Discounted margin

Another way to calculate the yield return is the discounted margin. It differs from the simple margin because the first one amortizes the bond s premium or discount at a constantly compounded rate. The main disadvantage of this method is that it requires estimation of the reference rate over the bond s life. Assuming a bond paying semi-annual coupons, the discounted margin is given by (10.5) ... 

Therefore, the discount rate is the one that equals the bond s price to the present value of all its cash flows. As explained above, if the quoted margin is equal to the discount margin, the bond trades at par. 

Chapter 8 shows several spread measures that can be used to compare fixed-rate bonds. Conventionally for floating-rate notes, traders use the discounted margin. To analyse a floating-rate note with a fixed-rate note, one method is to compare the discounted margin of a floater with the asset swap spread of fixed-rate bonds. 

There are several yield spread measures or margins that are routinely used to evaluate floaters. The four margins commonly used are spread for life, adjusted simple margin, adjusted total margin, and discount margin. To illustrate these measures, we will assume a floater that has a coupon formula equal to 3-month LIBOR plus 45 basis points and delivers cash flows quarterly. 

One common method of measuring potential return that employs discounted cash flows is discount margin. This measure indicates the average spread or margin over the reference rate the investor can expect to earn over the security s life given a particular assumption of the path the reference rate will take to maturity. The assumption that the future levels of the reference rate are equal to today s level is the usual assumption. The procedure for calculating the discount margin is as follows ... 

Step 4. Compare the present value of the cash flows as calculated in Step 3 to the price. If the present value is equal to the security s price, the discount margin is the margin assumed in Step 2. If the present value is not equal to the security s price, go back to Step 2 and select a different margin. 

For a security selling at par, the discount margin is simply the quoted margin. 

EXHIBIT 3.16 Calculation of the Discount Margin for a Floater Floater Maturity = 6 years Coupon rate = Reference rate + 80 basis points Resets every 6 months Maturity value = 100 ... 

Exhibit 3.16 presents the calculation of the discount margin for this security. Each period in the security s life is enumerated in Column (1), while the Column (2) shows the current value of the reference rate. Column (3) sets forth the security s cash flows. For the first 11 periods, the cash flow is equal to the reference rate (10%) plus the quoted margin of 80 basis points multiplied by 100 and then divided by 2. In last 6-month period, the cash flow is 105.40—the final coupon payment of 5.40 plus the maturity value of 100. Different assumed margins appear at the top of the last five columns. The rows below the assumed margin indicate the present value of each period s cash flow for that particular... 

There are several drawbacks of the discount margin as a measure of potential return from holding a floater. First and most obvious, the measure assumes the reference rate will not change over the security s life. Second, the price of a floater for a given discount margin is sensitive to the path that the reference rate takes in the future except in the special case when the discount margin equals the quoted margin. 

To see the significance of the second drawback, it is useful to partition the value of an option-free floater into two parts (1) the present value of the security s cash flows (i.e., coupon payments and matnrity value) if the discount margin equals the quoted margin and (2) the present value of an annuity which pays the difference between the quoted margin and the discount margin mnltiplied by 100 and divided by the number of periods per year. 

This framework is also quite useful for addressing the question For a given discount margin, how does the present value of the floater s cash flows change given different assumptions about how the reference rate is... 

EXHIBIT 8.17 Bond Values Assuming Different Discounted Margins and Alternative Interest Rate Paths... 

Discounted Margin Assumed Interest Rate Path ... 

For ease of exposition, assume that we value the security on its coupon anniversary date. Let s consider two paths that 6-month LIBOR can take in the next three years. In the first path, we assume that 6-month LIBOR will remain unchanged at say, 5.25%. In the second path, we assume that 6-month LIBOR will increase by 10 basis points each period for the next three years (i.e., 5.25%, 5.35%, 5.45%, 5.55%, 5.65%, 5.75%). Finally, we will value the floater assuming three different values (in basis points) for the discount margin 0, 50 and 100. The values for the floaters associated with each discount margin and under each interest rate path are given in Exhibit 3.17. 

There are several implications that we can draw from the results in Exhibit 3.17. First, as discussed previously, when the discount margin equals the quoted margin, the value of the floater equals 100 regardless of the assumed interest rate path. This result holds because any change in the discount rate is exactly offset by a corresponding increase/ decrease in the coupon. Flowever, when the discount margin differs from the quoted margin, the present value of the security s cash flows will depend on the assumed interest rate path. 

The discounted margin for an FRN paying semiannual coupons can be solved for from equation (13.3). (Equation (13.3) may also be stated in terms of discount factors instead of the reference rate.)... 

DM = the discounted margin re = the current value of the reference index rate re = the assumed (or forecast) value of the reference rate over the remaining life the bond... 

The discounted margin is the solution to Equation (1.27) shown below, given for an FRN that pays semiannual coupons. 

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