Yield To maturity

[Sikanderkt]

Just a quick question on Yield to Maturity

According to IFT Notes Fixed income Valuation

YTM is based on three important assumptions

A- The investor holds the bond to maturity

B- The issuer does not default on payments

C - The investor is able to re invest all proceeds at the YTM

My question is in relation to assumption C

The coupon payments are a cash inflow to the Bond Buyer it is at his discretion if he wants to invest the cash inflow he is receiving during the tenor of the bond.

Even if he wants to invest it - that investment will not be a part of the current bond structure is fixed, the investor will receive coupon payments and the face value at the end of the period.

My confusion is since that money is being generated as a inflow from the bond investment it has nothing to do with the future cash-flows, how is it impacting the YTM?


ST

 

[Harrogath]

To understand that assumption I would set 2 different scenarios, one with a zero-coupon bond yielding 5% (price today and principal at the maturity with no coupon cash) and the second, a bullet bond that pays 5% coupon annualy.
The zero-coupon bond contains in the discount of the price the “supposed” coupons it is not giving. For example a 10-year maturity $1000 face value bond would trade at a $615 price to yield 5% annualy (Discount = $385, the only source of profit for bondholder)
The bullet bond has a face value of $1000 and price of $1000 (at par) and 5% coupons. This bond has two sources of profit, the discount (profit) or premium (expense), and the coupon cash flows. The combination of both gives those 5% annual interest.
Knowing this, if you invest in a zero-coupon bond you are actually investing those $615 until to maturity (n=10) in order to get $1000 at the end. If you calculate 615 x (1.05)^10 = 1000
In the bullet bond you will receive 50 cash flow each year. Since price and face value are the same (1000 both) there is no discount profit there, it is 0. So imagine you never reinvested those cash flows of $50. At the end of year 10 you will have $500 (50x10) in coupons recieved. Calculate the average annual interest rate of this: (1500 / 1000)^(1/10) -1 = 4.14% only. This proves that if you dont reinvest those coupon cash flows at YTM (5%) you will not get the annual YTM along the maturity life of the bond.
Now let’s calculate a reinvested coupon cash flow stream:
50 x (1.05)^9 + 50 x (1.05)^8 + …. + 50 x (1.05) + 50 = 629
629 + 1000 = 1629
(1629 / 1000) ^ (1/10) -1 = 5.00000%
You must reinvest coupons at YTM in order to get that YTM along the maturity of the bond.
Hope this helps

 

[S2000magician]

I need to write an article about this one day.
First, note that YTM is nothing more nor less than the IRR of the bond.
There are two schools of thought regarding IRR (and, hence, regarding YTM):

• One believes that the IRR (or YTM) should apply to the initial investment and any cash flows that result from the investment until maturity. For this group, the reinvestment assumption is important, and it must be (on average) the same as the IRR (or YTM) for the total (periodic) return on the investment at maturity to be the IRR (or YTM). They treat the IRR (or YTM) as a rate of return at maturity.
• The other believes that, because the IRR (or YTM) is used as a discount rate, it should apply only to the amount of the money that remains in the investment, but not to cash flows that can be removed from the investment. For this group, the reinvestment assumption is irrelevant: the cash flows are removed from the investment, so the rate of return that they earn thereafter isn’t part of this investment.

Therefore, assumption C is necessary only for those in the first camp.
As you’ve no doubt inferred, CFA Institute falls firmly into the first camp.

 

[Sikanderkt]

Gentlemen,
Thank you for your response.
Both the responses were quite help full in understanding the concepts of reinvestment of coupon. As I further explored the topic credit risk and return for Fixed Income I came accross the workings of reinvestment of coupon payments.
I think the more rational way would be to not consider the return generated by the reinvestment of coupon payments as a part of the bond return since reinvestment to generate further return is not taking place in the same intrument.
This was my confusion in the first place but CFA insitute thinks otherwise and since I am enrolled as a cadidate I will have to abide by the rules.
s2000magician if you could share the article you wrote it would be a pleasure to read it!