chapter 12 introduction to asset liability management what is in this chapter? introduction duration...
Post on 22-Dec-2015
239 views
TRANSCRIPT
![Page 1: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/1.jpg)
CHAPTER 12Introduction to Asset Liability Management
What is in this Chapter?
INTRODUCTION
DURATION GAP
SOURCES OF INTEREST-RATE RISK
ALM RISK versus MARKET RISK
Mortgage-backed Securities (MBS)
![Page 2: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/2.jpg)
INTRODUCTION
Asset liability management (ALM) interest rate risk: The interest-rate risk arises from the
possibility that profits will change if interest rates change.
liquidity risk: The liquidity risk arises from the possibility of losses due in the bank having insufficient cash on hand to pay customers.
Both risks are due to the difference between the bank's assets and liabilities.
![Page 3: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/3.jpg)
INTRODUCTION
The best illustration of ALM : U.S. savings and loan (S&L) crisis Savings and loan banks: retail banks, receive retail
deposits and make retail loans For many years, interest rates stable. Deposits for
around 4% (floating rate), and they lent 30-year mortgages paying about 8% at fixed rates.
Then in the 1980s, the Federal Reserve allowed interest rates to float. Short-term interest rates rose to 16%.
![Page 4: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/4.jpg)
Many deposit customers withdrew their funds or demanded the higher rates
The rate of mortgages is fixed with 8%, however the rate of deposits is floating and the banks have to pay 16% to deposit customers
This causes the banks a lot of loss and go to bankrupt
![Page 5: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/5.jpg)
INTRODUCTION
Several keys of the above example The rate of deposit is floating and the rate of mortgage
is fixed The deposit (loan) is more (less) sensitive to interest
rate Or, the deposits (one kind of banks’ liabilities) is rate-
sensitive and the mortgage (one kind of banks’ assets) is rate-insensitive
The interest rate risks will rise when the RSL (rate-sensitive liabilities) is not equal to RSA (rate-sensitive assets)
![Page 6: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/6.jpg)
Duration of First National Bank's Assets and Liabilities
Duration in year (or in %)
0.4 X (5/100)
![Page 7: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/7.jpg)
Review: Duration Analysis
![Page 8: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/8.jpg)
![Page 9: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/9.jpg)
9
Duration Gap Analysis
%V DUR r
r 5%, from 10% to 15%
Asset Value = %P Assets
= 2.7 .05 $100m
= $13.5m
Liability Value = %P Liabilities
= 1.03 .05 $95m
= $4.9m
NW = $13.5m ($4.9m) = $8.6m
DURgap = DURa [L/A DURl]
= 2.7 [(95/100) 1.03]
= 1.72
%NW = DURgap r
= 1.72 .05
= .086 = 8.6%
NW = .086 $100m
= $8.6m
![Page 10: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/10.jpg)
Example of Finance Company
![Page 11: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/11.jpg)
![Page 12: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/12.jpg)
Duration Analysis
If r 5%
Duration Gap Analysis
DURgap = DURa [L/A DURl]
= 1.16 [90/100 2.77] = 1.33 years
% NW = DURgap X r
= (1.33) .05
= .0665 = 6.5%
![Page 13: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/13.jpg)
Managing Interest-Rate Risk
Strategies for Managing Interest-Rate Risk
In example above, shorten duration of bank assets or lengthen duration of bank liabilities
To completely immunize net worth from interest-rate risk, set DURgap = 0
Reduce DURa = 0.98 DURgap = 0.98 [(95/100) 1.03] = 0
Raise DURl = 2.80 DURgap = 2.7 [(95/100) 2.80] = 0
![Page 14: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/14.jpg)
SOURCES OF INTEREST-RATE RISK
Figure 12-1a illustrates a possible scenario
Figure 12-1b shows the net interest income (NII), i.e., interest income minus interest costs
![Page 15: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/15.jpg)
SOURCES OF INTEREST-RATE RISK
Figure 12-1c: noninterest expenses are partially floating
Figure 12-1d : the result is the net earnings for the bank
![Page 16: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/16.jpg)
ALM Risk vs. Market Risk
The measurement of ALM risks is made more difficult than the management of a simple bond portfolio. because of the indeterminate maturities of assets and
liabilities. The indeterminate maturity describes the uncertainty as
to when customers will make or ask for payments We will discuss the above behaviors in detail in the
following discussion Uncertain prepayment and withdraw behaviors
![Page 17: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/17.jpg)
ALM Risk vs. Market Risk
What are the differences between the risk of the structural interest-rate position and the market risk of the trading room? In the trading room, all transactions are clearly
structured. With bonds, the maturity is known, and the term is fixed by the contract underlying the security.
![Page 18: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/18.jpg)
ALM Risk vs. Market Risk
In contrast, ALM products such as mortgages and deposits have many implicit or embedded options that make the values dependent not only on market rates, but also on customer behavior.
For example, customers have the option to withdraw their deposit accounts whenever they wish, or to prepay a mortgage early if they find a cheaper mortgage elsewhere.
![Page 19: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/19.jpg)
Mortgage-backed Securities (MBS)
In the United States, there is a large market of traded mortgage-backed securities (MBS) 不動產抵押貸款債券 In an MBS, the payments from many mortgages are pooled together. This pool of payments is then used to guarantee payments on several tranches of bondsThe tranches can also be split as to whether they are entitled to the interest payments only (IO) or principal payments only (PO)
![Page 20: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/20.jpg)
Mortgage-backed Securities (MBS)
The value of a tranche principal payments increases when prepayments increase because the cash flows happen sooner
Tranches entitled to interest payments drop significantly in value when prepayments occur because the interest-payment stream stops
The valuation of payment streams therefore depends heavily on customer behavior.
![Page 21: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/21.jpg)
Mortgage-backed Securities (MBS)
The Public Securities Association (PSA) has published a standard for the expected conditional prepayment rate (CPR)固定提前清償率 It says that 0% are expected to prepay in the first month, rising linearly to 6% per annum at month 30
Thereafter, each year 6% of the remaining borrowers are expected to prepay
An MBS with a prepayment rate matching this profile is said to be at 100% PSA. An MBS with twice the prepayment rate would be at 200% PSA
![Page 22: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/22.jpg)
Mortgage-backed Securities (MBS)
A term related to CPR is the SMM (single monthly mortality rate)
This is the percentage of the remaining poll that prepays each month
The CPR and SMM are simply related:
![Page 23: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/23.jpg)
Figure 12-2 shows the amount of principal outstanding on a 20-year, 8% mortgage, assuming that the installments are equal and there is no prepaymen
Mortgage-backed Securities (MBS)
![Page 24: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/24.jpg)
Mortgage-backed Securities (MBS)
Figure 12-3 shows the same mortgage but with prepayments at 100% PSA
>100% PSA: in each year, 6% of the remaining borrowers are expected to prepay
With prepayment, the stream of interest payment is reduced
With prepayment, the principle payment will increase first and drop in the last
![Page 25: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/25.jpg)
Mortgage-backed Securities (MBS)
Table 12-1 shows the NPV of the principal and interest payments for different speeds of prepayment
> Notice that as the PSA increases, the value of the principal payments increases, and the value of the interest payments decreases
![Page 26: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/26.jpg)
Mortgage-backed Securities (MBS)
The PSA standard is a very simple model. The main simplification is that in reality, the prepayment rate is strongly affected by changes in interest rates. When market rates drop, new mortgages have lower interest payments, and homeowners are tempted to refinance their homes by taking out a new mortgage and prepaying the old one In other words, the prepayment is not a constant and is related with interest rate
![Page 27: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/27.jpg)
Mortgage-backed Securities (MBS)
The value of the option to prepay is the difference in the NPV of the two alternative sets of interest payments, minus the strike price
The strike price includes any prepayment penalties and the plain hassle involved in refinancing
A typical prepayment function can be approximated as a logistic function:
![Page 28: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/28.jpg)
Mortgage-backed Securities (MBS)
>The value equals one when x equals negative infinity and equal to zero when x equals positive infinity
>the function has the shape of S curve between one and zero
![Page 29: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/29.jpg)
Mortgage-backed Securities (MBS)
The prepayment rate as a percentage of the PSA can be modeled as follows:
100% PSA: in each year, 6% of the remaining borrowers are expected to prepay
r is the market-refinancing rate
>if r decrease, then prepayment rate?
a, b, c and d are constant
![Page 30: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/30.jpg)
Mortgage-backed Securities (MBS)
>Typical values for the parameters are given in the equation above
>This function is shown in Figure 12-4
![Page 31: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/31.jpg)
Mortgage-backed Securities (MBS)
![Page 32: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/32.jpg)
Mortgage-backed Securities (MBS)
Constant prepayment rate: 6% in each year
The non-constant prepayment rate and the prepayment rate is negatively relative with interest rate
Figure 12-5 shows the effect of rate changes on the NPV of principal-only (PO) payments.
>The sudden drop in value occurs in the region where prepayment rates drop and the average time for the cash flows increases dramatically
![Page 33: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/33.jpg)
Mortgage-backed Securities (MBS)
>As the rate begins to increase from 6% to 8%, the value drops because of the greater discounting
>From 8% to 10% as rates increase, so does the value of the security. This is because there are significantly fewer prepayments of principal, and therefore more interest payments
Once the prepayment rate stabilizes at a new low level, the discounting effect again begins to dominate
Hint: the interest rate has two effects: (1) the discounting effect (2) prepayment effect!!
![Page 34: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/34.jpg)
MAIN PRODUCT CLASSES HELD IN ALM PORTFOLlOS
The example above shows that the change in value of an MBS can be a complex function of interest rates
In reality, the value of an MBS is even more complex because customer payments are also path dependent
They are path dependent because the prepayment rates depend not only on the current market rate, but also on the previous rates
![Page 35: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/35.jpg)
Mortgage-backed Securities (MBS)
If rates have previously been low, most of the financially sophisticated borrowers will have already prepaid, and a renewed drop in rates will not cause a significant increase in prepayments
The accurate valuation of mortgage-backed securities is highly complex and the subject of many trading models, but the key points to be aware of are as follows:
![Page 36: CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION GAP SOURCES OF INTEREST-RATE RISK ALM RISK versus](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649d7a5503460f94a5e3f6/html5/thumbnails/36.jpg)
Mortgage-backed Securities (MBS)
Mortgage-backed securities can be structured to have values that are very complex functions of interest rates.
The value of an MBS is greatly dependent on the prepayment rate.
The prepayment rate is a complex function of interest rates.