## Thursday, November 17, 2011

### Measuring Interest Rate Risk

CFA Level 1 - Fixed Income Investments

The Full Valuation Approach
The full valuation approach to measuring the interest rate risk is to re-value the bond or portfolio for a given interest-rate change scenario. This rate change can be parallel or non-parallel. It is also referred to as a scenario analysis because it involves the way in which your exposure will change as a result of certain interest rate scenarios.   For example, an investor may evaluate the portfolio based on an increase in rates of 50, 100 and 200 basis points. Each bond is valued and then the total value of the portfolio is computed under the various scenarios.

The Duration/Convexity Approach
In contrast, the duration/convexity approach just looks at one time parallel move in interest rates using the properties of price volatility.

Because the full valuation approach uses various outcomes to measure the risk of the bond or portfolio, as compared to a one time move for the duration/convexity approach, it bears that the full valuation approach is better suited to measuring interest-rate risk even though it can be very time consuming.

Example: Compute the Interest-Rate Risk Exposure
Let's take an option-free bond with an 8% coupon, ten-year bond with a price of 125. Yield to maturity is 7%

Scenario 1 is an increase of 50bps that drives the price down to 120 (this is just an estimate). To see the percentage change you take the new price after the yield change and subtract it from the initial price after the change divided by the initial price.

120 - 125 / 125 = -.04 = a 4 % decrease in the price of the bond due to a 50 bps change

Scenario 2 is an increase of 100 bps that drives the price down to 114.

114 - 125 / 125 = - .088 = an 8.8% decrease in price due to a 100 bps change.

You can use this for any type of scenario concerning a change in yields.

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