 # Bond Question

Hi, i have encountered this sentence: The Bondholder will actually realize YTM (yield to maturity) on his initial investment only if all payments scheluded are paid, the bond is held to maturity and, importantly, all interim payments (coupons) are reinvested at the YTM. what does it mean that: “all interim payments (coupons) are reinvested at the YTM”? for e.g. we have a 5 year bond, 8% seminually payment coupons, par = 1000, YTM is 7% so the first coupon payment is 40 (4% from 1000), and now what? i must reivested this 40 at 7% (Annual basis). But where to reinvest it? I dont get it… Also, can someone refresh my memory how to compute A. price B. YTM of the bond C. coupon payment on BaII+ calculator having rest of the data? Example A. Price, from YTM, coupon, N, par etc. Thanks in Advance SFR

It means exactly what you said above, it is assumed the coupon is reinvested at the YTM, int his case 7%. If you think about it, YTM is nothing more than an internal rate of return for a bond. I’m not sure I understand your question, are you referring to the time value of money functions or the bond function?

Yeah but where should i reinvest this 40? buy another bond for this 40? both, i just forgot how to deal with bonds on BaII+. I ve passed lvl 1 on Dec 2007 and my technical knowledge is a bit rusty.

That is what is called the reinvestment risk associated with bonds. \$40 has been given to you as a coupon payment and in order to get your theorized YTM, you would need to find an investment which gives you the same risk adjusted return of 7%. Now, in a falling interest rate market, it may not be possible for you to reinvest your interim payment into something that gives you the same yield. This is the reinvestment risk associated with that bond. In general, higher the coupon rate of a bond, higher coupon payments (interim payments) it will be making and higher will be the reinvestment risk. But if a bond is paying a higher coupon, its price risk will be lower. So, increased reinvestment risk is compensated by it lower Price risk.

If you think YTM is not realistic, ask yourself what’s the YTM for a stock? At least with bonds, you have some way of measauring your return.

ok so , i have 2 year semiannual coupon 8%, at par 1000, Price 900 and i must assess YTM BaII+ gives me answer that YTM is 9,7420 so: reinevesting 40 at the YTM each year we have 172,0746 and principal 1000 year 0.5 = 40 = 40 year 1 = 40 + 40*(1,048710) = 81,9484 year 1.5 = 40 + 40*(1,048710) + 40*(1,048710)^2 = 125,9401 year 2 = 40 + 40*(1,048710) + 40*(1,048710)^2 + 40*(1,048710)^3 = 172,0746 year 2 = 1000 pricipal so summing up i have 1172,0746 FV now, putting it back to present i have 40 + 41,9484 / (1,0487) + 43,9917/(1,0487)^2 + 46,1345/(1,0487)^3 + 1000/(1,0487)^3 40 + 40 + 40 + 40 + 867,0298 = 1027,0298 initial inv = price of the bond = 900 1027,0298 / 900 is 1,14 so 14% return, not 9,7420 as the YTM states… I don’t get it… can somebody explain this reinvesting coupons with relation to YTM on example? I would be grateful , thanks.

I think the YTM is 13.90%

The “internal rate of return” or YTM does NOT depend on reinvestment of the coupons. The example posed by SFR on 11Jan2010 was: “ok so , i have 2 year semiannual coupon 8%, at par 1000, Price 900 and i must assess YTM” The cash flow for this example is: (-900, 40, 40, 40, 1040) That is, the stated coupon of 8% is paid semianually, is 40 and is taken as a benefit at the end of each 6 month period. NO reinvestment is necessary. I find the “internal rate of return” or YTM to be 14.38% For the above cash flow, no reinvestment has taken place. If you require reinvestment at whatever rate you can get then you must readjust the cash flow and recalculate the “internal rate of return” for the new cash flow.

so why in the book they wrote this: “The Bondholder will actually realize YTM (yield to maturity) on his initial investment only if all payments scheluded are paid, the bond is held to maturity and, importantly, all interim payments (coupons) are reinvested at the YTM”?

WLITTLE IS WRONG. Other posters before were right. For any Internal rate of return concept to work 1. all cash flows have to be reinvested at the internal rate of return. 2. the cash flows have to be realized to maturity. if neither of these happens - you do not achieve your IRR number. For bonds - YTM is the IRR - and the two above should be true for the YTM to be realized. Otherwise you have the reinvestment rate risk.

ok cpk, so we have 3 source of income: A. Pricipal repayment at maturity B. Coupons C. Income from Reivesting from Coupons. can you show me the \$ value for each of this A, B ,C component with relation to YTM? Assume that for simplicity we have: - 8% annual coupon - price 900 - par value 1000 i would be grateful , thanks

1. What do you mean in relation to YTM? 2. This is something that is laid out in the level I books on Fixed Income. Read those. You forgot the life of the security. Assume 4 years. repayment at maturity would be 1000 coupons would be 80 for each annual period the reinvestment income: YTM: Since you paid 900 and fv was 1000 at the end of 4 years - YTM is 11.24% How much is the future value of what you paid to buy the bond: 900*(1.1124)^4 => 1378.12 Coupons Future Value => 378.11 = FV(80,4,11.24%) 1000 is the End maturity Value When you reinvest everything at the YTM: 1000+378.11 - 1378.11 = 0 But if you were looking only at say Coupon rate of 8% 900*(1.08)^4 = 1224.44 FV(80,4,8%) = 360 about Maturity Value = 1000 How much you need to reinvest to achieve your YTM: 1360-1224.44 = 136.56 approx. This was seriously discussed in the Level I material on Fixed income. break out the seal on the books. I too will do so - since what I have written above is based on memory.

ok thanks, this means that YTM is unrealistic, cuz it is virtually impossbile to reinvest coupons at the same yield 4 year in a row. This is the main limitation of YTM right?

It’s the YTM *if* you reinvest at the same rate,that’s what it should be called. It’s just an approximation, or a sophisticated guess really, of your return. In your example: 1) You pay \$900 now and receive \$1000 at the end of the 2nd year, after 4 semi-annual periods. 2) You receive \$40 at end of 1st, 2nd, 3rd, and 4th periods, which you invest at the same internal rate of return. 3) You solve for the rate that would make \$900 today equals to all that stream of cash flows. That magical (usually computer-generated) rate you get in step 3 is called the YTM.

Again in the example by SFR on 11Jan2010: “ok so , i have 2 year semiannual coupon 8%, at par 1000, Price 900 and i must assess YTM” The cash flow for this example is: (-900, 40, 40, 40, 1040) … CF1 This cash flow shows that the 40 units at the end of each 6 months are received but NOT reinvested and so can be used for any purpose ie to buy food or they may be given away. Here the benefits are said to be consumed. They do not take any further part in the project. Recall that the IRR for CF1 is 14.38% If the 40 units payments are reinvested at lets say 14.38% then the cash flow of the reinvested payments at 14.38% is: (0, -40, -40, -40, 137.46) … CF2 Now add CF1 + CF2 for the cash flow of the original problem but with the payments reinvested at 14.38% and get: (-900, 0, 0, 0, 1177.46) … CF3 The IRR for the problem with payments reinvested ie CF3 is also 14.38%. The IRR for the reinvested cash flow is called modified internal rate of return or MIRR. Conclusion: The IRR of a cash flow problem has the same numerical value whether the benefits are consumed OR are reinvested at the same IRR as the unreinvested project. Some comments. 1. In practice if the benefits are not consumed but reinvested at a realistic rate less than the IRR of 14.38% then the MIRR will be smaller than the IRR. 2. Dreary has found the YTM or IRR to be 13.90% This is the semiannual yield times 2. For the annual percentage yield: ((1+13.90/200)^2 -1)*100 which is 14.38% I agree with your comments regarding your calculation procedure except for your item 2) where you reinvest the coupons, but if you do as described, you will obtain the same IRR as not reinvesting. 3. SFR quoted: “The Bondholder will actually realize YTM (yield to maturity) on his initial investment only if all payments scheluded are paid, the bond is held to maturity and, importantly, all interim payments (coupons) are reinvested at the YTM”? This statement refers to the yield on the INITIAL INVESTMENT of the bond and assumes that any payments are reinvested until maturity. The IRR of a project measures the yield on the PROJECT BALANCE which takes into account cash flows into or from the project during its life so the IRR or YTM of a bond gives the yield assuming that the coupons are consumed and the bond is held to maturity. 4. I think most people in this discussion are thinking of the IRR or YTM on the INITIAL INVESTMENT of a bond whereas since the coupons are paid out we should be calculating the yield on the PROJECT BALANCE of the bond and so use the actual cash flow. 5. When discussing a cash flow problem, it is most important to write down the actual cash flow as in CF1, CF2 and CF3 in the above example. This statement of cash flow then clearly shows if benefits are consumed or reinvested as the case may be. Perhaps in further discussion you will write down the cash flow of any example.

Dude how did u pass L1 if ur having so much trouble grasping such a basic concept as is YTM? better crack open those L1 books and give them a refresher otherwise u have an interesting 4months to look forward to.

Dude how on earth did u pass L1 if ur having so much trouble grasping such a basic concept as is YTM? better crack open those L1 books and give them a refresher otherwise u have an interesting 4months to look forward to.

jorgeam86 Wrote: ------------------------------------------------------- > Dude how on earth did u pass L1 if ur having so > much trouble grasping such a basic concept as is > YTM? better crack open those L1 books and give > them a refresher otherwise u have an interesting > 4months to look forward to. +1

well… i have passed L1 on December 2007, i just forgot some bond basics… i understand what is YTM etc, my question was rather concerning reinvesting coupons…

I agree, YTM is a basic concept but when some of you can hardly construct sentances, spell correctly, or express yourselve then you may have difficulties in understanding most things.