## Bank ALM: Liquidity Risk. Cost-to-Close Example

*in*Asset Liability Management

# Bank ALM reports. Cost to Close gaps

Earlier we had considered an ALM Liquidity risk measure, namely the Cost-to-Close Liquidity Gap methodology. In this post we will look at an example of this risk measurement technique.

The measure is illustrated below for Bank Example at a high level, i.e. it is assumed that individual asset and liability cash flows have already been slotted into the relevant time buckets and have been summed:

**Time Buckets (in years)**

(USD in millions) | 0.08 | 0.25 | 0.50 | 0.75 | 1 | 3 | 5 |

Assets | 1 | 3 | 4 | 9 | 10 | 8 | 7 |

Liabilities | 2 | 4 | 0 | 5 | 12 | 3 | 2 |

Liquidity Gap | –1 | -1 | 4 | 4 | -2 | 5 | 5 |

We will assess a Gross Cost-to-Close first by taking into account only positive gaps and then by taking into account both negative and positive gaps. For positive gaps the gap will be filled by borrowing from the market at the borrowing rate. For negative gaps the gap will be filled by lending the excess funds at the lending rate. This is illustrated for Bank Example below:

**Time Buckets (in years)**

(USD in millions) | 0.08 | 0.25 | 0.50 | 0.75 | 1 | 3 | 5 |

Liquidity Gap | -1 | -1 | 4 | 4 | -2 | 5 | 5 |

Lending Rate | 15% | 14% | 0.50 | 0.75 | 1 | 3 | 5 |

Borrowing Rate | 12% | 11% | 11% | 11% | 13% | 14% | 15% |

Gross Cost to Close (only positive gaps) | – | – | 0.22 | 0.33 | – | 2.10 | 3.75 |

Cumulative Gross Cost to Close (only positive gaps) | – | – | 0.22 | 0.55 | 0.55 | 2.65 | 6.40 |

Gross Cost to Close (all gaps) | (0.01) | (0.04) | 0.22 | 0.33 | (0.30) | 2.10 | 3.75 |

Cumulative Gross Cost to Close (all gaps) | (0.01) | (0.05) | 0.17 | 0.50 | 0.20 | 2.30 | 6.05 |

For each time bucket, the Gross Cost to Close (only positive gaps) is calculated as the Liquidity Gap (if positive) times the Borrowing Rate applicable to that time bucket times the Time Bucket Tenor (upper bound expressed in years). For example, for the time bucket with upper bound 6 months (o.5 years):

Gross Cost-to-Close (only positive gaps) = 4*11%*0.50 = USD 0.22 million.

Cumulative Gross Cost-to-Close (only positive gaps) is the cumulative sum of Gross Cost-to-Close (only positive gaps) for each time bucket up to and including the relevant bucket. For example the Cumulative Cost-to-close (only positive gaps) for time bucket 5 years is the sum of all the Gross Cost-to-Close (only positive gaps) time buckets up to 5 years, i.e. USD 6.4 million.

The Gross Cost-to-Close (all gaps) is calculated as:

the Liquidity Gap

times

either the Borrowing Rate if the Gap is positive or the Lending Rate if the Gap is negative

times

the Time Bucket Tenor (upper bound expressed in years).

For example the Gross Cost-to-Close (all gaps) for the time bucket 9-12 months (1 year) = -2*15%*1 = USD -0.30 million.

The Cumulative Gross Cost-to-Close (all gaps) is the cumulative sum of Gross Cost-to-Close (all gaps) for each time bucket up to the relevant bucket. For example the Cumulative Cost-to-Close (all gaps) for time bucket 5 years is the sum of all the Gross Cost-to-Close (all gaps) time buckets up to 5 years, i.e. USD 6.05 million.

We will also calculate an annualized cost to close, i.e. we will scale the cost to close amounts for those buckets which are beyond 1 year to 1 year. Cost to close amounts for periods less than one year will be taken as is. This is illustrated below:

**Time Buckets (in years)**

(USD in millions) | 0.08 | 0.25 | 0.50 | 0.75 | 1 | 3 | 5 |

Annual Cost to Close (only positive gaps) | – | – | 0.22 | 0.33 | – | 0.70 | 0.75 |

Cumulative Annual Cost to Close (only positive gaps) | – | – | 0.22 | 0.55 | 0.55 | 1.25 | 2.00 |

Annual Cost to Close (all gaps) | (0.01) | (0.04) | 0.22 | 0.33 | (0.30) | 0.70 | 0.75 |

Cumulative Gross Cost to Close (all gaps) | (0.01) | (0.05) | 0.17 | 0.50 | 0.20 | 0.90 | 1.65 |

For each time bucket, the Annual Cost to Close (only positive gaps) is calculated as the Liquidity Gap (if positive) times the Borrowing Rate applicable to that time bucket times the Time Bucket Tenor (upper bound expressed in years). The tenor is subject to a maximum of 1 year. For example, for the time bucket with upper bound 3 years:

Annual Cost-to-Close (only positive gaps) = 5*14%*1 = USD 0.70 million.

Cumulative Annual Cost-to-Close (only positive gaps) is the cumulative sum of Annual Cost-to-Close (only positive gaps) for each time bucket up to the relevant bucket. For example the Cumulative Annual Cost-to-close (only positive gaps) for time bucket 5 years is the sum of all the Annual Cost-to-Close (only positive gaps) time buckets up to 5 years, i.e. USD 2 million.

The Annual Cost-to-Close (all gaps) is calculated as the Liquidity Gap times either the Borrowing Rate if the Gap is positive or the Lending Rate if the Gap is negative times the Time Bucket Tenor (upper bound expressed in years). The tenor is subject to a maximum of 1 year. For example the Annual Cost-to-Close (all gaps) for the time bucket 3-5 years (5 years) = 5*15%*1 = USD 0.75 million.

The Cumulative Annual Cost-to-Close (all gaps) is the cumulative sum of Annual Cost-to-Close (all gaps) for each time bucket up to the relevant bucket. For example the Cumulative Annual Cost-to-Close (all gaps) for time bucket 5 years is the sum of all the Annual Cost-to-close (all gaps) time buckets up to 5 years, i.e. USD 1.65 million.

When there is a positive gap it means that the bank has invested or lent money. This cash outflow will earn an interest income. We are therefore also interested in what the net cost to close will be across all positive gaps after taking into account the average return that will be earned on assets. This is illustrated below for Bank Example:

The weighted average return on assets the Bank Example will earn is the sum product of the positive gaps times the lending rates applicable to the relevant time buckets divided by the total of all the positive gaps, i.e.

Average Return on Assets (%) = (4*14%+4*14.5%+5*18%+5*18%)/(4+4+5+5) = (0.56+0.58+0.90+0.90)/18 = 2.94/18 = 16.33%.

Average Return on Assets = 16.33% * 18 = USD 2.94 million

Net Cost-to-Close = Cumulative Gross Cost to Close (only positive gaps) – Average Return on Assets = 6.4 -2.94 = USD 3.46 million.

We have presented a simple example of the Cost-to-Close Liquidity Gap methodology above which may be used to measure the liquidity risk as part of a bank’s ALM and Liquidity Management process.