Lecture Materials ASSET/LIABILITY MANAGEMENT – YEAR 1

Lecture Materials

ASSET/LIABILITY MANAGEMENT – YEAR 1

Thomas A. Farin Chairman of the Board

FARIN Financial Risk Management Fitchburg, Wisconsin

[email protected] 608-661-4219

August 4, 2017

Introduction to Interest Rate Risk

Jim JohannesPuelicher Center for Banking Education

UW-MadisonPresented by: Tom Farin

Why Interest Rate Risk (IRR) is Important in Banking?1. If your earnings are volatile because of interest rate

movements, the stock market will punish your stock price. The stock market does not like volatile earnings.

2. There are actually two sides of a bank.

Interest Side (NIM) Non Interest Side (Burden)

Interest Income (000’s) $10,354,697 Non Interest Income $2,543,240Interest Expense (000’s) $ 1,132,473 Non Interest expense $8,174,598

NII $9,222,224 Net Non Interest Income -$5,631,358

Data is for Discover Bank 2013

→ Interest Side is really Important! If you lose on the Interest Sideyour bank is

All Commercial Banks $300-$500 million

Also, a bank’s ROA can be really sensitive to what happens on the Interest side of the bank!

Net Income ROA NIM Burden

Banks $300-500 Million 2656401 0.0099 0.0373 -0.0228

Banks $1 -10 billion 14196511 0.0114 0.0389 -0.0197

If lose 20% of NII and tax

Banks $300-500 Million 707357 0.0026 0.0298 -0.0228

Banks $1 -10 billion 5533080 0.0044 0.0311 -0.0197

Punch line20% NII or NIM gamble is a 73% ROA gamble!

Why such a large difference? NII or NIM is before the effect of the burden.

ROA is after the effect of the burden.

-20%-73%

However, this is not to say fee income is not important! Fee Income is very important as well.

Without fee income, ROAs would be negative. Is fee income subject to changes in interest rates? What if a substantial portion of fee income is mortgage origination fees?

3. Regulators are very interested in Capital Plans at insured financial institutions. Interest risk impacts ROA and therefore K/A ratio …so you better know how to measure and manage interest risk!

We talked about the role of ROA in the BPA section on capital planning.

DIDMCA 1980Garn-St. Germain 1982

Interstate Banking Act 1994

Financial Modernization Act 1999

4 ...and margin is already harder and harder to come by to begin with!

5. If you cannot protect margins only alternative is to grow (i.e. apply lower margins to more earning assets)

or get merged out of existence!

Income Statement

Two types of interest risk!

Balance Sheet

Two Major Types of Interest Risk

1. Income Statement Risk

risk that movements in interest rates will cause your net interest income to vary. This is commonly referred to as Net Interest Margin Risk

Government Yield Curve

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8

Maturity (years)

Inte

rest

Rat

e

Loan Yield – 8%

Visualizing the basic problem…HOW Bank’s MAKE $: Typical situation: borrow 1 year CD’s, make 5 year auto loan

Initial Spread8% - 2% = 6%

X

Rates rise 3%Funding Cost increases to 5%Spread will fall to 8% - 5% = 3%

CD Cost – 2%

2. Balance Sheet Risk

Risk that movements in interest rates will cause true value of your assets and liabilities to vary, thereby causing the true value of your equity capital to vary. This is called Net Economic Value (NEV) or Economic Value of Equity (EVE) Risk

Market Value Risk of Assets & Liabilities

$100 $90

Assets Liabilities & Equity

$10$88

-$1

..and if FDIC had to take you over they would lose money, the deposit insurance fund would decrease and somebody would end up getting taxed!

$89

So, the term interest risk, or interest sensitivity, refers to changes in Net Interest Income or Market Value of Capital caused by

1) changes in interest rates and 2) the maturity (repricing possibilities) of assets and liabilities.

The KEY point to notice is that we Can’t control these … but we can to large degree control this

30 Year Conventional Mortgage RateBank Prime Rate

So to manage interest risk, we will use things we can control (asset and liability maturities) to offset Impact of things we cannot control (interest rates)

Now we will look at the basic forces at work in each type of interest risk • For income statement risk it is the impact

interest rates have on interest income and interest expense because of the maturities of our assets and liabilities

• For balance sheet risk it is the impact interest rates have on market valuations of our assets and liabilities

…and we will look at the diagnostic tools we use to identify, measure and manage Interest Risk

• For income statement risk it is our “GAP” and our asset and liability “betas”

• For balance sheet risk it the “duration” of our assets and liabilities

I. Income Statement Risk or NIM Risk

Start by visualizing the bank’s Assets and Liabilities

And FOCUS on how quantities of these will matter. We will address other issues that will matter shortly.

Basic Types of Assets & LiabilitiesDefine Rate Sensitive Assets (RSA) as assets that will be repriced(ie. Interest rate will change) within GAPPING PERIOD.

maturity test (does it mature before end of GAP period)

amortization test (do I recover $ I can reinvest before end of GAP period)

refinance test (will someone prepay, forcing me to reinvest, before end of GAP period)

Rate Sensitive Liabilities (RSL) as liabilities that will be repricedwithin gapping period

Then define GAP = RSA - RSL

Think about us rewriting our balance sheet to look like this:

Rate Sensitive Assets(RSA’s)

Rate Sensitive Liabilities(RSL’s)

Fixed Rate Assets(FRA’s)

Fixed rate Liabilities (FRL’s)

Assets Liabilities

RSA’s

So why is this “GAP” so important?

$400

RSL’s$300

FRA’s$100

FRL’s$200

No Risk In This PartRSA’s funded by RSL’sSo Whatever HappensOn one side of B/S gets Offset on the Other Side

No Risk In This partBecause No Rate Change Here To Begin With.FRA’s funded by FRL’s

This Part Is RISKYRSA’s funded by FRL’s

Examples to Demonstrate the Basics

Let’s set up a “straw” bank to get the basics down:Simple “Textbook” Bank

Assets So in this part of bank Liabilities

RSA FUNDED

BY RSL

FRA FUNDED

BY FRL

Rate SensitiveAssets RSA$400

Rate SensitiveLiabilities RSL

$400

Fixed Rate Assets FRA$100

Fixed Rate LiabilitiesFRL $100

.10*$100 = $10

.09*$400 = $36

.11*$400 = $44

.07*$400 = $28

Interest Income $46 less Interest Expense $35 = $11If rates up 2% $54 less $43 = $11If rates down 2% $38 less $27 = $11

.07*$400= $28

.09*$400= $36

.05*$400= $20

.07*$100 = $7

So is the key to explaining this result?

This is called a match funded bank• It has a zero GAP because RSA-RSL =0• All of its RSA’s are funded by RSLs• RSA = RSL or RSA/RSL = 1

If there is no funding mismatch, there will be no impact on our NII if rates change.

Why? Because all of our repriceable assets ($400) are financed by an equal amount of repriceable deposits ($400).

Therefore, if rates rise, whatever extra interest we pay on deposits ($8 in this case) will be offset by an equal interest gain on loans ($8).

Assets So in this part of bank Liability

RSA $400

FRA $100

RSL $300

FRL $200

RSA’s are partially funded with RSL’s

FRA’s are funded with FRL’s

$100 of RSA’s are funded by$100 of FRL’s!

09*$400 = $36.11*$400 = $44.07*$400 = $28

.07*$300= $21

.09*$300= $27

.05*$300 = $15

.10*$100 = $10 .07*$200 = $14

Interest Income $46 less Interest Expense $35 = $11If rates up 2% $54 less $41 = $13

If rates down 2% $38 less $29 = $9

So what is the key to explaining this result?

This is called an asset sensitive bank. It has more assets that might reprice than liabilities.• It has a positive GAP because (RSA-RSL)>0• Some of its RSA’s are funded by FRLs• RSA > RSL or RSA/RSL > 1

If there is a funding mismatch movements in interest rates will cause our NII to change!

Why? In this case because we have $100 of repriceable assets that are financed by liabilities that will not reprice.

Therefore, if rates rise we will make extra money ($2) because we will get 2% more on the $100 of repriceable assets but we do not have to raise the rate on the $100 of fixed rate liabilites that funded the $100 of assets!

If rates fall, we will lose $2? Why?


RSA $200

FRA $300

RSL $300

FRL $200

RSA’s are funded with RSL’s


$100 of FRA’s are funded by$100 of RSL’s!

09*$200 = $18.11*$200 = $22.07*$200 = $14

.07*$300= $21

.09*$300= $27

.05*$300 = $15

.10*$300 = $30 .07*$200 = $14



So what is the key to explaining this result?

This is called a liability sensitive Bank because if rates change more liabilities might reprice than assets. • It has a negative GAP because RSA-RSL< 0• It has FRA’s funded by RSL’s• RSA < RSL and RSA/RSL < 1

Again, if there is a funding mismatch movements in interest rates will cause our NII to change!

Why? In this case because we have $100 of fixed rate assets that are financed by $100 of liabilities that will reprice!

Therefore, if rates rise we will lose $2 because we will have to pay 2% more on the $100 of repriceable liabilites but we cannot raise the rate on the assets the $100 financed.

…but, if rates fall, we will make $2? Why?

Quick Summary

The difference between RSA and RSL is called the banks

GAPIf the difference is zero, NII is “immunized” (in this simple world).

If the difference is not zero, you have a potential problem.

If the difference is positive, rising rates lead to increasing NII.

If the difference is negative, falling rates lead to increasing NII.

So GAP measures funding mismatch or your interest risk exposure

Example of Real $GAP Table that Tries to Identify Interest Risk Exposure

Gold Banc, Kansas

Incremental GAP or

Maturity bucket

Cumulative GAP (Sum of Incremental Gaps)

$GAP/EA !! OUR RISK EXPOSURE MEASURE

Maturity Buckets (also called incremental gaps)

Why Do We Use Incremental GAPS (Multiple Buckets)?

$400 RSL’s

$400 RSA’sJan Feb Mar Apr May Jun Jul Aug Sept Oct Nov

Dec

What is the bank’s 1 Year GAP? 0!!What will happen to NII if rates rise on Jan 1 by 1%?Pay extra $4 in interest expense ($400 x 1%)but make only $0.33 in interest expense $400 x 1%/12 so we would lose $3.67 even with a 0 GAP!

SO WHAT HAPPENS IN THE REAL WORLD?

TWO THINGS HAPPEN IN THE REAL WORLD THAT MAKE OUR SIMPLE “rules of thumb for GAP ” WRONG.

1) When market rates change, distribution of assets & liabilities across the buckets change. (Option risk)

2) Rates on assets & liabilities change by different amounts in response to changes in market rates (Basis risk and different pricing betas).

Let’s look at these issues a bit.

Consider this positively gapped bank

Assets Liabilities

1. FRA 100 FRL 200

RSA 400 RSL 300

2. iFRA = .10 iRSA = .09 iFRL = .07 iRSL = .07

3. NII = .10(100) + .09(400) - .07(200) - .07(300)

= $10 + $36 - $14 - $21 = $11

Suppose Rates Rise by 2% SIMPLE RULE TELLS US TO EXPECT THIS

4. ∆NII = (RSA - RSL)∆I = GAP • ∆I = ($400-$300)(.02) = $100 x .02 =$2

∆NII = .10(100) + .11(400) - .07(200) - .09(300) = $13

WHAT WILL HAPPEN REALLY?

5. NII = .10(150) + .11(350) - .07(50) -.09(450)

= $15 + $38.50 - $3.50 - $40.50 = $9.50

150

350

50

450

What Really Happened? We lost $1.50 not gained $2!

Example – On asset side increaseIn rates causes prepayments to slow.On liability side increase in ratescauses CD customers to break theircontracts to reset CDs to higher rates.This is what caused the ’Thrift Crisis.’

This says that in the real world you need something that can account for changes in quantities and types of assets & liabilities and that is a SIMULATION MODEL

You need this sort of model for another reason as well, rates can change by different amounts!

Jargon: Asset and Liability BetasIn finance, a stock beta describes how an individual stock’s return moves with the overall market.

In banking, the rate you charge on your loans might not change exactly as the market rate in your area.

Similarly, the rate you pay on your deposits might not change exactly as the market rate in your area.

This latter phenomenon is commonly referred to as your banks “asset beta” and “deposit beta”. These “betas” capture the idea that your rates do not move exactly with the market.

I will now demonstrate the implication of this differential pricing for income statement interest risk management.

This is the phenomenon we want to capture

This is a real world problem for banks as this discussion from a bank 10K indicates!Says even though Asset and liabilities might have the same maturities, the rates on these identical maturity assets and liabilities might change by different amounts!

So, how can we address this real world problem?

What if rates on assets & liabilities move by different amounts? Suppose your asset rates move with the market but your liability rates

do not.

Liability (Deposit) rates might be sluggish relative to asset rates because you don’t want to be the first bank in town to lower your deposit rates (or raise them) after the Fed lowered (raised) rates

Asset (Loan) rates might be sluggish because loans are tied to prime and deposits to LIBOR

Now what do we do to assess and manage interest risk?

Two Examples to Help You Understand the basics of What is Going On

Example I: A Zero Gapped Bank

What would our textbook model say would happen to its NII if interest rates change?

Nothing, the bank is match funded!

But what if your asset beta =1 (i.e. your loan rates move with the market) and your liability beta is .33 (i.e. your liability rates moves 1/3 of the market movement).

Now assume asset rates change 3% and therefore liability rates change by 1%.


RSA $600

09*$600 = $54.12*$600 = $72.06*$600 = $36

FRA $400

RSL $600

.07*$600= $42

.08*$600= $48

.06*$600 = $36

FRL $400



.10*$600 = $60.07*$400 = $28



Example II:

• Negative GAP positions in banking are quite natural because depositors tend to deposit short and borrowers tend to borrow long.

• So suppose we have a negative GAP and rates rise. What would the textbook model say will happen? NII will fall!

• Let’s see what actually happens if liability rates are sluggish (deposit rates lag behind movements in market rates.)


RSA $400

FRA $1000

RSL $1200

FRL $200




09*$400 = $36.12*$400 = $48.06*$400 = $24 .07*$1200= $84.00

.08*$1200= $96.00

.06*$1200 = $72.00

.10*$1000 = $100

.07*$200 = $14


If rates down 3% $124 less $86 = $38Immunized!

Suppose your ALM group, anticipating rising rates, tried to set a positive GAP but couldn’t quite get there.

So with rate rises imminent, you are worried that NII will drop because of this negative GAP

Let’s see what happens.


RSA $600

FRA $800

RSL $1200

FRL $200




09*$600 = $54.12*$600 = $72.06*$600 = $36 .07*$1200= $84.00

.08*$1200= $96.00

.06*$1200 = $72.00

.10*$800 = $80

.07*$200 = $14.00


If rates down 3% $124 less $86 = $30Had a negative GAP andMade more when rates rose!

What? A negative GAP can immunize NII in a rising rate environment?

Yes, and a negative GAP can increase NII if liability rates are sluggish (lag behind movement in market rates)!

GAP

0 GAPImmunizing GAP( RSA - βRSL) or-$800 in our example

For all GAPS larger than -$800 (like our -$600 GAP) NII rises if rates rise (even a 0 GAP!)

For all GAPS smaller than -$800, NII will fall if rates rise.

Intuition? If liability rates change by 1/3 of asset rates (i.e alpha = .33) we need 3 times more RSL liabilities than RSA assets to generate equal size but offsetting changes in interest expense and interest income!

Cumulative $GAP is NEGATIVE $200(RSA’s = $750 mill, RSL’s = $950 mill)

A Real Bank

What should happen if rates rise?

…but what does the Simulation Result say?

Says if rates go up 300bp (3%) income will go up $3.4 million!How can this be?

Now if quantities are not fixed AND rates rise by different amounts you really have a problem using simple “back of the envelope” rules like

ΔNII = ( RSA - RSL) * ΔiRSAor

ΔNII = ( RSA - αRSL) * ΔiRSA

so you need a

Simulation Model

to run different scenarios.

Intro to another type of interest riskNet Economic Value (NEV) Risk

“Institutions should measure the potential impact of changes in market interest rates on the economic value of capital. Measuring risk to capital generally requires institutions to use some type of long-term economic or market-value-based process. Risk to capital has traditionally been measured by analyzing the effects of various interest rate scenarios through either a long-term discounted cash flow model such as economic value of equity (EVE), net economic value (NEV), or models assessing anticipated changes in net present value (NPV) or duration.”

NEV Risk has to do with the other dimension of interest rates:

As interest rates change the value of your assets and liabilities to other changes!

Assets Liabilities

$100 $90

What FDIC getsFor your assets if they have to sell them What they have to pay someone to takeyour assets your liabilities

This is what the regulators will insist you can produce

How do rate changes Affect Market Value of Capital

How do rate changes affect Market Value of K/A

Let’s start with “How does a change in interest rates change the market value of my capital?”

Market Values! ∆K/K∆(K/A)

The Basic Principles You Need to Understand this Interest Risk

• Real Value of an asset is what you can sell it for, i.e. its market value.

• MKT Value of Capital equals MKT Value of Assets minus MKT Value of Liabilities

Original K/A ratio = $25/$100 = 25% New K/A ratio = $5/$75 = .07%

Assets $100 Liabilities $75

Net Worth = Capital = $25

● Market Value depends on level of Interest Rates. If rates rise, market value falls.

• Impact Rates have on market prices depends on maturity of assets or liabilities. Usually, longer the maturity the bigger is the change in price given a change in interest rates

$75

$70

$5

TWO Key Concepts for NEV Risk:

1. Asset Prices and Interest Rates

Q? What would you pay another bank for a loan or bond that promised you $100 in 1 year?

A: It’s present value….so if interest rates are 1% you would pay $99

PV = Asset’s Price to an investor = = $99

Q? What would you pay if the interest rate in the market was 10% ?

PV = Asset’s Price to an investor = = $91

$100 1.01

$100 1.10

So asset values and interest rates move in opposite directions

2. Not all asset or liability valuations respond the same way to changes in interest rates.

Some are very sensitive meaning if rates change by some amount (say 1%) their price will change a lot!

Some are less sensitive meaning if rates change by some amount (say 1%) their price will not change by a lot!

Two important sub-points:

• In general, this sensitivity depends on the maturity of the asset or liability.Usually, the longer is the maturity the more sensitive is the value to changes

to interest rates (see next slide)

• This sensitivity has a name in finance. It is called “duration”

But, it is not really the Maturity that matters but the DURATION.

In General The Longer the Maturity of Cash Flows the More Sensitive an Asset’s Price is to Interest Rates, i.e. the longer is its Duration. An example.

Consider a Longer Term 10 year Loan Consider A Shorter Term 3 year Loan

Period

Cash Flow Loan A

Present Value at 3%

Present Value at 6% Period

Cash Flow Loan B

Present Value at 3%

Present Value at 6%

1 $100 97.09 94.34 1 $100 97.09 94.342 $100 94.26 89.00 2 $100 94.26 89.003 $100 91.51 83.96 3 $100 91.51 83.964 $100 88.85 79.215 $100 86.26 74.73 282.86 267.306 $100 83.75 70.507 $100 81.31 66.518 $100 78.94 62.749 $100 76.64 59.19

10 $100 74.41 55.84

853.02 736.01

Price Falls by 13.72% Price Falls 5.5%

Duration is just a measure of how much the market price of a financial asset changes when interest rates change. That is

…and the change is inverse- if rates up, prices down and vice versa.

Percent change in pricePercent change in interest rates

Using Duration

- .10 = - 5 x .02- .08 = - 8 x .01

Percent Change in Price Duration Change in Interest Rates

$100 $ 90

$10

$90 $81

$9

Example of 1st case: Rates rise 2% and duration of both assets and liabilities is 5. Both will fall 10% in value

Simple Application of ThisPrinciple:

Is now a good time to Invest in Bonds?

15 year fixed 30 year fixed

Look How Duration Rises if Rates Rise!If you have these in portfolio and rates rise you will have huge capital losses.

Duration of ARM is a little less than the lock period and pretty stable so not as much risk.

Where do you get the durations of assets and liabilities?

1. From services like Bloomberg2. Web based calculators3. From Your Own ALM Software Systems4. From regulators

To understand Net Economic Value further look at this bank which has LT assets and ST liabilities (durations in parentheses)

100 (5) 99 (1)

1 NEV

If rates rise 1%

95 98

-3 NEV

Mkt Value K = 1%Mkt Value A

Mkt Value K = -3%Mkt Value A

So what happened here? It’s assets had a higher duration and were therefore moreSensitive to the increase in interest rates. As a result asset value fell more than liabilityvalue and capital was lost.

100 (5) 99 (1)

1 NEV

If rates fall1%

105 100

5 NEVSo what happened here? Again, assets had a higher duration and were more sensitive to interest rates so when rates fell the value of assets increased more than the value of liabilities. Hence the value of capital increased.

Could have a million examples!

Point is that how sensitive the market value of your K and K/A ratio is to interest rate changes depends on how sensitive your assets and liabilities are-i.i on the durations of your assets and liabilities.

Same bank, different interest rate change (rates fall)

Mkt Value K = 1%Mkt Value A

Mkt Value K = 4.8%Mkt Value A

Now let me show you 3 really important things

• Because banks are highly levered, the market value of your equity (K) can be really sensitive to changes in interest rates even if your assets and liabilities are not that sensitive

• The strategy that immunizes K is different from the one that immunizes K/A

• To immunize K/A you need to match durations. To immunize K you need to set

dA = (L/A)dL

A. Just because your bank has short-term assets and short-term liabilities does not mean the entire bank is protected against interest risk. In particular, your capital (market value) might be very exposed. Example: let subscripts denote duration

1002 951 Let Rates Rise 1% 98 94

5 Becomes 4

A 1% change in interest rates changes the market value of the bank’s capital by 21%. I will show you in a minute that leverage is the culprit!

This is a 20%change in Capital!

B. Matching durations does not immunize capital.

10010 9010 Now let rates 90 81

10 rise 1% 9

Capital not immunized. It falls from 10 to 9.

What does it immunize?

K/A ratio 10/100 = 10% K/A Ratio = 9/90 = 10%

Matching immunizes the K/A ratio!

How would you immunize K if you wanted to do that?

The immunizing strategy is to set dA = (L/A)dL .

1009 9010 91 81

10 10

Example: Suppose rates are expected to rise. For the market value of K to rise, dGAPK must be negative; i.e.

LdAL

Ad <

1008 9010 92 81

10 11

Assuming rates rise 1%.

How did I know all this?Because there are relevant formulas!

iA)LdAL

Ad(K ∆−−=∆

iKA)LdA

LAd(K

K ∆−−=∆

iAL)LdAd(A

K ∆−−=∆

(1)

(2)

(3)

% Change in K = - (duration of K) Δi

Leverage Impactclearly shows up here!

Immunize K set ( ) =0!

Immunize K/A set ( ) = 0

• DOESN’T THIS CREATE AN INCONSISTENCY?• TO MANAGE ∆NII USING $GAP, IF RATES RISE I WANT A

POSITIVE $GAP• NOW, TO MANAGE MARKET VALUE ∆K USING DGAP, I

NEED TO HAVE A NEGATIVE DGAP• HOW CAN I DO BOTH?

• REALLY THE SAME THING!• POSITIVE $GAP → RSA>RSL→HAVE STA, LTL• NEGATIVE DGAP→DA<(L/A)DL→HAVE STA,LTL

• SAME BALANCE SHEET STRATEGY

Q. Suppose your boss says “immunize the bank against interest risk!” What do you ask him or her?

A. Immunize what? NII or K or K/A

Q. What do you say if the boss says “immunize everything!”.

A. Impossible!!

To immunize K set da - L/A dL = 0

To immunize K/A set da - dL = 0

Both cannot be true at same time unless L/A = 1 which means you have no capital to begin with and the regulators would have shut you down!

Also what is the likelihood that the GAP that immunizes NII, especially in the alpha world will create the right duration gap?

Summarizing our Primer on Interest Risk

The Universe is Expanding…

but what is it expanding into?

http://www.robgendlerastropics.com/NGC7331NMM.html

http://www.robgendlerastropics.com/NGC7331NMM.html

Lecture Materials ASSET/LIABILITY MANAGEMENT – YEAR 1

Documents