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Aug 3, 2006 9:03 am

Hi, I've been trying to put together all of the topics I've learned in the past 2 weeks...can someone check this to see if this correct:


Assume:


1000 PAR -- 3% Coupon, paid semi anually -- 6 years to maturity -- YTM= 8% -- Price=765.37


(1) Total Return= [(1000-765.37) + 180] / 765.37 = 54.17


(2) "Simple" Avg Annual Return... 54.17/6 = 9.0928...but, this does not take compunding into account....so we use...


(3) CAGR= geometric avg of the annual growth rate= takes compouding into account....it says, ' if you invested 765.37 at this amount on an annual basis, you would have produce the same total amount'.....1180= 765.37 * (1+i)^6 ...we use 6 because we are calculating the compund ANNUAL growth rate. = 7.48%


(4) YTM assumes that all coupon payments are invested at the same rate as the YTM...therefore, if we treat the 12 coupon payments as annnuity with a discount rate of 4% (8%/2)...we get...FV Ordinary annutiy= [((1+.04)^23) -1) / .04] 15 = 225.38...225.38 + 1000 par we rec at maturity = 1225.38...NOW, calculate the FV of 765.37 @ 4% semi-annual rate for 12 periods= 765.37(1.04^12)=1225.38


(5) Can also convert the 4% + 4% YTM into an EAR...EAR= (1+.04)^2 -1=.0816=8.16%..........765.37(1.0816^6)= 1225.38



Thanks for any feedback or corrections...it gets me very confused!


Thanks,


Joe

Aug 3, 2006 10:58 am

What is EAR?

What exactly is confusing to you?

Aug 3, 2006 11:22 am

Sorry....EAR= effective annual rate. 


I'm just not sure if what I did was correct...we've learned these concepts over a two week period, and I tried to combine them and understand how they all fit together-


Thanks,


Joe

Aug 3, 2006 11:33 am
Mrjoe1008:

Sorry....EAR= effective annual rate. 


I'm just not sure if what I did was correct...we've learned these concepts over a two week period, and I tried to combine them and understand how they all fit together-


Thanks,


Joe



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