# Economic value of equity (EVE) or market value of equity (MVE) at risk reporting

Economic value of equity (EVE) at risk or Fall in market value of equity (MVE) depicts a change in the market value of equity due to changes in market values of assets and liabilities. The respective change in assets and liabilities is computed from the interest rate shock derived, based on the value at risk (VaR) approach.

### Step 1: Determine look back period

Determine the period over which the risk is to be evaluated. For illustration purposes let us assume a look back period from 1st January 2009 to 30th June 2009, inclusive.

### Step 2: Data collection

The data is interest rate data for all available buckets. In our example we use the PKRV rates (these are government treasury rates) at all available buckets for the determined look back period.

Economic value of equity at risk – Calculating interest rate volatility

### Step 3: Calculated the return series

Calculate the returns series for all the interest rate buckets by taking the natural logarithm of the ratio of successive rates. This is determined as follows for the given illustration.

Economic value of equity at risk – Calculating interest rate volatility – step 2

### Step 4: Calculate the days to maturity/ days to reset

Calculate days to maturity and in case of floating rate instruments, days to next reset across the balance sheet items. For example in our illustration the days to maturity for the following instruments have been calculated as follows:

Settlement Date = 30/06/2009

Economic value of equity at risk – Calculating DTM

### Step 5: Calculate individual weights for each asset and liability

Calculate the weights of each individual asset and liability with respect to the total (interest bearing) asset and liability portfolio (based on their MTM). This is done for our example as follows:

Economic value of equity at risk – Calculating weights for report template

### Step 6: Obtain return series for each individual asset/ liability

Based on the days to maturity/ days to reset calculated in Step 4 obtain the relevant return series calculated in Step 3 for each individual asset and liability. In our example for the individual asset “Term Finance Certificates” which had 328 days to maturity, this is the return series for interest rate bucket 271-365 days.

### Step 7: Calculate weighted average return series for assets and liabilities separately

Using the weights determined in Step 5 and the return series obtained above, weighted average return series for assets and liabilities are derived. In our example, this is illustrated for liabilities as follows:

Economic value of equity at risk – Rates volatility – step 3

### Step 8: Compute VaR

Using the weighted average series compute the volatilities and Holding VaRs for both assets and liabilities. In our example the volatilities and 10-day holding VaRs at the 90% confidence interval for the asset and liabilities are as follows:

Economic value of equity at risk – Rates volatility

[For a more detailed step-by-step procedure for calculating VaR you may like to review the course “Calculating Value at Risk”].

### Step 9: Compute the MTM weighted average yield to maturity (YTM)

Calculate the weight average YTM for assets and liabilities respectively. This is carried out in two stages as follows. Note that the YTMs for individual instruments are based on market rates:

• Step 9a- First; calculate the weighted average YTM for each asset/liability within each asset/ liability category.
• Step 9b- Next; calculate the weighted average YTM of each category to the total (interest sensitive) asset/ liability portfolios.

This is illustrated step-wise for the asset portfolio. Illustration of step 9a:

Economic value of equity at risk – Rates weighted average YTM

Illustration of Step 9b:

Economic value of equity at risk – Rates weighted average YTM

### Step 10: Compute Rate Shock

The rate shock will be calculated using the following formulas:

• Rate-Shock Assets= MTM weighted YTM for assets × Holding VaR for Assets
• Rate-Shock Liabilities= MTM Weighted YTM liabilities × Holding VaR for Liabilities

This is illustrated in our example as follows:

Economic value of equity at risk – Rates shock

### Step 11: Compute the weighted duration of assets and liabilities

Calculate the weighted average duration for assets and liabilities respectively. As for the case of YTM this is carried out in two stages as follows:

• Step 11a- First; calculate the weighted average duration for each asset/liability within each asset/ liability category.
• Step 11b- Next; calculate the weighted average duration of each category to the total (interest sensitive) asset/ liability portfolios.

This is illustrated step-wise for the asset portfolio. Illustration of step 11a:

Economic value of equity at risk – weighted average duration

Illustration of Step 11b:

Economic value of equity at risk – weighted average duration

### Step 12: Fall in EVE / MVE

The fall in MVE is calculated as the ‘Fall in Assets’ MTM Value’ less the ‘Fall in Liabilities’ MTM Value’.

• Fall in Assets’ MTM Value = Weighted Duration of assets × Rate Shock Assets × MTM Total Assets[1]
• Fall in Liabilities’ MTM Value = Weighted Duration of liabilities ×Rate Shock Liabilities × MTM Total Liabilities

Our example illustrates this as follows for the 90% confidence level:

Economic value of equity at risk – Calculating EVE / MVE

The complete range of values for confidence levels 86% to 99% is given in the table below as well as depicted in the following two graphs:

Economic value of equity at risk – Plot and risk limit curve

Economic value of equity at risk – rate shock plot

Economic value of equity at risk – MVE / EVE rate shock plot

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[1] Total Assets and liabilities include interest and non-interest sensitive assets and liabilities.

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