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Note on Floating Rate Securities_ A Simplified Method of Computing


									Note on Floating Rate Securities: A Simplified Method of Computing the Effective Margin
Kenneth R. Stanton Floating rate securities have cash flows that depend on some specified reference rate. For example, the interest payment may be set to equal the 6-month LIBOR rate, plus a spread of 120 basis points, where the rate is adjusted at six-month intervals. Given that the reference rate is likely to change over the life of the security, the cash flows are not known in advance. Since the cash flows are unknown, it is not possible to compute the yield to maturity. One conventional measure that is used to evaluate floating rate instruments is the effective margin. The effective margin is an estimate of the average spread over the reference rate that an investor can expect over the life of the security. This measure is best understood by explaining how it is computed, using a concrete example. Suppose that the security described above, that has floating rate payments determined as 6 -month LIBOR plus 120 basis points, has a remaining maturity of 5 years, and is selling at a price of 98.5405. If 6-month LIBOR currently stands at 6.5 percent, then the steps to compute the effective margin are as follows: 1. Assume that the reference rate remains unchanged over the life of the security, and compute the cash flows. 2. Compute the IRR of the cash flows from Step 1, using a financial calculator, a spreadsheet, or trial-and-error. 3. Subtract the reference rate used in Step 1, from the IRR computed in Step 2. The result of this subtraction is the effective margin. In our example, since LIBOR equals 6.5 percent, we have 10 semiannual interest payments of ((.065 + 120 basis points)/2)  $100 = $3.85, plus a final cash flow of $100 to repay the principal. If we purchased the security today, we would have an initial cash outlay of 98.5405. Therefore, the cash flows are: Time period 0 1 2 3 4 5 6 7 8 9 10 Cash flow -98.5405 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 103.85

Using a spreadsheet, the IRR for this set of cash flows is equal to 8.0604 percent. Subtracting our reference rate of 6.5 percent, we find that the effective margin equals 1.5604 percent. Notice that the stated premium over LIBOR is 120 basis points, but based on the current LIBOR rate, and the market price, the effective margin is 156 basis points. Fabozzi’s text does not make apparent the link between the effective margin and the familiar IRR. Although many students fail to recognize it, his approach is to use trial-anderror to find a spread over the reference rate, which equates the present value of the cash flows with the observed price. The approach we use in this note is intended to point out the link to the familiar IRR and the underlying simplicity of the effective margin measure.

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