大浩浩的笔记课堂——FRM考试学习笔记118

Topic 47

Risk Capital Attribution and Risk-Adjusted Performance Measurement

1.Risk capital(economic capital):

⑴risk capital vs. regulatory capital:

⑵to allocate risk capital:

For financial institutions,there are 4 major reasons for using economic capital to allocate risk capital:

①Capital is used extensively to cushion risk.

②Financial institutions must be creditworthy.

③Difficulty in providing an external assessment of a financial institutions creditworthiness.

④Profitability is greatly impacted by the cost of capital.

⑶to diversify risk capital:

①aggregating a firm´scapital:

A.The overall risk capital for a firm should be less than the total of the individual risk capitals.

B.Risk reduction due to diversification effects is very difficult to 

measure.

②allocating economic capital to different business lines:

A.A business unit that are highly correlated to the overall firm need to be allocated more risk capital.

B.Having business lines that are counter cyclical in nature allows the overall firm to have stable earnings and to attain a given desired credit rating using less risk capital.

·特别注意！

·It is therefore common practice to adjust for the diversification effects by lowering the confidence level(99.97%→99.5% or lower) used a the business level.

③There are 3 different measures of risk capital:

A.stand-alone risk capital:

a/ definition:

It is the risk capital calculated without any diversification benefits.

b/ formula:

the sum of the stand-alone capital of the individual≥stand-alone risk capital of the total business unit

·特别注意！

·Most institutions allocate the portfolio effect pro rata with stand-alone risk capital.

B.fully diversified risk capital:

The capital attributed to each actively X and Y,taking into account all diversification benefits from combining them under the same leadership.

C.marginal risk capital:

It is the additional risk capital required by an incremental deal,activity,or business.It takes into account the full benefit of diversification.

④The choice of risk capital measure depends on the objectives:

A.stand-alone risk capital:

incentive compensation

B.fully diversified risk capital:

a/ Assessing the solvency of the firm and minimum risk-pricing.

b/ Assessing the extra performance generated by the diversification effects.

C.marginal risk capital:

active portfolio management or business mix decision

2.Risk-adjusted return on capital(RAROC):

⑴definition:

The RAROC measure is essential to successful integrated risk management.Its main function is to relate the return on capital to the riskiness of firm investments.

⑵characteristics:

①It uses economic profits.

②If it is below the cost of equity,there is no value being added.

③It has the flexibility to consider deferred or contigent compensation.

④A restriction on the firm´s growth due to leverage limitation may result in higher profits.

⑶formula:

⑷advantages:

Benefits of using the RAROC approach include:

①performance measurement using economic profits instead of accounting profits

②use in computing increases in shareholder value as part of incentive compensation within the firm and its divisions

③use in portfolio management for buy and sell decisions and use in capital management in estimating the incremental value-added through a new investment or discontinuing an existing investment

④using risk-based pricing,which will allow proper pricing that takes into account the economic risks undertaken by a firm in a given transaction

3.RAROC for capital budgeting:

⑴formulas:

①after taxes="×(1-t)"

②return on risk capital=R_free×economic capital

③economic capital=risk capital+strategic risk capital=unexpected loss=principal amount×unexpected loss rate

④risk capital=credit risk capital+market risk capital+operational risk capital+etc

⑤strategic risk capital=good will+burned-out capital

⑵factors:

①risk capital:

It is the capital arise that the bank must set aside to cover the worst-case loss from market risk,credit risk,operational risk and other risks.

②strategic risk capital:

It is the risk of significant investment about whose success and profitability there is high uncertainty.

③burned-out capital:

It is an allocation of capital to account for the risk of strategic failure of recent acquisitions or other strategic initiatives built organically.

⑶hurdle rate and capital budgeting decision rule:

①characteristic:

The hurdle rate should be reset periodically(6 months),or when it has changed by more than 10 percent.

②formula:

A.CE:common equity

B.PE:preferred equity

③rules:

capital budgeting decision rules:

A.if RAROC>hurdle rate→value creation from the project and accepted

B.if RAROC<hurdle rate→value destruction and rejected/discontinued

⑷adjusted RAROC:

①definition:

Its measure was developed to better align the risk of the business with the risk of the firm´s equity.

②formula:

③rule:

Accept(reject) projects whose ARAROC is greater(smaller) than R_F.

4.RAROC for performance measurement:

⑴RAROC horizon:

①Practitioners usually adopt one-year time horizon:

A.For market risk,short time horizons require adjustments.

B.factor to lower the current risk level to the core risk level

②There is a lot of subjectivity in selecting the time horizon:

A longer time horizon could be selected to account for the full business cycle.

⑵RAROC default probabilities:

①point-in-time(PIT)probability of default:

A.It could be used to compute short-term expected losses and to price financial instruments with credit risk exposure.

B.Rating is more likely to change.

②through-the-cycle(TTC)probability of default:

A.It is more commonly used for being taken by the rating agencies,calculating economic capital,current profitability,and strategic decisions.

B.It is used for lower volatility of economic capital.

⑶RAROC confidence level:

①The confidence level chosen in the economic capital calculation should be consistent with the firm´s target credit rating:

For example,a high rating such as AA or would require a confidence level in excess of 99.95%.

②This confidence level as the quantitative expression of the risk appetite of the firm.

③Choosing a lower confidence level will not likely reduce the amount of risk capital required if the firm has little exposure to operational risk,credit risk and settlement risk.

⑷RAROC and other common measures of risk/return:

①RAROC and ROE(or ROA):

RAROC has two specific adjustments:

A.In the numerator,it deducts expected loss(the risk factor) from the return.

B.In the denominator,it replaces accounting capital with economic capital.

②RAROC and others:

The discount rate for the NPV is a risk-adjusted expected return that uses beta(captures systematic risk only) from the capital asset pricing model(CAPM).In contrast to NPV,RAROC takes into account both systematic and unsystematic risk in its earnings figure.

5.RAROC in practice:

Some recommendations for implementing a RAROC system:

⑴senior management commitment:

"What counts is not how much income is generated,but how well the firm is compensated for the risks that it is taking on."

⑵communication and education:

It is to all the management layers of the firm.

⑶ongoing consultation:

"parameter review group"

⑷maintaining the integrity of the process

⑸combine RAROC with qualitative factors:

①quality of earnings→strategic importance/long-term growth potential

②quantity of earnings→RAROC return

⑹put an active capital management process in place

大浩浩的笔记课堂之FRM考试学习笔记合集