Yield To Maturity and Bond Equivalent Yield

[e2lcfa]

I am having a hard time trying to grasp these concepts. Is it fair to say that:
The YTM is the yield you can expect if you hold a bond/fixed income instrument to maturity? I know this is the rate of return that will make PV of cash flows = market price + accrued interest but just trying to think of it another way!
Also, how would you explain the difference between YTM and Bond Equivalent Yield in simple english?
Please help! Thank you! Any clarification,examples, additional explanation would greatly help!

 

[PBR]

That definition of YTM is true, but doesn’t fully explain why it’s used.
YTM is the yield that takes into account 3 things: The par value returned at maturity, gain or loss (when the bond is trading at premium or discount) at maturity, AND the coupon payments (it assumes those coupon payments are reinvested at the YTM rate~ this is crucial).
When they refer to YTM in the book, it’s usually the bond equivalent version of YTM. This is they convention that is used.
If the YTM yield stated is NOT on the bond equivalent basis, that means it is the effective annualized rate. You would take the square root of it and multiply by 2 to get the bond equivalent version of it. (someone can correct me if this is wrong).

 

[e2lcfa]

Thanks PBR…that was helpful. I’m still not very comfortable though - rereading will hlep I think.
More questions – I’m sure this is simple:
1) “The current yield will be greater than the coupon rate when the bond sells at a discount”
Is this the case because the value of a bond issued at discount is below the par value? Any other explanation. I know this is easy but having a hard time with this stuff.
2) What is the YTM of a 6% 15-year bond selling for for $84.25? The answer is 7.8%. When I plug the inputs (PV = -84.25, FV=100, n=30,pmt=3 solve for I/Y) my answer is 46.7973 and then i divided by 12 to get 3.8998 adn then multiplied by 2 to get 7.8%. Is there a way I can avoid dividing by 12…is there a settin gin the calculator?
thanks ina dvance for help.

 

[NByz]

1) Yes. I always think of there being two components to the bond’s yield. First, the coupon payments. Second, how much the “principal” appreciates or depreciates. If you buy a bond at 97 (at a discount), it’ll ‘yield’ an additional $3 over its coupon payments over the term of the bond (because you get $100 back at the end).
2) Yes. The setting (on the BA II plus) is “P/Y” (how many periods per year). Press “2nd” “P/Y” and set it to either 1, 2 or 12 (or occasionally 4), as appropriate, before each question.

 

[cpk123]

If you consistently kept the P/Y to 1 – you would directly get the 3.89997% answer in the question above.
when P/Y is 1 - remember to multiply N by # of periods. and i/Y divide by # of periods. By that I mean
If annual interest - you have to do nothing.
in the problem above - you have a semi-annual payment - and hence you said PMT=3, N=30 (15 * 2) so you get I/Y for a semiannual mode - and you need to multiply by 2 to get your annualised YTM.

 

[e2lcfa]

Thank you NByz and cpk123! that’s helpful!