Theme
Demand Deposit
Title
Hedging Interest Rate Margins on Demand Deposits
Author
Mohamed Houkari, Jean-Paul Laurent ;
Université de Lyon, Université Lyon 1, ISFA Actuarial School, and BNP Paribas Financial
Models Team
Year
2010
INTRODUCTION
Under IFRS – the new 2005 international accounting standards – banks account demand deposits at amortized cost. Moreover, the US Securities and Exchange Commission asks American banks to report in annual (10-K) and quarterly (10-Q) documents, indicators concerning interest rate margins and their sensibilities to interest rate shocks. However, in internal processes, many banking establishments perform the computation of full fair-value indicators for the market value of equity. As for demand deposits, the well-known fair-value approach developed for example in Hutchison and Pennacchi (1996) and Jarrow and van Deventer (1998) has been the main way to assess demand deposits so far.
PROBLEM
A worldwide study of the Bank for International Settlements shows that risk mitigation in interest rate margins has been a significant concern for banks during these last twenty years.
PURPOSE
Show how interest rate margins have become a major point of concern for banking establishments today, with a focus on the US case. Propose a modeling framework for demand deposits, interest rates and the interest rate margin.
RESEARCH METHODOLOGY
With Modeling Framework
Market Rates
We consider some time horizon T such that we deal with the corresponding quarterly interest rate margin. Besides, we assume that the forward Libor rate at horizon date T for the time period δT > 0 of the interest rate margin follows a Libor Market Model, as defined in Brace, Gatarek and Musiela (1997) and Miltersen, Sandmann and Sondermann (1997): dL L ( dt dW (t)) t t L L L = μ +σ , (1)
Demand Deposit Amount
We assume that the demand deposit amount follows:
dK K ( dt dW (t)) t t K K K = μ +σ (2)
where K W is a standard Brownian motion. For simplicity, the trend K μ and the volatility K σ
The correlation between the variations of demand deposit amount and that of interest rates can be related to money transfers between deposit accounts and other types of deposits.
We refer to the Engle and Granger method detailed in Ericsson and MacKinnon (1999) to estimate the correlation parameter between the deposit amount and the market rate. Janosi et
al. (1999) use a very similar method, although they also pay attention to autocorrelation and short term effects.
RESULTS AND ANALYSIS
The negative values for the ES and the VaR in the upper line are due to the fact that the margin at final date is mostly positive16. Thus, the VaR at 99.95% of the interest rate margin is (-1.90) for an initial deposit amount of 100. We see, in Table 5.6a above, that using the optimal dynamic hedging strategy makes the risk decrease by 0.39 to (-2.29), thus constituting a better risk reduction than other strategies, in this VaR framework. The same actually holds for the ES and the standard deviation.
In general, the risk reduction implied by the optimal dynamic strategy is almost always more significant: even when there is no customer rate, it goes to 0.45 in ES and 0.46 in VaR. This shows some robustness of the optimal dynamic strategy also with respect to the choice of the risk criterion. Moreover, this somehow makes us confident with the meanvariance optimization framework, more tractable than some mean-VaR or mean-ES framework.
CONCLUTIONS
In this article we dealt with the mitigation of the risk contained in interest rate margins. We assume the demand deposit amount to carry some source of risk called ‘business risk’, orthogonal to market risk. Thus, we compared these dynamic strategies with some static strategies. We show that identifying the interest rate-related optionality in interest rate margins is a quite satisfactory alternative to dynamic hedging strategies. Moreover, both this method and the use of dynamic strategies lead to quite robust results, with respect to the margin’s profile specification.
However, the use of dynamic strategies also better deals with the specific risk embedded in demand deposits. Moreover, we show that they also exhibit some robustness with respect to the risk criterion. This is a positive conclusion for the use of mean-variance optimization and the related dynamic hedging strategies, since they display good results with respect to other risk measures.
Senin, 01 Agustus 2011
JOURNAL ANALYSIS
Theme
Demand Deposit
Title
Global Games and Demand-Deposit Contracts:
An Experimental Study of Bank Runs _
Author
Alexander Klos, Norbert Sträter
Finance Center Münster
Year
January 2008
INTRODUCTION
Firstly, the global games approach can eliminate the multiplicity of equilibrium present in classic panic based bank run models (Diamond and Dybvig (1983)). Therefore, the probability of a bank run can be calculated, which is a useful number when thinking about policy implications. Secondly, the global games approach allows an integration of two related, but different views found in the literature on financial stability. The panic-based view stresses that bank runs are random events, unrelated to changes in the real economy. Panic-based bank runs might even occur when the economic environment issue efficiently strong. In contrast to this, the fundamental view assumes that bank runs are a natural of the business cycle and only occur in connection with negative real shocks. In the global games approach, it is possible that fundamental runs occur, if the fundamentals of the economy and therefore the signals which agents receive are very bad. However, in other situations, fundamentals may be good enough so that the prevention of a bank run is desirable from the viewpoint of the depositors, but runs still occur due to strategic uncertainty about others' beliefs. Moderate signals about the fundamental state of the economy may lead to the belief that other agents withdraw with a high probability. In such a situation it is rational to withdraw also. In that sense, moderate expectations about the fundamental state of the financial system can trigger panic-based bank runs.
PURPOSE
Our paper is related to the recently started experimental investigation of bank runs. Schotter and Yorulmazer (2005) investigate in a policy oriented study the factors that affect the severity of fundamental bank runs. In their setup a bank run occurs by any means; they investigate how quickly the depositors withdraw their money. Their results indicate that partial deposit insurance and the existence of insiders may mitigate bank runs.
RESEARCH METHODOLOGY
In laboratory scenarios inspired by theoretical models, subjects receive a noisy private signal about the true fundamental state of the banking system. Subjects employ threshold strategies and low rates of deviation from threshold strategies.
Reviewing the theory generates a number of hypotheses which follow directly from the intuitions mentioned in the introduction. We focus on two of them:
Hypothesis 1: Subjects use threshold strategies.
Hypothesis 2: Banks become more vulnerable to bank runs when they offer more risk sharing.
RESULTS AND ANALYSIS
that higher thresholds for higher repayment rates can be observed in between- and withinsession comparisons. This result contradicts the view that within-designs point subjects to the differences the researcher investigates, and are therefore not as reliable as between-subjects experiments (see Camerer (2003), page 41 _ 42, for a brief discussion).
To test the statistical significance of the results, we take two different approaches. In light of the discussion of different matching protocols in section 2, the most conservative way to analyze the data is to analyze estimated thresholds on the session level.
Evidence on the session level
We have two observations per session (TS), one for r1 = 1.25 and one for r1 = 1.5, resulting in a total of 16 observations, eight for model A and eight for model B. We run linear regressions separately for both models to infer the influence factors of session thresholds. Dummy variables for the degree of risk sharing (RD) and the ordering of risk sharing conditions (OD) are used as explanatory variables.
TSi = const + _1 • RD + _2 • OD + _i
It turns out that the dummy for a low degree of risk sharing is significantly negative for both models as predicted by the theory. The ordering of risk sharing conditions does not have a significant impact.
Evidence on the individual level
Stronger evidence for the key role of offered risk sharing can be provided by the analysis of thresholds estimated on the individual level. As already mentioned above, we estimate an individual threshold for decisions under the conditions r1 = 1.25 and r1 = 1.5. Therefore, we have two matched observations per subject. We apply a non-parametric Wilcoxon test, separately for every session, consequently based on thirty matched observations of individual thresholds.
CONCLUTION
Our results suggest that the global games approach applied to bank runs leads to experimentally valid predictions with respect to the comparative statics. Both hypotheses are supported by the data: Our subjects use threshold strategies and increased risk sharing leads to increased thresholds at the individual and the aggregate level.
However, the rather small reaction of thresholds to changes in the repayment rates is at odds with the theory. This result is important with respect to the socially optimal repayment rate. One major advantage of the global games approach is the ability to trade off the benefits of high repayment rates (increased risk sharing) with its costs (increased probability of a bank run). Such a social optimization requires valid predictions about how people react to changes in the repayment rates. At least in our experimental setup, this assumption is questionable.
Demand Deposit
Title
Global Games and Demand-Deposit Contracts:
An Experimental Study of Bank Runs _
Author
Alexander Klos, Norbert Sträter
Finance Center Münster
Year
January 2008
INTRODUCTION
Firstly, the global games approach can eliminate the multiplicity of equilibrium present in classic panic based bank run models (Diamond and Dybvig (1983)). Therefore, the probability of a bank run can be calculated, which is a useful number when thinking about policy implications. Secondly, the global games approach allows an integration of two related, but different views found in the literature on financial stability. The panic-based view stresses that bank runs are random events, unrelated to changes in the real economy. Panic-based bank runs might even occur when the economic environment issue efficiently strong. In contrast to this, the fundamental view assumes that bank runs are a natural of the business cycle and only occur in connection with negative real shocks. In the global games approach, it is possible that fundamental runs occur, if the fundamentals of the economy and therefore the signals which agents receive are very bad. However, in other situations, fundamentals may be good enough so that the prevention of a bank run is desirable from the viewpoint of the depositors, but runs still occur due to strategic uncertainty about others' beliefs. Moderate signals about the fundamental state of the economy may lead to the belief that other agents withdraw with a high probability. In such a situation it is rational to withdraw also. In that sense, moderate expectations about the fundamental state of the financial system can trigger panic-based bank runs.
PURPOSE
Our paper is related to the recently started experimental investigation of bank runs. Schotter and Yorulmazer (2005) investigate in a policy oriented study the factors that affect the severity of fundamental bank runs. In their setup a bank run occurs by any means; they investigate how quickly the depositors withdraw their money. Their results indicate that partial deposit insurance and the existence of insiders may mitigate bank runs.
RESEARCH METHODOLOGY
In laboratory scenarios inspired by theoretical models, subjects receive a noisy private signal about the true fundamental state of the banking system. Subjects employ threshold strategies and low rates of deviation from threshold strategies.
Reviewing the theory generates a number of hypotheses which follow directly from the intuitions mentioned in the introduction. We focus on two of them:
Hypothesis 1: Subjects use threshold strategies.
Hypothesis 2: Banks become more vulnerable to bank runs when they offer more risk sharing.
RESULTS AND ANALYSIS
that higher thresholds for higher repayment rates can be observed in between- and withinsession comparisons. This result contradicts the view that within-designs point subjects to the differences the researcher investigates, and are therefore not as reliable as between-subjects experiments (see Camerer (2003), page 41 _ 42, for a brief discussion).
To test the statistical significance of the results, we take two different approaches. In light of the discussion of different matching protocols in section 2, the most conservative way to analyze the data is to analyze estimated thresholds on the session level.
Evidence on the session level
We have two observations per session (TS), one for r1 = 1.25 and one for r1 = 1.5, resulting in a total of 16 observations, eight for model A and eight for model B. We run linear regressions separately for both models to infer the influence factors of session thresholds. Dummy variables for the degree of risk sharing (RD) and the ordering of risk sharing conditions (OD) are used as explanatory variables.
TSi = const + _1 • RD + _2 • OD + _i
It turns out that the dummy for a low degree of risk sharing is significantly negative for both models as predicted by the theory. The ordering of risk sharing conditions does not have a significant impact.
Evidence on the individual level
Stronger evidence for the key role of offered risk sharing can be provided by the analysis of thresholds estimated on the individual level. As already mentioned above, we estimate an individual threshold for decisions under the conditions r1 = 1.25 and r1 = 1.5. Therefore, we have two matched observations per subject. We apply a non-parametric Wilcoxon test, separately for every session, consequently based on thirty matched observations of individual thresholds.
CONCLUTION
Our results suggest that the global games approach applied to bank runs leads to experimentally valid predictions with respect to the comparative statics. Both hypotheses are supported by the data: Our subjects use threshold strategies and increased risk sharing leads to increased thresholds at the individual and the aggregate level.
However, the rather small reaction of thresholds to changes in the repayment rates is at odds with the theory. This result is important with respect to the socially optimal repayment rate. One major advantage of the global games approach is the ability to trade off the benefits of high repayment rates (increased risk sharing) with its costs (increased probability of a bank run). Such a social optimization requires valid predictions about how people react to changes in the repayment rates. At least in our experimental setup, this assumption is questionable.
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