volatility of our estimates, we would prefer to argue for categories of risk — possibly three for South African 34 banks (see Section 6.4). 35 Secondly, the fluctuation of average premiums over time provides an assessment of banking sector risk, which may be cyclical 36 or have some secular trend. We argue that this is beneficial for estimating insurance premiums. For now, we prefer to average out 37 long‐term variations on the assumption that it smoothes out cyclical market risk. 38 The underlying issue is that the model is very sensitive to estimates of asset volatility — a result of the Black‐Scholes model. 39 The effect is that during periods of uncertainty in the stock market, the model can produce very volatile movements in the 40 calculated deposit insurance premiums. 41 42 6.2 Flat versus Risk‐Adjusted Premiums 43 UNCORRECTED PROOFS 44 The results suggest that the two small banks (African Bank and Capitec Bank) have similar risk profiles, the ‘big 4 banks’ have 45 similar profiles, and Investec stands out as a consistently higher risk. This presents a case for a multi‐tiered deposit insurance 46 premium. There are two main issues: the volatility of the calculated premium and cross‐subsidization. 47 The calculated annual premiums vary in relation to the perceived market risk as observed in the stock market. Such fluctuation 48 creates an additional variable cost to be passed on to the depositor, which is not desirable. Rather, a premium representing the 49 average over a business cycle might be used. In our case, the average option‐based premium over the period 2000 to 2009 is 50 R7,325 per million or 0.007325 per cent of deposits — at the higher end of international standards. 51

1 If we were to introduce a flat‐rate premium, it might seem logical to introduce it at a rate that is the average of the big 4 bank’s 2 risk premium, because they hold about 85 per cent of the assets in the banking industry. However, because the smaller banks are 3 less risky, they would be subsidizing the big 4 banks. Such cross‐subsidization toward riskier, larger banks increases barriers to 4 entry to the banking sector and reduces competition, which is not desirable. Existing literature examining the effects of increased 5 competition within the banking sector show that benefits include increased efficiency (Biekpe, 2011; Mwega, 2011) and 6 decreased risk (Zhao and Murinde, 2011). 7 In our view, a 3‐tier rate structure would provide a competitive advantage to more cautious (lower‐premium) banks, which may 8 not be bad, even if it would be resisted by higher‐risk banks. This would still leave open the issue of a periodic revision of risk to 9 allow for a change in risk categories. Some rule could be established for a shift in premium if a bank maintains a lower risk level 10 for a certain number of years. 11 12 13 6.3 Costs 14 15 Who should bear the financial burden of financing a deposit insurance scheme? If there is an implicit deposit insurance scheme, it 16 becomes a fiscal problem, and the government has to foot the bill using tax payers’ money. An explicit deposit insurance scheme, 17 even if only a partial deposit insurance scheme, has the benefit of more clearly defining the private and public risk exposure. 18 We would also argue that deposit insurance creates positive externalities for the government/SARB in terms of increased 19 stability of the financial sector. This may warrant a government subsidy, as this insurance provides a legitimate social benefit. The 20 exact level of subsidy might be quantified within a cost‐benefit analysis, but we explore some hypothetical situation below. 21 It is our assumption that the costs of deposit insurance would ultimately be passed on to the depositor in the form of higher bank 22 fees or lower deposit rates. Our view is that there is a low likelihood of the banks absorbing the cost out of profits, although 23 banking customers could be reaching their cost limit. 24 25 26 6.4 Hypothetical Historical Example 27 28 For comparison purposes, on a purely hypothetical basis, we assume that one of the big 4 banks fails once every 20 years and loses 29 assets sufficient to cause a loss of half of its deposits. For example, let us use Absa bank, which had deposits in 2009 of R350.8 30 billion that represented 53 per cent of its total liabilities. Let us simplify the calculation by assuming that there is no inflation or 31 cost of debt or administrative costs; so we divide this loss equally among all banks’ depositors over 20 years. This requires an 32 annual contribution of R8.77 billion to the insurance fund. We assume that all seven banks have the same ratio of deposits to total 33 liabilities, which implies total customer deposits of R1,350 billion, based on total banking sector liabilities. Depositors would 34 have to pay a premium of 0.0065 rand per rand insured in order to cover the annual insurance contribution of R8.77 billion. This 35 premium rate, R6,500 rand per million (0.65 per cent) is not substantially different than the weighted average option‐ 36 based premium of R7,325 per million (Table 2). The high premium reflects the concentrated nature of the South Africa banking 37 system — one large banking failure might be equivalent to 10 smaller bank failures. 38 39 40 6.5 Proposal 41 42 We think that a fully private deposit insurance scheme based on the weighted average insurance premium for the seven banks for 43 the 2000–2009 period wouldUNCORRECTED be costly at R7,325 per million rand of deposits PROOFS or 0.7325 per cent. 44 We see two possible modifications. In the first instance, the government provides a flat 50 per cent subsidy, substantially 45 cutting down the incremental cost to the depositor to 0.34 per cent, but still creating a cross‐subsidization problem. This size 46 subsidy is large and fundamentally assumes that the public benefits of this insurance are equal to the private benefits. This level 47 would put South African deposit insurance on a very comparable level to other comparator countries (Table 1). 48 In the second modification, a 3‐tier premium structure is implemented on top of the 50 per cent government subsidy. For this 49 simplified analysis, we calculate a ‘low’ premium as the annual liability‐weighted average premium for African Bank and 50 Capitec; the ‘average’ premium as the average premium of the ‘big 4’; and a ‘high’ premium as the average premium for Investec 51 (Table 3). This 3‐tier approach is intended to assign an appropriate price to different ordinal levels of bank risk, and minimize

1 Table 3: Possible 3‐tier premium scale 2 Premium level Average annual premium without subsidy, cost per million rand 3 4 ‘Low’ 1,619 5 ‘Average’ 7,651 6 ‘High’ 27,744 7 Mean 7,325 8 Source: Calculation by authors, based on liability‐weighted average. 9 10 11 cross‐subsidization. Although the ‘high’ premium level may be excessive in this case, it serves as an example and could easily be 12 readjusted with modest subsidies from the other categories. 13 In conclusion, the authors believe in the public benefits of deposit insurance, and we have presented a strategy for calculating 14 insurance premiums according to an option‐based model, using a multi‐tier premium scale, and including government 15 participation. Such an approach may be the most promising course of action for South African deposit insurance. However, 16 Mwenda and Mutoti (2011) also warn that financial reforms should be done within strong financial infrastructure, lest 17 unintentionally increasing the risk of financial instability. 18 19 Notes 20 21 1. Much has also been written about the traditional moral hazard problem with a deposit insurance scheme, where banks are 22 incentivized to undertake riskier activities (Laeven, 2002) and may even destabilize the financial system (SARB, 2005), but 23 this is not relevant to the focus of this paper. 24 25 26 References 27 28 Biekpe, N. (2011), ‘The Competitiveness of Commercial Banks in Ghana’, African Development Review, Vol. 23, No. 1, 29 pp. 75–87. 30 Chuang, H.‐L., S.‐C. Lee and M.‐T. Yu (2009), ‘Estimating the cost of deposit insurance with stochastic interest rates: the case of 31 Taiwan’, Quantitative Finance, Vol. 9, No. 1, pp. 1–8. 32 ‐ ‘ ’ 33 Demirgüç Kunt, A. and E. Detragiache (1999), Does Deposit Insurance Increase Banking System Stability? Policy Research 34 Working Paper No. 2247, World Bank. 35 Demirguüç‐Kunt, A. and T. Sobaci (2001), ‘A New Development Database: Deposit Insurance around the World’, World Bank 36 Economic Review, Vol. 15, No. 3, pp. 481–90. 37 Duan, J.‐C. (1994), ‘Maximum Likelihood Estimation Using Price Data of the Derivative Contract’, Mathematical Finance, 38 Vol. 4, No. 2, pp. 155–67. 39 40 Duan, J.‐C. (2000), ‘Correction: Maximum Likelihood Estimation Using Price Data of the Derivative Contract’, Mathematical 41 Finance, Vol. 10, No. 4, pp. 461–62. 42 Duan, J.‐C. and J.‐G. Simonato (2002), ‘Maximum likelihood estimation of deposit insurance value with interest rate risk, in 43 Journal of Empirical FinanceUNCORRECTED, vol. 9, pp. 109–132. PROOFS 44 45 FDIC (2010), ‘Failed Bank List’, available at: http://www.fdic.gov/bank/individual/failed/banklist.html (accessed 23 46 August 2010). 47 Flood, M. D. (1990), ‘On the UseQ1 of Option Pricing Models to Analyze Deposit Insurance’, Federal Reserve Bank of St. Louis Q1 48 Review, pp. 19–35. 49 ‘ ’ 50 Giammarino, R., E. Schwartz and J. Zechner (1989), Market Valuation of Bank Assets and Deposit Insurance in Canada , Canadian Journal of Economics, Vol. XXII, No. 1, pp. 109–27. 51

Goldfeld, S. M., R. E. Quandt and H. F. Trotter (1966), ‘Maximization by quadratic Hill‐climbing’, Econometrica, Vol. 34, pp. 541–51. Humphrey, D. B. (1976), ‘100 Percent Deposit Insurance: What Would It Cost?’ Journal of Bank Research, Vol. 7, pp. 192–98. IADI (2010), ‘IADI Members Country DI Information’, available at: http://www.iadi.org/countrydiinfoupdate062209ﬁnalver.xls (accessed 23 August 2010). IMF (2008), ‘South Africa: Financial System Stability Assessment’, IMF Country Report 08/349, International Monetary Fund. Laeven, L. (2002), ‘International Evidence of the Value of Deposit Insurance’, Quarterly Review of Economics and Finance, Vol. 42, No. 4, pp. 721–32. Marcus, A. J. and I. Shaked (1984), ‘The Valuation of FDIC Deposit Insurance Using Option‐Pricing Estimates’, Journal of Money, Credit, and Banking, Vol. 16, No. 4, pp. 446–60. Merton, R. C. (1977), ‘An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees’, Journal of Banking and Finance, Vol. 1, pp. 3–11. Mwega, F. (2011), ‘The Competitiveness and Efﬁciency of the Financial Services Sector in Africa: A Case Study of Kenya’, African Development Review, Vol. 23, No. 1, pp. 44–59. Mwenda, A. and N. Mutoti (2011), ‘Financial Sector Reforms, Bank Performance and Economic Growth: Evidence from Zambia’, African Development Review, Vol. 23, No. 1, pp. 60–74. Ngaujake, U. (2004), ‘Protecting Depositors and Promoting Financial Stability in South Africa: Is There a Case for the Introduction of Deposit Insurance?’ unpublished Master’s thesis, Rhodes University. Okeahalam, C. C. (1988), ‘The Political Economy of Bank Failure and Supervision in the Republic of South Africa’, African Journal of Political Science, Vol. 3, No. 2, pp. 29–48. Ronn, E. I. and A. K. Verma (1986), ‘Pricing Risk‐adjusted Deposit Insurance: An Option‐based Model’, Journal of Finance, Vol. XLI, No. 4, pp. 871–95. SARB (2005), Bank Supervision Annual Report 2005, South African Reserve Bank, Pretoria, pp. 30–32. SARB (2011a), ‘Individual bank’s balance sheets – BA900’, available at: http://www.resbank.co.za/sarbdata/ifdata/periods.asp? type¼BA900 (accessed 27 February 2011). SARB (2011b), ‘Individual bank’s balance sheets – DI900’, available at: http://www.resbank.co.za/sarbdata/ifdata/periods.asp? type¼DI900 (accessed 27 February 2011). Scott, K. E. and T. Mayer (1971), ‘Risk and Regulation in Banking: Some Proposals for Federal Deposit Insurance Reform’, Stanford Law Review, Vol. 23, pp. 857–902. Thompson Reuters Datastream (2010), ‘Market value data’, accessed 10 August 2010. Zhao, T. and V. Murinde (2011), ‘Bank Deregulation and Performance in Nigeria’, African Development Review, Vol. 23, No. 1, pp. 30–43. UNCORRECTED PROOFS

© 2014 The Authors. African Development Review © 2014 African Development Bank 04TeAtos fia eeomn eiw©21 fia eeomn Bank Development African 2014 © Review Development African Authors. The 2014 © Africa South in Insurance Deposit of Valuation Appendix: Deposit Insurance Values

Year Equity Debt ms Assets Premium s.d. m s.d. s Sum of s.d. assets s.d. premium

Absa 2000 18 548 430 000 149 189 901 000 0.09733 0.09748 166 770 012 966 0.00649 0.13879 0.00204 75 511 235 0.00051 2001 22 763 980 000 179 517 943 000 0.18593 0.08197 201 739 341 199 0.00302 0.13327 0.00211 62 441 168 0.00035 2002 20 588 870 000 201 886 052 000 0.07146 0.08764 221 029 631 177 0.00716 0.13115 0.00190 108 928 177 0.00054 2003 27 435 460 000 206 979 978 000 0.04459 0.09638 233 329 904 968 0.00524 0.15831 0.00149 67 006 057 0.00032 2004 49 777 620 000 235 840 563 000 0.22193 0.07799 285 571 379 546 0.00020 0.15391 0.00166 8 519 008 0.00004 2005 67 352 310 000 330 882 808 000 0.20719 0.08136 398 118 430 548 0.00035 0.11611 0.00181 19 916 888 0.00006 2006 84 061 500 000 409 513 264 000 0.16458 0.08244 493 422 867 183 0.00037 0.11700 0.00177 24 814 303 0.00006 2007 75 321 560 000 533 922 295 000 0.18100 0.10405 606 044 715 075 0.00599 0.20006 0.00247 297 402 830 0.00056 2008 73 572 060 000 657 771 276 000 0.10863 0.19765 694 482 564 206 0.05604 0.37547 0.00465 1 862 852 924 0.00283 2009 92 289 880 000 603 579 332 000 0.06914 0.06452 695 665 414 311 0.00034 0.09398 0.00121 28 066 733 0.00005 African Bank 2000 3 331 890 000 3 179 261 000 0.59390 0.36649 6 495 182 507 0.00502 0.37182 0.00954 2 586 230 0.00081 2001 4 474 390 000 4 067 782 000 0.28307 0.25551 8 541 370 942 0.00020 0.26278 0.00532 183 488 0.00005 2002 2 808 930 000 4 176 065 000 0.21103 0.27697 6 966 227 964 0.00449 0.31786 0.00419 1 660 582 0.00040 2003 4 693 140 000 3 991 349 000 0.20948 0.16017 8 684 488 891 0.00000 0.16816 0.00295 53 0.00000 2004 8 731 940 000 4 751 280 000 0.42597 0.19213 13 483 219 992 0.00000 0.20765 0.00362 5 0.00000 2005 12 210 000 000 5 176 123 000 0.23818 0.21932 17 386 122 994 0.00000 0.21981 0.00823 7 0.00000 2006 14 240 250 000 6 457 512 000 0.16488 0.25795 20 697 760 095 0.00000 0.25939 0.01159 1 982 0.00000 2007 16 431 070 000 9 415 776 000 0.18886 0.20514 25 846 845 743 0.00000 0.20601 0.00886 300 0.00000 2008 20 667 290 000 14 845 364 000 0.26482 0.44563 35 415 738 250 0.00653 0.59442 0.00569 7 687 881 0.00052 2009 23 964 400 000 21 185 957 000 0.22178 0.24366 45 148 393 424 0.00009 0.25284 0.00813 802 986 0.00004 Capitec Bank 2000 2001 2002 161UNCORRECTED 130 000 25 686 000 0.95373 0.77824 PROOFS 186 728 969 0.00339 0.90524 0.01391 13 853 0.00054 2003 351 760 000 13 448 000 0.67211 0.59857 365 208 000 0.00000 0.60346 0.01752 0 0.00000 2004 917 090 000 267 155 000 1.17495 0.30752 1 184 244 979 0.00000 0.35253 0.00707 13 0.00000 2005 2 078 730 000 663 231 000 0.75828 0.27095 2 741 960 995 0.00000 0.27425 0.00970 6 0.00000 2006 2 589 420 000 1 085 758 000 0.30105 0.25728 3 675 177 893 0.00000 0.25859 0.00760 80 0.00000 2007 3 359 060 000 1 619 703 000 0.33582 0.26486 4 978 761 206 0.00000 0.27170 0.00626 878 0.00000 2008 2 401 140 000 3 282 983 000 0.11221 0.28463 5 671 357 687 0.00389 0.30796 0.00543 1 493 064 0.00045 2009 6 544 830 000 7 123 947 000 0.85876 0.21098 13 668 199 759 0.00008 0.29234 0.00344 114 334 0.00002 Firstrand 2000 45 740 520 000 108 067 309 000 0.03787 0.13888 153 776 207 446 0.00029 0.15574 0.00302 6 178 792 0.00006 2001 40 567 490 000 131 919 517 000 0.13181 0.10298 172 464 476 870 0.00017 0.12696 0.00265 5 406 735 0.00004 Continued 11 Appendix (Continued) 12 Year Equity Debt ms Assets Premium s.d. m s.d. s Sum of s.d. assets s.d. premium

2002 40 077 410 000 174 002 949 000 0.22827 0.20867 210 113 773 926 0.02280 0.30858 0.00380 227 360 781 0.00131 2003 48 706 030 000 210 768 499 000 0.20076 0.11601 259 066 634 973 0.00194 0.22132 0.00264 52 340 157 0.00025 2004 73 108 880 000 217 678 940 000 0.13401 0.12700 290 662 793 349 0.00057 0.15009 0.00116 8 751 999 0.00004 2005 103 597 300 000 283 487 685 000 0.20569 0.09497 387 080 663 505 0.00002 0.11526 0.00164 999 143 0.00000 2006 125 095 800 000 356 933 165 000 0.20506 0.11399 481 967 081 419 0.00017 0.13349 0.00286 14 772 915 0.00004 2007 111 331 000 000 455 424 615 000 0.17075 0.10868 566 293 536 984 0.00101 0.13300 0.00279 77 136 891 0.00017 2008 90 827 060 000 575 736 180 000 0.06167 0.15341 656 276 639 504 0.01787 0.24916 0.00237 488 686 212 0.00085 2009 103 399 600 000 513 066 356 300 0.05563 0.07088 616 405 537 705 0.00012 0.07831 0.00164 12 964 881 0.00003 Investec 2000 20 330 160 000 40 118 164 000 0.05325 0.12913 60 447 032 475 0.00003 0.13953 0.00272 345 613 0.00001 2001 15 433 290 000 46 984 951 000 0.01059 0.18100 62 161 327 209 0.00547 0.19401 0.00387 26 467 460 0.00056 2002 4 339 140 000 50 824 215 000 0.26164 0.30772 47 172 230 033 0.15723 0.68765 0.00676 272 854 180 0.00537 2003 5 632 000 000 55 580 992 000 0.09716 0.18589 58 170 657 249 0.05474 0.52116 0.00423 146 619 074 0.00264 2004 7 964 000 000 56 482 243 000 0.05440 0.12775 63 740 615 843 0.01249 0.17429 0.00209 37 816 383 0.00067 2005 12 144 000 000 85 927 844 000 0.34901 0.18553 94 959 623 276 0.03622 0.49511 0.00552 232 545 667 0.00271 2006 19 975 880 000 105 788 452 000 0.21791 0.12582 125 155 081 811 0.00576 0.20165 0.00301 61 401 581 0.00058 2007 15 288 800 000 131 289 335 000 0.11895 0.12061 144 581 509 341 0.01521 0.21512 0.00242 119 759 897 0.00091 2008 11 074 340 000 157 035 465 000 0.09320 0.12933 162 210 491 684 0.03757 0.23331 0.00268 264 782 391 0.00169 2009 14 365 070 000 166 697 427 000 0.06991 0.07969 179 798 551 860 0.00758 0.11281 0.00202 105 732 488 0.00063 Nedbank 04TeAtos fia eeomn eiw©21 fia eeomn Bank Development African 2014 © Review Development African Authors. The 2014 © 2000 41 398 390 000 95 931 374 000 0.14752 0.11755 137 325 479 068 0.00004 0.13786 0.00355 1 542 996 0.00002 2001 30 342 790 000 114 603 043 000 0.07104 0.09986 144 905 135 268 0.00036 0.11053 0.00268 8 783 522 0.00008 2002 29 994 040 000 130 709 765 000 0.10485 0.08948 160 657 102 698 0.00036 0.10910 0.00223 9 101 434 0.00007 2003 17 043 010 000 216 928 532 000 0.01059 0.07425 232 378 078 006 0.00735 0.10352 0.00149 104 140 119 0.00048 2004 30 667 360 000 236 109 296 000 0.12223 0.12015 263 911 285 311 0.01214 0.25166 0.00263 202 864 117 0.00086 2005 44 278 210 000 274 994 807 000 0.01252 0.10134 318 272 820 721 0.00364 0.14290 0.00160 71 661 346 0.00026 2006 60 193 050 000 346 658 885 000 0.22140 0.12306 404 547 481 949 0.00665 0.22366 0.00272 203 790 035 0.00059 2007 62 461 790 000 397 517 045 000 0.12697 0.06954 459 782 616 004 0.00049 0.10692 0.00145 28 168 353 0.00007 2008 44UNCORRECTED 783 700 000 472 505 716 000 0.09494 0.08889 PROOFS 513 114 155 519 0.00884 0.13697 0.00244 372 850 760 0.00079 2009 61 860 080 000 474 212 076 000 0.03026 0.04785 536 032 197 506 0.00008 0.05369 0.00090 6 820 773 0.00001 Standard Bank 2000 42 948 730 000 128 992 406 000 0.09312 0.09646 171 935 232 525 0.00005 0.10312 0.00292 2 054 135 0.00002 2001 41 335 300 000 160 107 450 000 0.16110 0.09688 201 390 687 480 0.00033 0.11563 0.00214 9 358 753 0.00006 2002 40 132 000 000 188 289 875 000 0.11717 0.12768 227 622 965 002 0.00424 0.17100 0.00245 71 184 942 0.00038 2003 52 451 410 000 208 193 142 000 0.13391 0.10978 260 449 843 606 0.00094 0.12995 0.00132 15 552 855 0.00007 2004 88 968 630 000 255 083 880 000 0.26115 0.10074 344 039 840 169 0.00005 0.16291 0.00175 2 518 859 0.00001 Cheng R. and Ellyne M. 2005 102 524 100 000 408 715 204 000 0.11699 0.08198 511 203 265 734 0.00009 0.08738 0.00121 5 309 453 0.00001 2006 128 723 700 000 493 935 001 000 0.17788 0.10634 622 348 174 214 0.00063 0.14493 0.00191 40 226 646 0.00008 2007 137 369 400 000 613 253 984 000 0.18486 0.10061 750 046 654 863 0.00094 0.14367 0.00205 76 480 660 0.00012 2008 126 575 600 000 829 304 023 000 0.18923 0.18770 928 170 630 829 0.03341 0.29791 0.00415 1 598 824 906 0.00193 2009 158 942 100 000 759 707 970 000 0.04528 0.07117 918 580 192 152 0.00009 0.08691 0.00134 12 720 584 0.00002