IIMFC2022016-V006400

Summary

This script delves into the concept of duration gap analysis, a critical tool for financial institutions to assess their exposure to interest rate risks. It explains the process of calculating the market value of equity and the weighted average duration of assets and liabilities. The example provided illustrates how a 1% change in interest rates can significantly impact the market value of a firm's equity, emphasizing the importance of this analysis for understanding and managing financial risk.

Takeaways

• 📊 Duration Gap Analysis is a method to measure a bank's exposure to interest rate risks, focusing on the sensitivity of the market value of its equity to interest rate movements.
• 🏦 The market value of equity is calculated by multiplying the number of equity shares issued by the firm by the market price per share.
• 📈 The process involves three main steps: bucketing risk-sensitive assets and liabilities, computing the modified duration of these assets and liabilities, and assessing the impact on net interest income and market value of the firm when interest rates change.
• 📋 Duration is a key concept in this analysis, representing the weighted average time to receive the present value of cash flows from an asset or liability.
• 📉 The duration of an asset or liability is calculated by multiplying the present value of cash flows by the time period and dividing by the market value of the asset or liability.
• 💹 The weighted average duration for assets and liabilities is used to calculate the duration Gap, which indicates the bank's overall interest rate risk exposure.
• 📝 The net interest income is derived from the interest earned on assets and the interest paid on liabilities, reflecting the bank's profitability from interest rate spreads.
• 📉 An increase in interest rates will generally decrease the market value of assets with longer durations more significantly than those with shorter durations.
• 📈 A decrease in the duration Gap indicates a reduction in the bank's interest rate risk exposure, as the weighted average duration of assets becomes more aligned with that of liabilities.
• 💡 Duration Gap Analysis is a valuable tool for financial institutions to manage interest rate risk and is often a mandatory reporting requirement by central banks.
• 🌐 The impact of interest rate changes on a bank's market value of equity can be substantial, affecting stakeholders and investors' confidence in the institution.

Q & A

What is duration Gap analysis in the context of a financial institution?

Duration Gap analysis is a method used to measure the sensitivity of a bank's market value of equity to changes in interest rates. It assesses the bank's exposure to interest rate risks by examining the impact of interest rate movements on the market value of its equity.

What are the steps involved in performing a duration Gap analysis?

The steps in duration Gap analysis include: 1) Bucketing all risk-sensitive assets and liabilities based on residual maturity or repricing dates into various time bands, 2) Computing the modified duration of the risk-sensitive assets and liabilities, and 3) Using these measures to assess the impact on net interest income and the market value of the firm when interest rates change.

How is the market value of equity calculated?

The market value of equity is calculated by multiplying the number of equity shares issued by the firm by the market price per share. It reflects the current market price at which the firm's shares are trading.

What is the significance of the 'duration' column in the spreadsheet example?

The 'duration' column is fundamental to duration Gap analysis. It represents the sensitivity of the market value of the assets and liabilities to changes in interest rates, and it is used to determine the potential impact of interest rate changes on the financial institution.

Can you explain how the duration of a financial instrument is calculated?

The duration of a financial instrument is calculated by summing the present value of each cash flow, multiplied by the time period it is received, and then dividing this sum by the total present value of all cash flows. This gives a weighted average time to receipt of cash flows, which is the duration.

What is the purpose of calculating the weighted average duration for assets and liabilities?

The weighted average duration for assets and liabilities helps to determine the overall sensitivity of a financial institution's balance sheet to interest rate changes. It provides a measure of how much the net interest income and market value of equity might change with a shift in interest rates.

How is the net interest income calculated in the context of duration Gap analysis?

Net interest income is calculated by taking the interest income from assets, such as loans and bonds, and subtracting the interest expenses on liabilities, such as deposits. The rates used are the current market rates, and the calculation takes into account the market values of these financial instruments.

What is the duration Gap, and how is it calculated?

The duration Gap is the difference between the weighted average duration of risk-sensitive assets and the weighted average duration of risk-sensitive liabilities. It is calculated by subtracting the duration of liabilities (adjusted for their market value as a proportion of total assets) from the duration of assets.

What impact does a change in interest rates have on the market value of equity according to the duration Gap analysis?

A change in interest rates affects the market value of equity inversely to the duration Gap. If interest rates rise, and the duration Gap is positive (assets have a longer duration than liabilities), the market value of equity will decrease, and vice versa.

Why is duration Gap analysis important for financial institutions and their stakeholders?

Duration Gap analysis is important because it helps financial institutions manage and communicate the risk associated with interest rate fluctuations. It provides stakeholders with insights into how sensitive the institution's profitability and equity value are to changes in the interest rate environment.

How might central banks use duration Gap analysis in their regulatory framework?

Central banks may mandate the inclusion of duration Gap analysis in financial reporting requirements to ensure that financial institutions are transparent about their interest rate risk exposure. This allows regulators and investors to assess the institution's risk profile and financial stability.

Outlines

00:00

📊 Duration Gap Analysis Fundamentals

This paragraph introduces the concept of Duration Gap analysis, a method used to assess a bank's exposure to interest rate risks. It explains how the market value of equity is calculated and how the analysis involves three main steps: bucketing risk-sensitive assets and liabilities, computing the modified duration of these assets and liabilities, and estimating the impact on net interest income and the market value of the firm due to interest rate changes. A spreadsheet example is used to illustrate the calculation of duration for different financial instruments like CDs, commercial loans, and treasury bonds, emphasizing the importance of duration in assessing interest rate risk.

05:03

📉 Impact of Interest Rate Changes on Duration and Equity Value

This section delves into the weighted average duration calculation for both assets and liabilities, and how it affects the net interest income. It also explains the concept of the duration Gap, which is the difference between the weighted average duration of assets and liabilities. The paragraph presents a hypothetical scenario where a 1% increase in interest rates impacts various financial instruments differently, based on their duration. It demonstrates how this change affects the market value of assets and liabilities, ultimately leading to a decrease in the market value of equity for the financial institution. The summary highlights the importance of understanding the sensitivity of a firm's equity to interest rate fluctuations.

10:07

🏦 Duration Gap Analysis in Financial Regulation

The final paragraph discusses the practical application of Duration Gap analysis in the financial industry, emphasizing its importance in regulatory compliance. It mentions that several central banks mandate the inclusion of Duration Gap analysis in financial reporting to ensure stakeholders are informed about the institution's exposure to interest rate risks. The paragraph concludes with an example of how a 1% interest rate increase can significantly impact the market value of equity, illustrating the substantial effect of interest rate changes on a financial institution's valuation.

Keywords

💡Duration Gap Analysis

Duration Gap Analysis is a financial tool used to measure a bank's exposure to interest rate risk by assessing the sensitivity of the market value of its equity to changes in interest rates. It is central to the video's theme as it is the main method discussed for evaluating interest rate risk. The script explains how it involves bucketing risk-sensitive assets and liabilities, computing their modified durations, and then using these measures to predict the impact on net interest income and market value of equity when interest rates fluctuate.

💡Market Value of Equity

The market value of equity refers to the total value of a firm's outstanding shares of stock at the current market price. It is a key concept in the video, as the changes in this value due to interest rate movements are the primary focus of duration gap analysis. The script clarifies that this is calculated by multiplying the number of equity shares by the market price per share and is used to illustrate the financial impact of interest rate changes on a firm's equity value.

💡Risk-Sensitive Assets and Liabilities

Risk-sensitive assets and liabilities are financial instruments whose cash flows are affected by changes in interest rates. In the context of the video, these are the components that are 'bucketed' and analyzed in the duration gap analysis. The script provides examples such as CDs, commercial loans, and treasury bonds, which are categorized based on their repricing dates into different time bands to assess their interest rate risk.

💡Modified Duration

Modified duration is a measure used to calculate the sensitivity of a bond's price to changes in interest rates. It is a critical component in the video's explanation of duration gap analysis. The script demonstrates how to calculate the modified duration for different financial instruments, such as CDs, commercial loans, and treasury bonds, by multiplying the present value of cash flows by the time period and dividing by the bond's market value.

💡Net Interest Income

Net interest income is the difference between the interest income earned on a bank's assets and the interest expenses paid on its liabilities. It is a key financial metric in the video, as changes in this income due to interest rate fluctuations are a direct result of the duration gap. The script shows how to calculate net interest income by applying interest rates to the market values of assets and liabilities and then adjusting for the duration gap.

💡Weighted Average Duration

Weighted average duration is the average duration of a portfolio of financial instruments, weighted by their market values. It is used in the video to summarize the overall interest rate risk of a bank's assets and liabilities. The script illustrates the calculation by summing the products of market values and durations for each instrument, then dividing by the total market value of the portfolio.

💡Interest Rate Risk

Interest rate risk is the risk that the value of a firm's fixed-income securities will decline due to a rise in market interest rates. The video discusses this risk extensively, explaining how duration gap analysis helps financial institutions understand and manage this risk. The script provides a scenario where a 1% increase in interest rates impacts the market value of equity, demonstrating the practical implications of interest rate risk.

💡Yield to Maturity (YTM)

Yield to maturity, or YTM, is the total return anticipated on a bond if it is held until it matures. It is a fundamental concept in the video's discussion of bond valuation and duration calculation. The script uses YTM to calculate the present value of cash flows for various financial instruments, showing how changes in YTM affect their market values and durations.

💡Macroeconomic Context

The macroeconomic context refers to the economic environment in which financial institutions operate, including factors such as interest rates, inflation, and economic growth. The video uses a change in the macroeconomic context to illustrate how a 1% increase in interest rates affects the duration gap and the market value of equity. This concept is essential for understanding the external factors that can influence a bank's financial performance.

💡Financial Reporting Requirements

Financial reporting requirements are the mandatory standards and guidelines that financial institutions must follow when presenting their financial statements. The video mentions that several central banks have mandated the inclusion of duration gap analysis in these reports. This highlights the importance of transparently communicating a bank's exposure to interest rate risk to stakeholders.

Highlights

Duration Gap analysis measures a bank's exposure to interest rate risks by assessing the sensitivity of the market value of equity to interest rate movements.

Market value of equity is calculated as the number of equity shares multiplied by the market price per share.

The process involves bucketing risk-sensitive assets and liabilities based on repricing dates into various time bands.

Computing the modified duration of both risk-sensitive assets and liabilities is a key step in the analysis.

The impact of interest rate changes on net interest income and the market value of the firm is measured using duration Gap.

A spreadsheet example illustrates the balance sheet of a financial institution with rate-sensitive assets and liabilities.

Duration is fundamental to Duration Gap analysis and is calculated for each financial instrument.

The duration calculation for a 3-year CD involves present value of cash flows and the face value realized at maturity.

Duration is computed by multiplying the present value of cash flows by the year and dividing by the market value.

The weighted average duration for assets and liabilities is calculated to determine the duration Gap.

Net interest income is derived from the interest earned on assets and paid on liabilities.

The duration Gap is calculated by subtracting the weighted average duration of liabilities from that of assets.

Equity is the residual market value after accounting for risk-sensitive liabilities.

A scenario analysis demonstrates the impact of a 1% interest rate increase on the financial institution's market value.

The change in interest rates affects the duration and market value of securities, with longer durations experiencing greater impacts.

An increase in interest rates results in a decrease in the market value of assets and equity for the financial institution.

Duration Gap analysis is a crucial tool for financial institutions to understand and manage interest rate risk.

Several central banks mandate the inclusion of Duration Gap analysis in financial reporting to inform stakeholders of interest rate risk sensitivity.

Transcripts

duration Gap analysis measures the level

of A bank's exposure to interest rate

risks in terms of the

sensitivity of the market value of its

Equity to movements in interest rates

please recall market value of equity is

the number of equity shares issued by

the firm multiplied by the market price

per share duration Gap analysis involves

the following steps one bucketing all

risk sensitive assets and risk sensitive

liabilities exactly as in the repricing

Gap analysis based on the residual

maturity or repricing dates in the

various time bands step number two

Computing the mol

duration of the risk sensitive assets

and risk sensitive liabilities and step

number three using the above measure the

impact on the net interest income the

duration Gap and most importantly the

market value of the firm when interest

rates change let's look at a spreadsheet

example to understand this in detail so

what we have here is a condensed balance

sheet of a financial

institution reflecting essentially the

assets and liabilities which are rate

sensitive and what is also shown here is

not the book value of the assets and the

book value of liabilities but it is the

market value of assets and the market

value of liabilities as already

explained earlier market value is the

price at which these instruments are

quoting in the market what you will also

notice is a column called

duration and this is fundamental to

duration Gap analysis we will see how

this duration is computed and what is

its role in determining interest rate

risk let's go through how this duration

is calculated let's take this threeyear

CDs the market value of this CD is 300

and the interest rate is 7% now what you

will see here is the duration

calculation for this CDs so what we have

here is the cash flows at 7% for 3 years

plus the face value which will be

realized at the end of the three years

and if you compute the present value of

these cash flows remember the coupon is

7% and the eeld to mature it is also 7%

so when you compute the present value of

the cash flows it should add up to 300

now to calculate duration what you do is

you take this figure multiply by the

year which is what is reflected in this

column so how did we arrive at

36.6 it is 18.34%

ated

as this figure divided by this figure

which in this case works out to

2.88 we've done exactly the same thing

for the six-year commercial loans the

six-year commercial loans is 700 at 12%

and what you see here is the cash flows

700 into 12% every year for 6 years and

the face value of 700 and you compute

the present value of those cash flows

the total should come up to 700 because

the yield to maturity at this point in

time is equal to the coupon rate of 12%

and finally the 10year treasury bonds we

do exactly the same arithmetic at 8% on

200 cash flows of 16 for 10 years at the

end of the 10th year the face value of

200 would be realized the present value

would be also 200 because YTM is 8% and

the coupon rate is also 8% and the

duration is calculated exactly as we did

before which is multiply the year into

the present value of the cash flow and

the total of that works out to as you

can see 1449 38 that 14 49.38.07

7 years so what we have transcribed here

is this

2.88 for the 3E CDs the

4.65 which is the duration for these

commercial loans and 7.24 7 which is the

duration for the 10-year treasury bonds

what you have here is the weighted

average of the duration for the

liabilities and the Assets Now how did

we calculate that it is uh 100 into the

duration cash duration is zero 700

into

4.65 + 200 into 7.24 7 divided by 1,00

would give you a figure of

4673 and this weighted average duration

is also computed in exactly the same

manner also important to note the net

interest income therefore is 700 into

12% plus 200 into 8% minus 620 into 5%

minus 300 into 7% That's how we arrived

at this figure of 48 and the duration

Gap let me explain this duration

calculation to you we have 4.67 3 years

on a total assets of 1,000 whereas this

1.59 is on a total assets of of

920 so in order for us to compute like

for like we need to take the duration

Gap we we start with 4.67 3 which is the

weighted average of the duration for the

risk sensitive assets minus

1.59 into

920 divided by 1,000 because remember

the risk sensitive liabilities are only

920 and therefore this 1.59 needs to be

adjusted in order to be able to do a

realistic subtraction and that gives you

a weighted average duration of

3.21 the other point to bear in mind and

I'm going to come back to this again a

little later the equity is the market

value of equity which is total assets

1,000 so by the law of accounting we

should have total liabilities also equal

to 1,000 but the risk sensitive

liabilities total up only to

920 and therefore the mark market value

of equity is the residue which is 1,

minus

920 what we have summarized here is what

we saw in the previous spreadsheet the

weighted average duration for the assets

was 4.67 3 and the weighted average

duration for the liabilities is

1.59 and the net interest income was 48

and the market value of equity was 80

now here's a scenario where let us say

the macroeconomic context in the country

changes and as a result the interest

rate on all risk sensitive assets and

liabilities would change for ease of

understanding I have assumed an interest

rate change of 1% so onee time deposits

the interest rate now goes up from 5% to

6% threee CDs it goes up from 7% to 8%

six-year commercial loans goes up from

12% to 133% and 10e treasury bonds goes

up from from 8% to 9% the Assumption

we've made here is all the changes in

interest rates are equal that's to make

our life simple in this example in the

real world they do not go up by exactly

the same proportion let us see what this

one% rate change does to our duration

and therefore to the market value of

equity of this financial institution if

you look at this computation threee CDs

remember earlier it was 300 so why did

it drop from 300 to

292.00 it's fairly straightforward the

cash flows that means the coupon on

these CDs is 7% so on 300 it is 21 each

year the YTM now is 8% and therefore the

present value of the cash flows would be

computed as shown in this column and the

total of that works out to

29227 and in the duration computation we

do exactly what we did before which is

multiply the present value into the

number of years and the total of that

works out to

8199 and if you now calculate the

duration for the CDs it is

8199 divided by

292.00 five years the point to note here

is with the 1% increase in interest

rates the duration which was earlier

2.88 has now come down to

2.85 and more importantly if you take

the 10year treasury bonds using exactly

the same logic the cash flows at 8% were

16 on 200 for a period of 10 years the

present value would now be because the

coupon was 8% and the YTM is now 9% the

present value of the cash flows will now

add up to

1887 and the duration computed would

change to

7146 which was

7247 earlier now please note because the

T bonds have a maturity of 10 years the

change in the duration is much more than

for example the change in the duration

in the case of the 3year CD

remember what we learned earlier longer

the duration more will be the impact on

the market value of the Securities you

will also notice that with these change

in interest rates the net interest

income would come down to

47800 more importantly if you look at

the weighted average duration it has

come down from

1.59 to 1.57 eight and the weighted

average duration of the asset has come

down from 4.67 3 to

4599 and the duration Gap as a

consequence has come down from 3.21 0 to

3.98 most important and this is where we

study the impact of interest rate risk

on the market value of the firm the

market value of assets have dropped to

9591

18 but if you look at the market value

of the risk sensitive liabilities it

totals up only to

market value of the equity falling from

80 to

46.9 so if you we an equity stockholder

in this financial institution you will

find this 1% increase in interest rate

has hurt the market value of your Equity

by substantial amount moving from 80 to

4691 so as we saw in that spreadsheet

example duration Gap analysis helps us

determine the magnitude of change in the

net interest income and more importantly

the market value of equity when interest

rates change this methodology would

apply equally effectively to any

financial

institution several central banks around

the world have mandated financial

institutions under their jurisdiction to

include duration Gap analysis as part of

the mandatory financial reporting

requirements in order that the

stakeholders of that financial

institution are made aware of the

sensitivity of interest rate risks on

the market price of that institution's

Equity stock price

[Music]