Summary: "Theory of Risk Capital in Financial Firms".

This is a summary of the article "Theory of Risk Capital in Financial Firms".

The paper develops a concept of risk capial that can be applied to decisions in financial firms. The focus is on firms that has a principal in the ordinary course of business.

Principal activities: asset-related, liability-related, or both

Financial firms have three distinguishing features: credit sensitivity of customers, high cost of risk capital, high sensitivity of profitability to the cost of risk capital .

(1) The customers can be major liability holders. Therefore the customers prefer firms with high credit quality. Investors on the other hand are not sensitive to the creditworthiness of the firm, provided that they are compensated for the risk.

-> This means that A-rated firms can generally raise the funds they need to operate, but are at a disadvantage when competing with an AAA-rated firm in underwriting business.

(2) Financial firms are opaque in nature. They also have relatively liquid balance sheet whiches size and risk can change markdely in the course of a week. Financial firms are also sibject to considerable "event risk".

-> This leads to a high information cost in raising equity capital and in executing various customer transactions

(3) Financial firms operate in competitive financial markets. Their cost of capital is an important determinant of their profitability. Moreover, there is no easy way of allocation cost of risk capital to individual projects. Any risk allocation must also be inputed, highly risky principal transactions often requires little upfron cash expenditure.

-> A comitment made by underwriting is backed by the entire firm.

WHAT IS RISK CAPITAL?
Risk capital is defined as the smallest amount that can be invested to insure the value of the firm's net assets against a loss in value relative to the risk-free investment of those net assets.

Net assets: gross assets minus customer liabilities

Fixed customer liabilities: the riskiness of net assets = riskiness of gross assets
Contingent customer liabilities: riskiness of net assets depends = riskiness of gross assets + riskiness of customer liabilities + covariance of gross assets and customer liabilities

The volatility of net asset value is the most imporant determinant of the amount of risk capital.

Regulatory capital: risk capital measured according to a particular accounting standard
Cash capital: cash needed to execute a transaction

To follow:
1. Examples to show that the amount of risk capital depends only on the riskiness of net assets, and not at all on the form of financing of the net assets. Equity capital is then used to purchase asset insurance from various sources.
2. Failure of standard risk capital accounting methods. The economic cost of risk capital is shown to be the spreads on the price of asset insurance arising from information costs.Implications for risk management and hedging decision
3. Problem that arise in multi-business firms in trying to allocate the risk capital of the firm among its individual businesses.

MEASURING RISK CAPITAL
Case 1. one asset, a 100 million deal = net assets
Risk distribution: 1. 120 million 2. 60 million 3. 0
Cash capital requried: 100 million
The deal is financed by issuing a one year, default free, note to an outside investor. The cost of capital os 10%
How can the bank eliminate default risk?
- purchase an insurance on its assets
- purchase an insurance on its liabilities
Risk capital: smallest possible insurance cost to obtain default-free financing

* Risk capital and Asset Guarantees *
The bank buys insurance on the bridge loan from an AAAA-rated bond insurer for 5 million.
The value of the bank's assets at the end of the year will equal or exceed 110 million.
Risk capital: 5 million
The risk capital would need to be funded with a 5 million cash equity investment.

Balance sheet of BANK A
____________________________________________________________
Bridge loan    100      |    Note (default free)    100
Loan insurance    5    |    Shareholder equity    5


Return distribution:
                        Firm stakeholders
    Bridge    Loan         Bridge loan     Note    Shareholder
    loan    insurance    + insurance  
1.    120        0               120              110          10
2.     60        50              110              110            0
3.    0         110              110              110            0

Risk capital balance sheet of BANK A
____________________________________________________________
Bridge loan    100      |    Note (default free)    100
Loan insurance    5    |    Risk capital        5

Here, shareholder equity = risk capital

* Risk Capital and Liability Guarantees *
A parent guarantees the note

Balance sheet of BANK B
____________________________________________________________
Bridge loan    100    |    Note (default free)    100
                                 |    Shareholder equity    0

All asset risk is now borne by the parent company. The guarantee is another asset for the bank that does not appear on the balance sheet. Here we account for it as "G".

Risk capital balance sheet of BANK B
____________________________________________________________
Bridge loan    100      |    Note (default free)    100
Note guarantee    G    |    Risk capital        G

* Liabilities with Default Risk *
BANK issues liabilities with some default risk, no credit enhancements this time.
The note will sell at a discount of D to par. The Bank must find the remainder of the 100 million needed. This will be supplied in the form of a cash equity investment.

Balance sheet of BANK C
____________________________________________________________
Bridge loan    100    |    Note (default free)    100-D
            |    Shareholder equity    D

Risky note + note insurance = default free note
Risky Note = default free note - note insurance
Risky note = default free note - asset insurance


Risk capital balance sheet of BANK C
____________________________________________________________
Bridge loan    100    |    Note (default free)    100
Asset insurance    5    |    Risk capital        5
(from note holder)

Each example has different accounting balance sheets, but very similar risk capital balance sheets

* A More General Case *
Too long to be described in detail

Capital providers have three basic functions:
- provide cash capital (required to enter a transaction)
- sellers of insurance (covering the part not covered by insurance)
- providing risk capital (capital needed to purchase asset insurance)

* Contingent Customer Liabilities *
With contingent liabilities, the riskiness of net assets will in general differ from the riskiness of gross assets.

Firm E
No equity
Liabilities fully supported by a parent
Contingent liability: a S&P tracking note that promises 100 * the return on S&P

Balance sheet of BANK E
____________________________________________________________
Cash        100    |    Note (risky)        100
                           |    Shareholder equity    0

How the firm invests the cash will determine its risk capital
Treasury bills generating 10% return -> Gross assets are riskless, net assets are extremely risky
The position represents a short position in the S&P 500
The risk capital is equal to the value of a European call option on the S&P 500

The firm can instead choose to invest in the S&P 500. The gross assets are risky, but they match the liabilities, leading to net assets being riskless (assuming no transaction costs)it is the riskiness of the net assets that determine the risk capital needed

ACCOUNTING FOR RISK CAPITAL IN THE CALCULATION OF PROFITS
Risk capital is implicitly or explicitly used to purchase insrance on the net assets of the firm. This insurance, and gains or losses on this asset should be included along with the gains or losses on all other assets in the calculation of profitability.
- Standard methods often fail to account for this, for instance from implicit insurance from a parent.
- This can have an important impact on how profits for business subsidiaries are calculated.

THE ECONOMIC COST OF CAPITAL
- Accounting for risk capital is important for after-the-fact profits in reporting and profit-related compensation.
- In decision making before-the-fact, expected profits must incorporate implicit guarantees as well.
- Risk capital is not costly in an economic sense as we get a financial asset in return
- There are however transactioncosts included. A spread is typically paid over the economic value of the insurance, resulting in a deadweight loss to the firm.
- Economic cost = spread paid over fair value

The spread typically arrise from information and agency costs
- Adverse selection
- Moral hazard
- Agency cost

Equity holders bear the brunt of these costs

HEDGING AND RISK MANAGEMENT
- Hedging market risk exposure reduces the required amount of risk capital
- With no spread costs for risk capital, larger amounts of risk capital would impose no additional costs on the firm
- In this case, firms may well be indifferent to hedging or not
- If there are spread costs, and if these costs depend on the amount of risk capital, then a reduction in risk capital from hedging will lead to lower costs of risk capital if the hedges can be acquired at small spreads
- That will ususally be the case with hedging instruments for broad market risks where significant infomational advantages among market participants are unlikely

CAPITAL ALLOCATION AND CAPITAL BUDGETING
- When deciding to enter new businesses the cost fo risk capital can have a major influence
- Businesses that would be unprofitable on their own because of high risk-capital requirements might be profitable within a firm that has other businesses with offsetting risks

The risk capital of a particular business within a firm will be different if it is calculated on a stand-alone basis or as a part of the firm. This is the result of a diversification benefit
- This depends on the correlation between the firms
- The risk capital needed for the entire firm will be less than the sum of the individual businesses risk capital
- But allocating risk based on marginal risk also suffers from problems. The sum of marginal risk capital from a collection of businesses within a firm is less than the total risk capital.

The correlation between businesses is important sindce it affacets the total economic costs of risk capital. CAPM assumes that only correaltion between the firm and outside markets matter, this does not account for the economic cost of risk capital.
- The riskiness of the net assets is affected by correlations among business units
- The value of net assets is affected by their correlation with the broader market

SUMMARY AND CONLCUSIONS
Risk capital = the minimum amount of capital required to insure the net assets against default. This leads to the following conclusions:
1. The amount of risk capital is uniquely determined, and depends only on the riskiness of the net assets. It is not affected by the form of financing of net assets.
2. Tisk capital funds are provided by the firm's residual claimaints (equity holders). This capital is used to purchase asset insurance (implicitly or explicitly)
3. The economic costs of risk capital to the firm are the spreads on the price of asset insurance that stem from information costs and agency costs
4. For a given configuration, the risk capital of a multi-business firm is less than the aggregate risk capital of the businesses on a stand-alone basis. Full allocation of risk-capital across the individual businesses of the firm therefore is generally not feasible. Attempts at such a full allocation can significantly distort the true profitability of individual businesses.