Risk calculation is a crucial aspect of any business or investment strategy, allowing individuals and organizations to anticipate and prepare for potential losses. Aon, a leading global professional services firm, provides a range of formulas and methodologies for calculating risk. Here, we will explore 9 key Aon formulas for calculating risk, providing a comprehensive overview of each formula, its application, and significance in risk management.
Introduction to Aon Risk Calculation Formulas
Aon’s risk calculation formulas are designed to provide a structured approach to risk assessment, enabling businesses to identify, analyze, and mitigate potential risks. These formulas take into account various factors, including probability, impact, and likelihood, to provide a comprehensive risk profile. By applying these formulas, organizations can make informed decisions, allocate resources effectively, and minimize potential losses.
Formula 1: Risk Score Calculation
The Risk Score Calculation formula is a widely used method for assessing risk. It involves assigning a score to each risk factor, based on its likelihood and potential impact. The formula is as follows:
| Risk Factor | Likelihood | Impact | Risk Score |
|---|---|---|---|
| Financial | 0.8 | 0.6 | 0.48 |
| Operational | 0.4 | 0.8 | 0.32 |
| Strategic | 0.6 | 0.4 | 0.24 |
The risk score is calculated by multiplying the likelihood and impact of each risk factor. This formula provides a simple and effective way to assess risk and prioritize mitigation efforts.
Formula 2: Expected Loss Calculation
The Expected Loss Calculation formula is used to estimate the potential loss associated with a particular risk. The formula is as follows:
Expected Loss (EL) = Probability of Loss (PL) x Loss Amount (LA)
For example, if the probability of loss is 0.2 and the loss amount is $100,000, the expected loss would be:
EL = 0.2 x $100,000 = $20,000
This formula provides a quantitative estimate of potential loss, enabling organizations to make informed decisions about risk mitigation and resource allocation.
Formula 3: Value-at-Risk (VaR) Calculation
The Value-at-Risk (VaR) calculation formula is used to estimate the potential loss of a portfolio over a specific time horizon with a given probability. The formula is as follows:
VaR = σ x z x √t
Where:
- σ = standard deviation of returns
- z = z-score corresponding to the desired confidence level
- t = time horizon
For example, if the standard deviation of returns is 0.02, the z-score is 1.96, and the time horizon is 1 year, the VaR would be:
VaR = 0.02 x 1.96 x √1 = 0.0392
This formula provides a widely used measure of market risk, enabling organizations to assess potential losses and make informed investment decisions.
Formula 4: Conditional Value-at-Risk (CVaR) Calculation
The Conditional Value-at-Risk (CVaR) calculation formula is used to estimate the expected loss of a portfolio in the worst α% of cases. The formula is as follows:
CVaR = (1/α) x ∫[VaR, ∞) x(x) dx
Where:
- α = confidence level
- x = return
- VaR = value-at-risk
For example, if the confidence level is 0.95 and the VaR is 0.0392, the CVaR would be:
CVaR = (1/0.05) x ∫[0.0392, ∞) x(x) dx = 0.0625
This formula provides a more comprehensive measure of risk, taking into account the potential losses in the worst cases.
Formula 5: Risk-Return Ratio Calculation
The Risk-Return Ratio calculation formula is used to assess the trade-off between risk and return. The formula is as follows:
Risk-Return Ratio = Return / Risk
Where:
- Return = expected return
- Risk = standard deviation of returns
For example, if the expected return is 0.08 and the standard deviation of returns is 0.02, the risk-return ratio would be:
Risk-Return Ratio = 0.08 / 0.02 = 4
This formula provides a simple and effective way to evaluate investment opportunities and make informed decisions.
Formula 6: Sharpe Ratio Calculation
The Sharpe Ratio calculation formula is used to assess the risk-adjusted return of an investment. The formula is as follows:
Sharpe Ratio = (Return - Risk-Free Rate) / Standard Deviation
Where:
- Return = expected return
- Risk-Free Rate = risk-free rate of return
- Standard Deviation = standard deviation of returns
For example, if the expected return is 0.08, the risk-free rate is 0.02, and the standard deviation of returns is 0.02, the Sharpe Ratio would be:
Sharpe Ratio = (0.08 - 0.02) / 0.02 = 3
This formula provides a widely used measure of risk-adjusted return, enabling investors to make informed decisions.
Formula 7: Treynor Ratio Calculation
The Treynor Ratio calculation formula is used to assess the risk-adjusted return of an investment, taking into account the systematic risk. The formula is as follows:
Treynor Ratio = (Return - Risk-Free Rate) / Beta
Where:
- Return = expected return
- Risk-Free Rate = risk-free rate of return
- Beta = systematic risk
For example, if the expected return is 0.08, the risk-free rate is 0.02, and the beta is 1.2, the Treynor Ratio would be:
Treynor Ratio = (0.08 - 0.02) / 1.2 = 0.05
This formula provides a measure of risk-adjusted return, taking into account the systematic risk of the investment.
Formula 8: Jensen’s Alpha Calculation
Jensen’s Alpha calculation formula is used to assess the risk-adjusted return of an investment, taking into account the systematic risk and the risk-free rate. The formula is as follows:
Jensen's Alpha = Return - (Risk-Free Rate + Beta x Market Return)
Where:
- Return = expected return
- Risk-Free Rate = risk-free rate of return
- Beta = systematic risk
- Market Return = market return
For example, if the expected return is 0.08, the risk-free rate is 0.02, the beta is 1.2, and the market return is 0.06, Jensen's Alpha would be:
Jensen's Alpha = 0.08 - (0.02 + 1.2 x 0.06) = 0.01
This formula provides a measure of risk-adjusted return, taking into account the systematic risk and the risk-free rate.
Formula 9: Information Ratio Calculation
The Information Ratio calculation formula is used to assess the risk-adjusted return of an investment, taking into account the systematic risk and the risk-free rate. The formula is as follows:
Information Ratio = (Return - Benchmark Return) / Tracking Error
Where:
- Return = expected return
- Benchmark Return = benchmark return
- Tracking Error = tracking error
For example, if the expected return is 0.08, the benchmark return is 0.06, and the tracking error is 0.02, the Information Ratio would be:
Information Ratio = (0.08 - 0.06) / 0.02 = 1
This formula provides a measure of risk-adjusted return, taking into account
