Bond total return calculation

(Mock 2014 version c) To calculate the total return on:

a bond with a beginning price of $103, a 5% semiannual coupon, an expected price at the end of one year of $102.5, and an annual reinvestment rate of 2%.

Step 1: The total value in 1 year = 2.5 + 2.5(1+2%/2) + 102.5 = 107.525

Step 2: The semi-annual return = (107.525 / 103)^0.5 - 1 = 2.173%

Step 3: Total return = 2.173% * 2 = 4.3459%

Can anyone explain why we need to “semi-anuallize” the return in step 2 and then double it to get the total return?

Why is it not right to just do 107.525/103 - 1 = 4.39%?

Bc bond coupon is paid semi-annually.

Btw, the answer is BEY (If question asks EAR, then ^2 -1)

Thanks Frank.

How does coupon being paid semi-annually require the total return to be semi-annualized? The capital gain part is not semi-annual though.

how do you get 2014 mocks? can I get it?

Thanks in advance.

BEY does not assume compounding. That’s why it’s lower. BEY is an annualized figure that allows you to compare quarterly and semi-annually pay bonds to annual pay bonds. As we know, the more you compound a return, the higher it will be. BEY simply removes the compounding component on the first coupon payment.

So it’s *2 in step 3.

Probably take a look at BEY formula will be helpful.

I get it now! thanks Chuck and Frank

By the way, the question did not explicitly ask for BEY. Is it true that for all Total Return computation, we should use BEY?

They’re going to tell us, especially if it’s a multiple choice question. If you see a question like this on the exam you are very likely to see two answers that are close in value. BEY is always lower than EAR for semi-annual bonds.

See if you like to solve it this way -

P0 = 103, P1 = 102.5, C=5%, RR=2% (Semiannual = 1%)

Return at the end of year = (P1 + CF’s - P0)/P0

= 102.5 + 1.01(2.5) + 2.5 - 103/103

= 0.043932 %

BEY = 2*[(1+0.043932)^0.5 -1] = 4.3459%