Semiannual coupon and annual coupon

[nit]

I am confused semiannual coupon and annual coupon, In schweser note, I saw many questions like following examples ( FRM 2013, Part 1, Book 3, page 54)
Compute the price of a $100 face value, 2 year, 4% semiannual coupon bond using the annualized spot rates

It is very easy to calculate this price by discounting the cash flows to present value, however, I don't know the semiannual coupon is 4% or 2%

It is clear that respect to the above red word, the semiannual coupon is 4%, but the Shweser note's answer uses the semiannual coupon of 2% to compute the price of bond

Could you please help me this problem? Thank in advance

 

[ShaktiRathore]

The semiannual coupon given 4% is given in yearly terms but the coupon are paid out semiannually so we discount them by 4/2%=2% to price the bond.

thanks

 

[nit]

The semiannual coupon given 4% is given in yearly terms but the coupon are paid out semiannually so we discount them by 4/2%=2% to price the bond.

thanks

Thank you very much Mr Shakti Rathore.
I understand the solution for this question, this is semiannual coupon with 4%/year. But, up to this moment, I don't know the answer when I meet a phrase like that "T bond pays 10% semiannual coupons". Is the semiannual coupon 10% or 5%?

Thanks

 

[ShaktiRathore]

Hi,
The meaning of 10% semiannual coupons is that the bond pays coupon at 10% of face value per year compounded semiannually. So the rate is 5% per semiannual period which is used to pay coupon at end of each half year. so that for a bond with face value 100 with 10% semiannual couponsmeans that coupons are paid semiannually(at end of each half year) at 10/2%=5% which is (5/100)*100=5 , so the semiannual coupon is 5% because the rate 10% is compounded semiannually.

thanks

 

[David Harper CFA FRM]

I agree with Shakti. This can be confusing. However, at least in the FRM, questions tend to consistently employ the so-called "nominal" (aka, stated) interest rate, and this nominal rate is presumed to be per annum. Specifically, for example:

• When we read: "T bond pays 10% semiannual coupon,"
• It means the same thing as: "T bond pays a 10% per annum semiannual coupon" or,
• And if we were really going to explicate it fully: "T bond pays a semiannual coupon with coupon rate of 10% per annum"

It's actually less confusing, in the long run, to depend on the convention that the coupon rate is specified as a per annum (and note, as a "nominal" rate, this implies that the effective annual rate will vary depending on the compound frequency. So the reference to "stated" or "nominal" per annum is deliberately different than the effective annual). Thanks,

 

[chiyui]

David and Shakti have explained the issue in detail, so I'll just add a simple comment for you to easily memorize the answer.

In nearly almost every cases, interest rates (as well as other percentage rates) are quoted yearly, just like what David said it is per annum. This is the habit in the finance world.
But how to compound the yearly interest rates is another issue.

So don't hesitate to divide the interest rate by 2 if the question asks you semiannual compounding,
don't hesitate to divide the interest rate by 12 if the question asks you monthly compounding,
and don't hesitate to divide the interest rate by ∞ if the question asks you continuous compounding.

Just divide it!

Unless the question explicitly mentions that the interest rate is quoted non-yearly, you have to use interest rate quoted in yearly term.