Actuarial Outpost Method of Equated Time
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#1
05-14-2007, 09:42 PM
 rad Member Join Date: Dec 2005 Posts: 382
Method of Equated Time

Does anybody remember the formula for the Method of Equated Time?

I saw 3 questions that used this in the ASM Manual..
#2
05-14-2007, 10:51 PM
 Spook Member Join Date: Feb 2007 Posts: 114

sum of (payments*time of payment)/total of payments.
like like MacD without the v terms.
#3
05-14-2007, 11:27 PM
 rad Member Join Date: Dec 2005 Posts: 382

Oh thanks,

Now their was another formula i was looking for...and i can't remember what its called.

Its like the method of equated time but for bonds....

(maybe this doesn't exist and i need some sleep)
#4
05-15-2007, 12:01 AM
 dec0y Member SOA Join Date: Mar 2006 Posts: 213

bond salesman formula?
#5
05-15-2007, 02:00 AM
 dec0y Member SOA Join Date: Mar 2006 Posts: 213

god i hope that isnt on the test. that or portfolio methods.
#6
05-15-2007, 09:28 AM
 rad Member Join Date: Dec 2005 Posts: 382

yea yea thats the one

what is the bond salesman formula?
#7
05-15-2007, 09:44 AM
 Spook Member Join Date: Feb 2007 Posts: 114

(nFr-C+P) / (n/2)*(C+P)
#8
05-15-2007, 10:26 PM
 jason. Member Join Date: Feb 2007 Studying for CFA II Favorite beer: Samuel Smith Old Brewery Pale Ale Posts: 888

Quote:
 Originally Posted by Spook (nFr-C+P) / (n/2)*(C+P)
That's not quite right (cf. below).

It seems as if the entire world would like you to believe that this formula is mysterious and difficult to remember but it's actually neither. The bond salesman's method is a truly beautiful formula.

Just remember the following: the yield to maturity on a bond is approximately the average amount of interest earned divided by the average amount invested. If you believe and grok that statement then you now understand everything there is to say about the bond salesman's method.

How do we get from that interpretation to the above formula?

The average amount of interest earned is the total interest earned divided by the number of periods. The (undiscounted) total interest earned is the sum of the coupons plus the difference between the redemption value $C$ and the price $P$ of the bond; in symbols this is $nFr + C - P$ and therefore the average amount of interest earned is ${n Fr +C-P \over n}$. The average amount invested is simply the average of the redemption value and the price of the bond, namely ${C + P \over 2}$. There ratio of these two is the bond salesman's method, namely ${ (nFr + C - P ) / n \over (C+P) /2} = {nFr + C - P \over (n/2)(C+P) }$.
#9
05-16-2007, 04:23 AM
 yuanweir Join Date: Apr 2007 Posts: 11
i

Quote:
 Originally Posted by j.a.s.o.n That's not quite right (cf. below). It seems as if the entire world would like you to believe that this formula is mysterious and difficult to remember but it's actually neither. The bond salesman's method is a truly beautiful formula. Just remember the following: the yield to maturity on a bond is approximately the average amount of interest earned divided by the average amount invested. If you believe and grok that statement then you now understand everything there is to say about the bond salesman's method. How do we get from that interpretation to the above formula? The average amount of interest earned is the total interest earned divided by the number of periods. The (undiscounted) total interest earned is the sum of the coupons plus the difference between the redemption value $C$ and the price $P$ of the bond; in symbols this is $nFr + C - P$ and therefore the average amount of interest earned is ${n Fr +C-P \over n}$. The average amount invested is simply the average of the redemption value and the price of the bond, namely ${C + P \over 2}$. There ratio of these two is the bond salesman's method, namely ${ (nFr + C - P ) / n \over (C+P) /2} = {nFr + C - P \over (n/2)(C+P) }$.
I haven't seen that in the study manual(2007edition,ASA),so,I wonder if there is nessery to learn and remember it just for the exam ?
#10
05-16-2007, 08:21 AM
 Bama Gambler James Washer / Notes Contributor SOA Join Date: Jan 2002 Location: B'ham, AL Posts: 17,196

Neither of these (method of equated time or bond salesman's formula) are on the syllabus anymore.
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