# Measuring Interest Rate Risk: Full Valuation Approach

We know that bond prices are sensitive to interest rate changes. A portfolio of bonds will suffer a loss if the interest rates rise and vice versa. Similarly, a short bond position will make losses when interest rates fall. What a portfolio manager is interested in is to know the exact losses his portfolio will suffer under different interest rate change scenario.

For example, he may be interested in knowing how the bond portfolio value will be affected if interest rates rise by 0.50%, 1% and 2%, so that he can hedge his portfolio accordingly.

There are two ways to measure the interest rate risk: 1) Full Valuation Approach, and 2) Duration/Convexity approach. In this article we will look at the full valuation approach.

The full valuation approach is the simplest yet comprehensive way to measure interest rate risk in a bond. We start with the current market yield and price of the bond. Then we fix on the different scenarios (interest rate changes) at which we want to value the bond, say a 0.5% increase in interest rates. We then re-value the bond for each interest rate scenario. The new value is then compared to the current value to determine the gain/loss due to changes in interest rates. This method is also sometimes referred to as scenario analysis.

While performing scenario analysis on a portfolio of bonds, each bond is re-valued at different interest rates and the portfolio value is recalculated.

Some institutions may want to test the behavior of bonds under extreme conditions where they will estimate the probable losses under extreme changes in interest rates. This is called stress testing the portfolio.

While this is the recommended and most accurate approach to measuring interest rate risk, it is not always practical especially when it’s a large portfolio. The full valuation approach is also very time consuming. Rather than having to revalue an entire portfolio, managers will prefer a simpler approach which could quickly give them an idea of how bond prices will change with changes in interest rates. This can be achieved by using the duration/convexity approach.

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