Performance (risk management)

The anglicism of performance ( German  achievement , success ) is to be understood in business administration as a measure of target achievement .

General

While under productivity , the ratio of real output quantity ( english output ) to real input quantity ( english input ) is understood, the performance of the ratio of actual output to a fixed (standard) output relative to the amount used. Thus, including the performance review of the result and the effort with the respective relevant goals, standards or references . Performance is therefore the ability of a system (such as a company ) to be able to perform certain tasks in quantitative or qualitative terms in a fixed time unit ( accounting period ). The measured variable performance thus also gains a potential character, which is perceived in companies through performance management . The difference to (absolute) profitability lies in the lack of monetary recording of the action results and the use of funds. Performance is therefore to be interpreted as a measure of target achievement.

Definition in finance

In the area of risk management, performance refers to the excess of the investment return achieved over a comparable, adequate benchmark return . The difference in return is normalized by dividing it with a risk measure.

• In the broadest sense, performance is a perspective estimate for assessing the success of capital investments .
• The components here are the observed return and the expected risk of the asset

The formula for the calculation in general is:

${\displaystyle Performance={\frac {{\text{Anlagerendite}}-{\text{Benchmarkrendite}}}{\text{Risikomaß}}}}$.

In the case of stocks, the benchmark return is often specified using a stock index . Depending on whether a stock is doing better, the same or worse than the benchmark, it is called an outperformer , market performer or underperformer . If a financial analyst makes this statement about a share with a view to the future, this corresponds to the recommendation to buy, hold or sell the share.

Attribution analysis

The performance of portfolio management can be measured using attribution analysis. The starting point is the question of what components make up the overall result. The service can be broken down into three components:

• market-related : This is a passive service that can be traced using the development of a benchmark.
• structure-related : decision regarding the exchange rate development or the performance development of different markets.
• For technical reasons : through overweighting and underweighting individual stocks.

Performance measures

General

Performance measures are key figures for assessing individual businesses or entire companies. A distinction can be made between risk-adjusted key figures and those that only take income into account. The latter are actually yield standards and no performance measures in the strict sense (examples: return on investment . (ROI) Financial Indicators include the return on equity (ROE, return on equity) and the return on assets (ROA Return On Assets)).

A risk-adjusted performance measure is formally obtained by combining the expected value of the result (e.g. profit , cash flow or return ) with an associated risk measure (e.g. standard deviation of the result).

A performance measurement can be carried out ex ante or ex post . An ex ante performance measure serves as a predicted measure of success for decision-making, e.g. B. for a tangible investment or financial investment. The uncertainty of every future forecast (via a result variable ), which is the basis of the economic decision, is explicitly taken into account. Such performance measures are therefore key figures that result from the combination (operationalized by a function f (..) of the expected result (e.g. expected profit)) with a suitable risk measure such as standard deviation or value at risk . The risk measure shows the scope of possible deviations from the plan. ${\displaystyle X}$ ${\displaystyle E(X)}$ ${\displaystyle R(X)}$

${\displaystyle P(X)=f(E(X),R(X))}$.

In the simplest case, the performance measure for the uncertain profit is obtained by reducing the expected value by means of a risk discount, which is directly dependent on the risk measure . B. of standard deviation or value-at-risk (of profit). Example: ${\displaystyle P(X)}$ ${\displaystyle X}$ ${\displaystyle E(X)}$ ${\displaystyle R(X)}$

${\displaystyle P(X)=E(X)-a\cdot R(X)}$.

The deduction of the risk discount from the expected value corresponds to the procedure for determining so-called safety equivalents ( safety equivalents), which express which safe result is equivalent to the uncertain result from the perspective of the evaluator . If, for example, the equity requirement is chosen as the risk measure , the size , the "price of the risk", can be interpreted as imputed additional costs for equity. This means that the risk discount corresponds precisely to the imputed cost of equity or risk costs. ${\displaystyle a\cdot R(X)}$ ${\displaystyle X}$ ${\displaystyle a}$

Risk-adjusted performance measures

The most important risk-adjusted performance measures are:

• Jensen Alpha : excess return on a portfolio with the same beta risk on the securities market line,

${\displaystyle \alpha _{PF}=\mu _{PF}-[r+(\mu _{M}-r)\beta _{PF}]}$

• Sharpe quotient : excess return relative to total risk. Decision dependent on individual risk appetite. There is a trade-off between diversification and excess return.

${\displaystyle SR(PF)=P_{PF}^{S}={\frac {\mu _{PF}-r}{\sigma _{PF}}}}$

Total risk as a risk indicator to which the premium is based. Suitable for broadly diversified portfolios .

• Treynor quotient : excess return relative to the beta risk taken:

${\displaystyle TR(PF)=P_{PF}^{T}={\frac {\mu _{PF}-r}{\beta _{PF}}}}$

Systematic risk in the form of the beta factor as a risk indicator to which the premium is based. Suitable for risk assessment of the contribution of a sub-portfolio to the overall portfolio.

The Sharpe and Treynor quotients are key figures that relate an excess to a risk. This follows the concept of relative coverage margins , which is used to resolve planning problems with bottlenecks. Treynor quotient and Jensen alpha are derived from the Capital Asset Pricing Model (CAPM). They are therefore also subject to the criticism that is being expressed about this capital market model.

The risk premium of the financial security is in the numerator. It is the difference between the return and the risk-free rate . ${\displaystyle x}$ ${\displaystyle r_{x}}$ ${\displaystyle i}$

The following table provides an overview of all risk-adjusted performance measures (the numerator is the excess return):

Risk measure (denominator)		Performance measure
Standard deviation		Sharpe quotient
Lower Partial Moments of Order	1	omega
	2	Sortino ratio
	3	Kappa 3
Drawdown (price deflection downwards)	maximum	Calmar ratio
	average	Sterling ratio
	Variance	Burke ratio
Value at Risk	default	Excess return on value at risk
	Conditional	Conditional Sharpe Ratio
	Modified	Modified Sharpe Ratio

Performance measures in the banking sector

Banking transactions are completed sequentially and in different organizational units. This requires a control system that takes into account the risk situation ( risk capital ) and scarce resources (regulatory capital ). The aim is to only conclude transactions that are overall positive.

RAPM ( risk-adjusted performance measures)

Refined risk-adjusted performance measures (RAPM) are used here. RAPM are used to compare banking transactions with different levels of risk. The valuation can relate to financial stocks as well as portfolios.

${\displaystyle RAPM={\frac {{\text{Einzahlungen}}-{\text{Auszahlungen}}-{\text{erwartete Verluste}}}{\text{Value at Risk}}}}$

• Deposits are scheduled payments that result from the loan agreement and assume an insolvency-free course of the loan.
• Payouts, on the other hand, include the loan payment , interest for refinancing the loan and the payment for (imputed) processing.
• Expected losses refer to expected defaults in interest and repayment payments .
• Value at Risk is the risk capital used to cover unexpected losses

Using RAPM, it is possible to compare individual banking transactions with different levels of risk.

RORAC (Return on Risk Adjusted Capital)

${\displaystyle RORAC={\frac {\text{Nettoergebnis}}{\text{Risikokapital}}}}$

${\displaystyle RAROC={\frac {\text{risikoadjustiertes Nettoergebnis}}{\text{Risikokapital}}}}$

It should be noted whether the numerator and / or denominator are risk-adjusted. RA stands for risk-adjusted, ROC for return on capital.

Net result = interest income - refinancing costs

Either an economic or a regulatory capital figure is used for the risk capital. The value at risk is often used here . This takes into account the scarce resources through which a surplus is to be achieved.

The difference between RAROC and RORAC is whether or not the net result is risk adjusted. Taking standard risk costs into account is not sufficient here, as these merely record expected losses. In addition, the costs for the reserved risk capital, i.e. the provision for unexpected losses, must be deducted for the risk-adjusted net result. One decides on the shops that have the highest RORAC or RAPM value.

However, it cannot automatically be concluded from a positive RORAC that the conclusion of the deal is worthwhile. A premium must be paid for taking on the risk ( hurdle rate ). In practice, the market return derived from the CAPM is used for , the so-called . ${\displaystyle RORAC_{z}}$ ${\displaystyle HurdleRateRORAC_{z}}$

In this way, the RORAC can be transferred to the RAROC:

${\displaystyle RORAC-RORAC_{c}={\frac {{\text{Nettoergebnis}}-{\text{Risikokapital}}\cdot RORAC_{c}}{\text{Risikokapital}}}=}$

${\displaystyle {\frac {\text{risikoadjustiertes Nettoergebnis}}{\text{Risikokapital}}}=RAROC={\text{Economic Value Added}}}$

The risk capital is related to the net results, it is a bottleneck factor.

A loan is value-creating when your RAROC is positive.

Greater consideration of risk and return

Current events have led to risk and return being given greater consideration in overall bank management.

• Implementation of the Basel II guidelines into German law and the binding risk-dependent capital adequacy requirements for loans
• Overarching bank control systems are increasingly used. Risk types are examined together and risk-adjusted performance measures are introduced (RORAC).
• The availability of integrated IT systems enables the handling of interfaces and the use of bank-specific software.

See also

• Balance cosmetics
• Information ratio
• Key performance indicator
• Performance Measurement
• Sortino ratio
• Sterling ratio

literature

• J. Wernz, A. Baumann: Risk-adjusted pricing. In: Claims Practitioner. 01-02, 2013, pp. 29-32.
• W. Gleißner: Quantitative methods in risk management: risk aggregation, risk measures and performance measures. In: The Controlling Consultant. 16/2011, pp. 179-204. ( online at: werner-gleissner.de )
• W. Gleißner: Risk analysis and replication for company valuation and value-oriented company management. In: WiSt. 7/2011, pp. 345-352.
• Thomas Hartmann-Wendels, Andreas Pfingsten, Martin Weber: Banking apprenticeship. 3. Edition. Springer, Berlin 2004, ISBN 3-540-21227-2 .
• Henner Schierenbeck, Michael Lister, Stefan Kirmße: Profit-oriented bank management. Volume 2: Risk Controlling and Integrated Risk / Return Management. 9th edition. Gabler, Wiesbaden 2008, ISBN 978-3-8349-0447-8 .

Individual evidence

1. ↑ Lutz J. Heinrich / Armin Heinzl / Friedrich Roithmayr, Wirtschaftsinformatik-Lexikon , 2004, p. 395
2. ↑ W. Gleißner: Quantitative procedures in risk management: risk aggregation, risk measures and performance measures. 2011.
3. ↑ for derivation: W. Gleißner: Risk analysis and replication for company valuation and value-oriented company management. 2011.