Quoted margin

Quoted margins are for the chemical industry. Margins for other industries might be different, although most R D services seem to be competitively supplied (Maurer 2005). 

Coupon rate = reference rate -f quoted margin... 

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. 

Spread duration Measuring the price sensitivity to change of quoted margin, maintaining a fixed reference rate. 

Floating-rate notes can include additional features. One example is the inclusion of cap, floor and collar clauses. A floater with cap feature means that the reference rate cannot overcome the threshold rate defined in the indenture. Usually the threshold is expressed in terms of coupon, that is after a coupon threshold (e.g. 6%, reference rate plus quoted margin) the investor receives at maximum the cap level. In this case, the floater is not completely covered by rising interest rates, in which after the threshold the floater trades as a conventional bond. In contrast, a floater with a floor feature represents the minimum coupon level that an investor can receive, hedging to the downside risk of interest rates. If the bond includes both cap and floor, this feature is known as collar or collared floating-rate note. The bond can include also a drop-lock feature that after a threshold it ceases to float. 

Thus far our coverage of valuation has been on fixed-rate coupon bonds. In this section we look at how to value credit-risky floaters. We begin our valuation discussion with the simplest possible case—a default risk-free floater with no embedded options. Suppose the floater pays cash flows quarterly and the coupon formula is 3-month LIBOR flat (i.e., the quoted margin is zero). The coupon reset and payment dates are assumed to coincide. Under these idealized circumstances, the floater s price will always equal par on the coupon reset dates. This result holds because the floater s new coupon rate is always reset to reflect the current market rate (e.g., 3-month LIBOR). Accordingly, on each coupon reset date, any change in interest rates (via the reference rate) is also reflected in the size of the floater s coupon payment. 

The discussion is easily expanded to include risky floaters (e.g., corporate floaters) without a call feature or other embedded options. A floater pays a spread above the reference rate (i.e., the quoted margin) to compensate the investor for the risks (e.g., default, liquidity, etc.) associated with this security. The quoted margin is established on the floater s issue date and is fixed to maturity. If the market s evaluation of the risk of holding the floater does not change, the risky floater will be repriced to par on each coupon reset date just as with the default-free floater. This result holds as long as the issuer s risk can be characterized by a constant markup over the risk-free rate. 

A floater whose quoted margin and required margin are the same and... 

A differential risk annuity that delivers payments equal to the difference between the quoted margin and the required margin multiplied by the par value. 

Quoted margin is also called the index spread. ... 

Since this floater matures in four years, there are 16 coupon payments to be made. Assume that 3-month LIBOR is 5% and will remain at that level until the floater s maturity. Finally, suppose the required margin is also 15 basis points so the quoted margin and the required margin are the same. Exhibit 3.5 illustrates the valuation process. 

The first column in Exhibit 3.5 simply lists the quarterly periods. Next, Column (2) lists the number of days in each quarterly coupon period assumed to be 91 days. Column (3) indicates the assumed current value of 3-month LIBOR. In period 0, 3-month LIBOR is the current 3-month spot rate. In periods 1 through 16, these rates are implied 3-month LIBOR forward rates derived from the current LIBOR yield curve. For ease of exposition, we will call these rates forward rates. Recall for a floater, the coupon rate is set at the beginning of the period and paid at the end. For example, the coupon rate in the first period depends on the value of 3-month LIBOR at period 0 plus the quoted margin. In this first illustration, 3-month LIBOR is assumed to remain constant at 5%. Column (4) is the quoted margin of 15 basis points and remains fixed to maturity. 

The cash flow is found by multiplying the coupon rate and the maturity value (assumed to be 100). However, the coupon rate (the forward rate in the previous period plus the quoted margin) must be adjusted for the number of days in the quarterly payment period. The formula to do so is... 

EXHIBIT 8.5 Valuing a Risk Floater When the Market s Required Margin Equals the Quoted Margin ... 

It is important to stress that this result holds regardless of the path 3-month LIBOR takes in the future. To see this, we replicate the process described in Exhibit 3.5 once again with one important exception. Rather than remaining constant, we assume that 3-month LIBOR forward rates increase by 1 basis point per quarter until the floater s maturity. These calculations are displayed in Exhibit 3.6. As before, the present value of the floater s projected cash flows is 100. When the market s required margin equals the quoted margin, any increase/decrease in the floater s projected cash flows will result in an offsetting increase/... 

To illustrate, we will value the same hypothetical 4-year floater assuming that the required margin is now 20 basis points. For this to occur, some dimension of the floater s risk or the market must have increased since the floater s issuance. Now in order to be reset to par, our floater would hypothetically have to possess a coupon rate equal to 3-month LIBOR plus 20 basis points. Since the quoted margin is fixed, the floater s price must fall to reflect the market s perceived increase in the security s risk. 

Quoted margin - Required margin) xNumber of days in period], ... 

The quoted margin and required margin are in Columns (4) and (5), respectively. These cash flows are contained in Column (6). The discount factors are computed as described previously with the exception of the larger required margin. The discount factors appear in Column (7). The present value of the each cash flow is in Column (8) and is just the product of the cash flow (Column (6)) and its corresponding discount factor (Column (7)). The present value of the differential risk annuity is -0.1813 and is shown at the bottom of Column (8). 

Once the present valne of the differential risk annuity is determined, the price of our hypothetical 4-year floater is simply the sum of 100 (price of the floater per 100 of par value when the quoted margin and required margin are the same) and the present value of the differential risk annuity. In our example,... 

When the required margin exceeds the quoted margin, the floater will be priced at a discount to par value. However, the size of the discount will depend on the assumed path 3-month LIBOR will take in the future. 

Let s discuss the case when the required margin is less than the quoted margin. Assume the required margin is now 10 basis points and... 

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

For example, suppose that a 6-year floater selling for 99.3098 pays the reference rate plus a quoted margin of 80 basis points. The coupon resets every six months. Assume that the current value of the reference rate is 10%. 

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. 

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. 

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