Financial Intermediation

1
Financial Intermediation

• Lecture 6
• Major Risks Faced by Banks

2
The nature of risk

• Risk is due to uncertainty so it is not the
  same!
• Ex post uncertainty and variability are the same,
  but ex ante the two differ one can have a large
  but certain variability
• Risk can be diversified (to some extent), but
  some of it will be around anyhow

3
Major risks faced by banks

• Default of credit risk (A) Physical hazard
  cash flow variations beyond the control of the
  bank (screening) (B) Moral hazard monitoring
• Interest rate risk by variations in market
  prices (and prepayment risk think of mortgages)
• Liquidity (withdrawal) risk

4
Term structure of interest rates

• Yield curve yield to maturity (YTM) is defined
  as the internal rate of return that equates the
  PV of future cash flows from a bondholder to the
  current market price
• The yield curve is defined as the relationship
  between YTM and the length of the time to
  maturity for debt instruments of identical
  default risk characteristics

5
Yield curve under certainty

• Pmt price of a bond of maturity m at t
• imt YTM of .
• Face value 1, zero coupon
• So P10F/(1YTM) 1/(1i10)
• And P20 1/(1i10)2
• One can also invest at time t1 in a bond that
  has the yield i11
• Arbitrage will lead to (1i20)2 (1i10)(1i11)

6
Spot rates and Forward rates

• Spot rate Present price for future delivery
• Forward rate Future price for future delivery
• General formula for the YTM on a bond of
  maturity n to be issued t period from now
• Shape is determined expectations that short-term
  interest rates will keep rising ? upward slope
• interest rates will keep falling ? downward
  slope

7
Yield curve under uncertainty (1)

• Complication under uncertainty investors face
  risk. A risk averse lender would require
  compensation for bearing this risk
• Modern arbitrage theory ruling out riskless
  arbitrage in equilibrium, analyze as if
  investors were risk neutral ? risk aversion
  becomes irrelevant and the valuation is
  preference free

8
Yield curve under uncertainty (2)

• First think of the yield curve under certainty
• Inverting both sides to express in terms of
  bond prices
• Forward rates uncertain ? calculate expected
  value by using probabilities (? as upstate
  probability (1- ?) as downstate probability in
  case of risk aversion we can calculate the risk
  neutral probability ?)

9
Term structure theory

• Theory no-arbitrage development of the term
  structure
• - The Expectations Theory
• - The Liquidity Preference Theory
• - Preferred Habitat Theory

10
The Expectations Theory

• Unbiased Expectations Hypothesis states that
  implied (one-period) forward rate for any
  period in the future must equal the expected
  spot rate on a one-period bond to be issued in
  that future period.
• This is inconsistent with the absence of
  riskless arbitrage opportunities in
  equilibrium ? under uncertainty the forward
  rate can not be equal to the expected value of
  the future spot rate

11
The liquidity preference theory

• Investors demand a risk premium for holding
  long-term bonds
• Variability of bond prices increase with
  maturity, liquidity premium does as well
• Hypothesis does not assert that long term
  yields must be higher than short term yield
• Long-term bonds are not necessarily less liquid
  than short term bonds ? liquidity premium is
  more a term premium

12
The Preferred Habitat Theory

• The bond with maturity closest to the
  investors investment horizon will be viewed as
  safest
• Investors require a higher expected return form
  bonds with different times to maturity
• Theory violates no-arbitrage condition in
  perfect capital markets
• Preferred Habitat misses importance of risk
  aversion

13
Duration (1)

• Interest risk can be measured by duration and
  duration-gap
• Duration is the weighted-average time to
  maturity using the relative PVs of the cash
  flows as weights
• Duration gap is the weighted duration of
  equity (weighted duration of assets - weighted
  duration of liabilities)

14
Duration (2)

• General formula for duration
• CF Cash Flow at end op period t
• DF Discount Factor

15
Duration (3)

• Economic interpretation D is the interest
  elasticity of the securitys price to small
  interest rate changes
• Convexity measure of how much a bonds
  price-yield curve deviates from a straight
  line. Greater convexity, price of a bond will
  fall more slowly as yields rise and rise faster
  as yields fall

16
Duration (4)

• Convexity factors that increase convexity
• Decreasing coupon
• Decreasing yield
• Increasing maturity
• Thus zero-coupon bonds with long maturities will
  have high convexity.

17
Duration (5)

• Duration gap
• - Positive gap FIs net worth will decline if
  the entire yield curve moves up and will
  increase if the entire curve moves down
• - Negative gap Opposite
• Maturity gap
• Although maturities may be perfectly matched,
  timings of cash flows may not be matched ?
  Better to use duration

18
Liquidity risk

• The risk of being unable to satisfy claims with
  impairment to its financial or reputational
  capital
• Informational asymmetry about asset quality
  plays an important role in creating liquidity
  risk
• Duration mismatching is an important, but not a
  necessary ingredient for interest risk

19
Credit risk analysis factors

• Capacity borrower has legal and economic
  capacity to borrow
• Character borrowers reputation
• Capital resolves private information and moral
  hazard problems
• Collateral additional reduction of risk, it can
  signal quality, and reduce moral hazard
• Economic conditions that determine the borrowers
  capacity to repay

20
Credit analysis sources of information

• Internal interview with applicant and banks own
  records
• External Borrowers financial statements, credit
  information brokers, other banks!
• One can use loan covenants special clauses
  designed to protect the bank and prohibit the
  borrower from taking actions that could adversely
  influence the likelihood of repayment

21
Complete contingent contract

• Amount of repayment/or additional loan
• Interest rate on the remaining debt
• Possible adjustment in the collateral required by
  the lender
• Actions (e.g. investment decisions) to be
  undertaken by the borrower
• All in all states of nature at each possible
  date!

22
Loan design

• Loans are typically incomplete contracts
• What should be taken care of in a contract and
  what kind of actions can be undertaken by
  governing the loan?
• A typical loan contract includes the repayment
  and collateral requirements only what is the
  theoretical foundation?

23
Theory of symmetric risk sharing

• Suppose we have a lender with utility function uL
  and a borrower with utility function uB. At date
  0 the borrower invests L and gets a return ye at
  date 1. The borrower has no wealth and the lender
  provides a loan L
• What is the optimal repayment function R(y)?

24
Symmetric risk sharing (2)

• We assume that there is limited liability
  0 ? R(y) ? y. The borrower gets y - R(y).
• The problem is max EuB (ye - R(ye) given EuL
  (R(ye)) ? UL0 and 0 ? R(y) ? y
• We could also maximize EuL (R(ye)) given EuB
  (ye - R(ye)) ? UB0 and 0 ? R(y) ? y
• The utility functions are Von Neumann-Morgenstern,
  monotonically increasing

25
Symmetric Risk Sharing (3)

• It is easy to see that the FOC reads
  uB (y - R(y)) - ? uL (R(y)) 0,
  taking logs gives
• log(uB (y-R(y))) - log(uL (R(y))) - log ? 0
• Differentiate with respect to y gives
• uB/uB (Y - R(y)) (1 - R(y))
  uL/uL (R(y)) R(y) 0
• Define IB -uB (x) / uB (x) and
  IL -uL (x) / uL (x)

26
Symmetric Risk Sharing (4)

• R(y) IB (y-R(y)) / IB (y-R(y)) IL (y)
• So R(y)1/1IL/IB. So if IL 0, a risk
  neutral lender, R(y) 1. If IB/IL is large the
  cash-flow sensitivity of the repayment is large
• This is not a realistic banking case R(y)R
  would be more common, or R(y) min (y,R) with
  limited liability
• So we need to know more about managing risk