Introduction to Risk Involving Financial FirmsAllen and Santomero (1998)

• They argue that the risk hedging, transfer and absorption services of financial firms is most important because derivatives and other sophisticated products must be handled by specialists.

• Individuals no longer participate directly in many financial markets, instead they buy financial products (mutual funds).

• Shifts from banks and insurance companies to mutual funds, pension funds and finance companies (GE Capital).

• Transactions costs theory of financial firms are less important as transactions, information and monitoring costs have declined, making transactions, information and monitoring services less valuable commodities.

• Example: With lower transactions and monitoring costs, mortgages are often originated by mortgage companies, packaged by investment banks and sold to pension funds and insurance companies - the monitoring services of banks and S&Ls can be reduced or eliminated.

• Sophisticated corporate risk management services are more in demand because of (1) managers’ desire to smooth corporate performance, (2) avoidance of progressive corporate tax, (3) avoidance of cost of financial distress, and (4) avoidance of high capital costs due fundraising while in financial distress.

• Financial firms are paid for their sophistication in analyzing and then buying (selling) under-priced (over-priced) risks.

How Intermediaries Handle Risk Inherent in Assets• Eliminate some risks through business practices - (1) underwriting standards, (2) due diligence, (3) portfolio diversification.

• Eliminate some risks by transferring them to others - e.g., sell asset-backed securities, use adjustable rate mortgages.

• Absorb risks that can be neutralized - financial firm’s equity capital fluctuates with payoffs on risky positions it holds for clients who wish to shed them.

Dimensions of Risk - Hedging, Diversification and InsuranceHedging

• Eliminates the asset price upside and downside variation.

• Futures are commonly used as an offset to another asset such that the hedger’s losses (gains) on the futures are offset by gains (losses) on the asset.

• Swaps are just a structured series of futures contract which can similarly be used to hedge risk for many time periods.

• Both sides of a futures or swap can be risk reducing as each side gives up upside potential (but from the opposite perspective) in exchange for downside protection.

• Next example: the Local Bank or Insurance Company loses on the futures contract but gains on the asset (Mortgage).

Hedging Locks in Profit - Eliminates Price Risk

SIMPLE HEDGING EXAMPLE - Mortgages

• A local bank makes commitments with customers for $5 million of mortgage loans today at a fixed rate of interest. The mortgages are not actually paid out until real estate closings in two months. The banks’ funding costs are $4 m.

• At the same time, an insurance company plans to buy $5 million in mortgage-backed securities in two months to support $6 million in insurance premiums it will receive.

Local Bank - short hedger - hedges risk by selling futures.Insurance Company - long hedger - hedges by buying

mortgage futures.

Timing Local Bank Insurance Co

now sell futures 5 buy futures -5

2 months cost -4 gets premiums 6 later

Net Profit 1 1

Price Changes Have No Net Impact

Suppose mortgage rates rise so the value of the $5 million mortgages is $3 million in two months. What happens?

Local Bank Insurance Co.Makes mortgages 3 Buys mortgages -3Buy back futures -3 Sell back futures 3

NET 0 0

What are the respective gains and losses for the Bank and the Insurance Co.?

Local Bank Insurance Co.Loss on mortgages -2 Gain on mortgages 2Gain on futures 2 Loss on futures -2

NET 0 0

Futures Gain (Loss) Offsets Asset Loss (Gain)Suppose mortgage rates fall so the value of the $5 million mortgages is $6 million in two months. What happens?

Local Bank Insurance Co.Makes mortgages 6 Buys mortgages -6Buy back futures -6 Sell back futures 6

NET 0 0

What are the respective gains and losses for the Bank and the Insurance Co.?

Local Bank Insurance Co.Gain on mortgages 1 Loss on mortgages -1Loss on futures -1 Gain on futures 1

NET 0 0

Diversification -Reducing RiskProbabilities are weights attached to scenarios or observation classes where i indexes scenarios.

Expected return = E(R1) = Probabilityi x Return1i

Return Variance = 2(R1) = Probabilityi x [Return1i - E(R1)]2

Sample mean and variance assumes that each observation has equal probability which is acceptable if sample covers a full economic cycle.

Return standard deviation = (R1) = [2(R1)]1/2

Example of Bank LoansSuppose a bank has made a ($70,000) loan for which it knows that it will be paid back $100,000 in one year with 80% probability or zero with 20% probability. The probability distribution is:Outcome Probability PayoffDefault 0.20 $0No Default 0.80 $100,000

The expected payoff is:

E(R) = 0.20(0) + 0.80($100,000) = $80,000

The risk of the payoff measured by its standard deviation is

(R) = [(0.20)(0 - 80,000)2 + (0.80)(100,000 - 80,000)2].5

= $40,000

Now suppose that instead of one loan for $100,000, two banks each with $100,000 loans agree to split up their loans with each taking half of the others’ loan (syndicated loans). Each bank now has two loans that each pays off $50,000 with 80% probability or zero with 20% probability. Assume the loans are independent. Each bank’s payoff distribution isOutcome Probability PayoffBoth Default 0.04 $0One Defaults 0.32 $50,000Neither Defaults 0.64 $100,00

The expected payoff stays the same:

E(R) = 0.04(0) + 0.32($50,000) + 0.64($100,000) = $80,000

The risk of the payoff measured by its standard deviation is

(R) = [(0.04)(0 - 80,000)2 + (0.32)(50,000 - 80,000)2 + (0.64)(100,000 -80,000)].5 = $28,284

• Notice that expected return stays the same but risk falls.

• Implicitly, by splitting up our money we have reduced the chance of making the full $100,000, from 80% to 64%, in return for reducing the chance that we will get zero, from 20% to 4%.

• For risk-averse investors, the trade makes them better off.

More DiversificationIf we make more loans in smaller amounts and assume each loan payoff is independent of the others then:

Number of Loans Loan Portfolio Standard Deviation1 $40,000 2 $28,28410 $12,649100 $4,00010,000 $4001,000,000 $40 = ($40,000)/(Number of Loans).5

Here again, as we split our funds into smaller amounts and make smaller independent loans, we continue to reduce the chance that we get a poor outcome overall, but we also reduce the chance of getting the best outcome.

Aggregate Loan Risk for All Aggregate Loan Risk for All Bank Loans CombinedBank Loans Combined Number of Loans Made Aggregate Standard Deviation

1 $40,000

2 $56,569

10 $126,491

100 $400,000

10,000 $4,000,000

1,000,000 $40,000,000 = (40,000)N.5

When banks syndicate all their loans, total loan risk does not change - it is just spread equally among banks. Syndication reduces the risk of individual banks but consequently, all banks have the same loan portfolio and so their risks are perfectly correlated. If all banks hold a single loan, their individual risks are larger but the risks are uncorrelated.

Aggregate Loan Risk With Two BanksDefinition of Aggregate (Portfolio) Risk:

(P) = [(R1)2 + 2Corr12 (R1) (R2) + (R2)2 ].5

where Corr12 equals the correlation between the loans of Bank 1 and Bank 2.

1. Aggregate Loan Risk - Each bank holds a single loan.

(P) = [(40,000)2 + 2(0)(40,000)(40,000) + (40,000)2].5

= $56,569

2. Aggregate Loan Risk - Each bank holds two, half-loans.

(P) = [(28,248)2 + 2(1)(28,248)(28,248) + (28,248)2].5

= $56,569

Insurance - Option Premiums• Firms can insure against the downside risk that they wish to shed.

• Example: Annual fire insurance premiums transfers risk from homeowner to insurer.

• The price of an option is called a “premium” because an option is equivalent to insurance whose price is a premium.

• Example: Car lease transfers a car’s price risk from the user (lessee) to the car dealer who retains ownership unless lessee exercises her option to buy are the lease expiration.

Insuring Against Loan RiskIn the previous loan example, banks used syndication to spread risk amongst themselves as a way to manage risk. An alternative is to buy insurance.

What should an insurance company charge for a premium if it is set up so that it will fail only once in a million times (to create a perfectly risk-less insurance company we would have to charge the maximum loss of $100,000)?

Number of Loans Covered Premium

1 $100,00010 $80,000100 $39,00010,000 $21,900100,000 $20,601

• This shows why large insurance companies have a competitive advantage; they can charge smaller premiums while maintaining a high probability of financial solvency.

• The actually fair premium, ignoring any of the insurer’s operating costs is just:

Expected loss per loan = (.2)($100,000) = $20,000.

• A risk averse bank would probably be willing to pay more than this to guarantee a profit on the loan.

1. Hedging eliminates downside risk and upside potential.

2. Diversification reduces, but does not eliminate, both.

3. Insurance limits the downside risk but allows upside.

Types of Risk Faced By Financial Firms1. Interest rate risk - refinancing and reinvestment.

2. Market risk - price risk from trading assets.

3. Credit risk - loan default - systematic and firm-specific.

4. Off-balance sheet risk - credit guarantees and derivatives.

5. Technology/Operational risk - changing technology makes firm uncompetitive and system malfunctions.

6. Foreign exchange - changes in income, asset and liability value due to exchange rate changes.

7. Country/Sovereign - change in laws or poor enforcement.

8. Liquidity/Insolvency - bank runs, losses larger than equity.