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Bond Salesman's Method

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  • Bond Salesman's Method

    I do not have the Kellison book and I was wondering if someone could tell me the formula for the bond salesman method. I think it is

    g - (1/n)[(p-c)/c] /
    1 + .5 [(p-c)/c]

    where g = coupon / redemption value
    n = number of periods
    p = price
    c = redemption value

    I have come to this formula through inferrence from problems solved in the FM study manual but the BS method formula is never explicitly stated in the book. I think it is probably right, although, I am not sure about the ".5" in the denominator. I am not sure if that part is always supposed to be .5 or if it was .5 in the two examples I saw because they involved coupons being paid semianually. Thanks.

    Live long and prosper,

    Mr. Spock

  • #2
    You have correctly stated the Bond Salesman's formula. (Actually, Kellison defines k = (P -C)/C and states the formula as (g - k/n)/(1 + .5k), which is equivalent to what you have.)

    Rather than memorize this formula in a form that is not very intuitive, I prefer to think of it this way:

    The approximate yield rate earned on a bond is the average amount of interest earned per period divided by the average investment over the term of the bond.

    The average interest earned per period is simply the total interest earned (i.e., the sum of the coupons and redemption value minus the price) divided by the number of periods, which equals [n(Cg) + C - P]/n.

    The average investment over the term of the bond is simply .5(P + C).

    Thus, the approximate yield rate is [n(Cg) + C - P]/.5n(P + C).

    You will find that if you multiply your (or Kellison's) formula by nC/nC and do a little bit of algebra, you will get it into the above form.

    IMO, the above version of the formula is better than the Kellison version because (1) it's much easier to remember, since it directly states a common sense way of approximating the yield rate (average interest earned divided by average investment) and (2) it's easier to apply to an actual bond. (For one thing, you don't have to explicitly compute g; Cg is simply the coupon, i.e., Fr.)

    (Mild plug): I don't know which FM manual you are using, but in my ASM manual, both the Kellison version and my version of the formula are shown (pages 336-337 of the 3rd edition). A more refined formula developed by Kellison is also shown (pages 337-338).

    Having said all of this, I should also point out that the Bond Salesman's formula has not appeared on the exam very frequently. However, it's on the syllabus, and you never know.
    FSA, MAAA, EA and CEO of Actuarial Study Materials -