FRA schwesernotes first example: investment in financial asset (amortized discount?)

Dear all,

Happy new year and hope everyone is doing well :slight_smile:

I have a question on FRA investment in financial assets, actually the question is not on the classification, but instead, on the calculation. On page 4 of the schweser FRA notes, the question says “purchased a 9% bond with a face value of 100,000 for 96,209 to yield 10%.” And end of year bond value is 98,500. We are to calculate the impact on balance sheet and income statement on the 3 different type of classifications.

So the 10% here means yield to maturity right? And in the answer below, there is a amortized discount of 621 (9,621 interest revenue - 9,000 coupon payment). I don’t understand this amortized discount or interest revenue. Can someone kindly explain??

Thanks a lot, really appreciate your help :slight_smile:



Cash flow = 0,09 X FV = always 9000.

YTM x Begin. of period BV = 0,1 X 96.209= 9.621

Discount amortization = 9.621 - 9000 = 621

Real income in P/L = 9000 + 621 = 9621 (collected coupon + discount amortization)

Amortization of bond in BS = 96.209 +621 = 96.830 until FV of 100.000 is reached.

If you have bond purchased with premium the offsetting in P/L is opposite, collected coupon - premium amortization and you again amortize bond but in opposite direction until FV is reached.

thanks for your reply flashback, but im still quite confused, in the example the notes say there is an interest revenue of 9,621 (96,209 beginning bond investment x 10% market rate at issuance). I don’t understand what is this, why this interest revenue mins the 9,000 coupon equals discount amortization? I dont think i see it in level 2 fixed income book, it was probably in level 1 and i just never understood it.

Maybe I did not clearly specified what the real P/L income of bondholder is. This is received periodical coupon payment and + periodical discount amortization amount (or - premium amortization amount). Since bondholder purchased bond at discount, there is a coupon income increase by periodical discount amount. This is exactly bondholder’s interest income.

Since the bond was purchased at a discount, but will be settled on maturity at par, you have another kind of income (other than interest) that you have to recognize. But you cannot recognize the entire discount at the start or end, you have to recognize the income on a systematic basis over the life of the financial asset. This is done by means of effective interest rate method: interest + discount income is recognized using effective interest rate (ytm rate), which is the rate that discounts all future cash flows to the present value on settlement (when you buy the instrument). The stated interest rate is rather the interest paid each period, which differs from the recognized income by the portion of discount/premium recognized in the current period.

That’s not an accurate way to express it.

All of the income you recognize is interest. Part of it is the coupon payment (cash) that you receive. Part of it is the amortization of the discount. But it’s all considered interest.

thank you guys, these topic within topic makes cfa so difficult. I guess there were adressed in lv1 as i dont see them in level 2 fixed income, and i probably did not understand it very well back then (i still not 100%)

hope i will come across more examples and learn it eventually.

Some of these are pretty abstract in theory. Got to get your hands dirty with questions and problems if you want to get the intuition behind the concepts.

Let me give it a try flashback…

Think of it in terms of market where the interest rate on similar kind of bond is 10%.

An investor will invest in a such a bond only when he gets 10% return/ excess cash / rent on his money.

Since the bond will actually pay a stated rate of less than what is justified(10%) he will get his further required return from a source other than stated interest/ coupon rate… The other source is the amount he will receive upon redemption. But since the amount is not received every year in cash like stated interest, he will get the shortfall compounded every year thereby adding the shortfall (621 in your example) in the principle so as to earn compounded interest on it every yr…

Also note that 621 is not 1% (10%-9%)… Why ?because rather than increasing his redemption amount of 100k by 1% compounded return, he has discounted his upfront investment below facevalue of 100,000 to create an impact of 1% shortfall…

If u still dont get it dont worry u’ll get a flashback of ut once you practise few random examples :-p

Hi, I’m struggling with the concept of interest and ytm in the question as well, could someone explain how they found the YTM (in this case -10%) or will this always be given, and do you need to accept this as a given in the questions?

This YTM will not always be given. This was a favor by the questioner :slight_smile:

YTM in its simplest form is the IRR. i.e at the time of investment 10% was the rate that brought the present value of all future cashflows of the Bond (interest + redemption amount) to its initial investment amount i.e 96,209.

If they told you that it’s a 5-year bond you could figure it out using the TVM buttons on your calculator; the original post doesn’t make it clear whether you were given the maturity or the YTM.

Don’t count on the YTM being given, but count on having enough information to calculate it if you need to.