# Economic Capital Calculation: Approaches

We know that economic capital is the amount of capital a bank needs to maintain to absorb the impact of unexpected losses during a time horizon at a certain level of confidence.

The approaches to calculating economic capital can be broadly classified into top-down and bottom-up approaches.

Top-down Approaches

Under the top-down approaches, the economic capital can be calculated using the aggregate performance information at the enterprise level. The information used can be Earnings Volatility, or Stock Prices.

The earnings volatility approach assumes that the value of capital is equal to the value of perpetual earnings stream, which is calculated as Expected Earnings/k, where expected earnings are the expected earnings for the next period, and k is the required rate of return. Since we are looking at calculating the economic capital, which is the capital required to sustain worst-case loss, we can calculate economic capital as EC = EaR/k, where EaR is the earnings at risk (i.e., the difference between worst-case earnings and expected earnings).

The problem with this approach is that very few companies have enough reliable data to arrive at an appropriate measure of EaR. Also, there is no direct connection between the economic capital calculated this way and the risks being measured. Under this approach, it is also difficult to segregate capital for credit, market and operational risk.

Another approach based on stock prices uses the Black-Scholes-Model to calculate the market value of capital. Under this approach the value of capital can be seen as a call option on the value of the firm’s debt. If the value of assets is above the value of debt, then the capital will be equal to the difference between the value of assets and debt. The economic capital can be calculated by applying the BSM model for a level of debt that is required for the firm to remain solvent even under worst scenario. This approach uses the firm’s stock prices for which the data is easily available.

Bottom-up Approach

Under the bottom-up approach, the economic capital is estimated by modelling individual transactions and business units and then aggregating the risk using statistical models. This approach is preferred over top-down approaches because of the high level of transparency and the ability to segregate credit risk, market risk, and operational risk. The firm uses VaR models to calculate individual risks, and then it calculates the capital across these risks. As a common practice, credit risk capital, market risk capital, and operational risk capital are added up.

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