Tuckman -Chapter 3-Realized Return, YTM, RE-Investment of Coupons

[gargi.adhikari]

Please refer to the last slide from Tuckman -Chapter 3. Where can I find the solution to the problem statement below- Rate of ReInvestment of Coupons? I have not been able to locate the same in the Learning Spreadsheet but I might have missed seeing the correct sheet..any inputs would be much appreciated..!

 

[Deepak Chitnis]

Hi @gargi.adhikari, what I can understand from your given information is that, coupon get reinvested @ 10% Yield. Hope that helps. You can derive is using the calculator also. N=10(because semi annual),I/Y=5%,PMT=4, FV=100 CPT---> PV=92.278
Thank you

 

[Nicole Seaman]

Hello @gargi.adhikari

On the second slide of this instructional video, it lists the spreadsheets that are associated with that specific video.



Also, I just wanted to make sure that you have found the spreadsheet bundles that are under the Topic 4 review. If you already have these, I'm sure someone can help to point out which spreadsheet can help you with this, but I wanted to make sure you were aware of those bundles.



Nicole

 

[gargi.adhikari]

@Deepak Chitnis Thanks so very much. That for sure helped a lot. By any chance for a clearer and theoretical understanding, what would be the formula to derive the Realized Return given the Yield? Also, I see that we are computing the PV so is the Realized Return = the same as the Bond Price that we calculate? How is the Realized Return different from the Bond Price?

 

[gargi.adhikari]

@Nicole Manley Thanks so much as usual for pointing to the spreadsheet bundles. Yes I am aware of these. But for this particular Problem Statement, it did not point to any spreadsheet.... I looked in T4.c bundle....to see if I could find the relevant sheet...so far did not....if someone is cognizant of the relevant sheet and can point to it- I would be very much grateful !

 

[brian.field]

I am unclear on what you are asking exactly. My impression is that there is some confusion between what is meant by a "yield" or "yield-to-maturity" and return, or realized return, or price.

 

[David Harper CFA FRM]

Hi @gargi.adhikari The really wasn't an XLS sheet for that concept, but I quickly re-worked an existing sheet (because it would be helpful to add this!). This is not quite pretty yet, but for notice, notice that (in YELLOW) you can vary the reinvestment rate and compare the effect on the realized return (in PURPLE), see https://www.dropbox.com/s/a3gq4gurzcutjn9/0302-YTM-reinvested.xlsx?dl=0

@brian.field gargi is looking, I think, for the XLS that "demonstrates" the concept, which is that coupons must be reinvested at the yield in order for the realized return to equal the original yield (aka, ytm). Thanks!

 

[gargi.adhikari]

@David Harper CFA FRM Thanks so much David !

 

[David Harper CFA FRM]

@gargi.adhikari sure thing, I am glad you asked ... this is, to me, another example (in a long list of examples) where I could read Tuckman's description, on the page, ten times and I'd never grok the idea. I need to see it working in spreadsheet/code/calcs. Thanks!

 

[gargi.adhikari]

@David Harper CFA FRM Quick Question on the calculation of the Realized Return:-
The Realized Return Formula used is : { [ (FV + Coupon ) / PV ] ^ (1/mT) } * m => How do we deduce this formula for Realized Return?- especially the power component of (1/MT)...?? Also, how does this formula align to the Realized Return formula of : [ P t+1 + Coupon - P t (or B Funding Price ) / P-Initial Price ]

Also, if we wanted to calculate the Realized Return using the Calculator what value should be used for the PMT as the PMT for each period is different..? The order and the value of the Calculator Keystrokes would be very helpful- Thanks a bunch in advance

 

[David Harper CFA FRM]

Hi @gargi.adhikari Tuckman's definition of realized return, [ P t+1 + Coupon - P t (or B Funding Price ) / P-Initial Price ], is just a (simple, discrete) holding period return and yield-to-maturity (yield) is just an ex ante (expected) internal rate of return (IRR), so I wouldn't let the contextual labels distract you from the fact that this is all just discounted cash flows. To get the realized return, the "trick" here, for me, is to capture the compounded coupon interest. So, I would do that first. For example, if the assume the coupons get reinvested at 8.0% (i.e., lower than the ex ante yield of 10%, by which i mean the yield implied by a price of $92.28 and the expectation that coupons get reinvested at the yield, as that is the implicit assumption of any bond yield calculation if we are pricing before the coupons pay).

1. To get the future value of the coupon reinvested at 8%, we can use: N = 10, 4 = I/Y, 0 = PV [i.e., only the coupons], 4 = PMT and CPT FV = $48.02,
   
2. So, in cash flows terms, we will pay $92.28 (time 0) and at the end we will "receive" $100 (the return of the par) plus $48.02 in coupons cumulatively reinvested; i.e., $148.02
3. We can retrieve the semi-annual rate with: N =10, PV=-92.28, PMT = 0 (because the coupons are in the final now), FV = 148.02 and CPT I/Y = 4.839% * 2 = 9.6783%; but this also just like a CAGR except the periodicity is semi-annual, so the rate implied by 92.28*(1+r/2)^(2t) = 148.02 is --> r = (148.02/92.28)^(1/10)-1]*2 = 9.6783%. I hope that explains!

 

[gargi.adhikari]

@David Harper CFA FRM Thanks so so very much David for putting this together! That was indeed very helpful

 

[gargi.adhikari]

@David Harper CFA FRM Dumb Question- Apologies- What did you mean by a CAGR...?

 

[Deepak Chitnis]

Hi @gargi.adhikari, CAGR means compound annual growth rate. Its just a rate with annual compounding. Hope that helps.
Thank you

 

[gargi.adhikari]

@Deepak Chitnis Thank so much !

 

[gargi.adhikari]

@David Harper CFA FRM In the YTM-reinvested spreadsheet you provided above, I was trying to derive the future value of the coupon reinvested at 5% using the following:-
N = 10,
1/Y= 5/2=2.5,
0 = PV [i.e., only the coupons],
PMT = 5% * (100) *( .5 )= 2.5
and CPT FV = 28.0085 instead of a $44.81 ( which we get if we do it by hand and calculate each of the discounted Coupon Cash Flows and then summing them up...)

I guess this is happening b/c the Coupon Re-Investment rate is different from the Yield and also the compounding has not been factored in...? So if I wanted to get to the Total Coupon FV= $44.81 using the calculator...what would I need to do/what would be the keystrokes so that I can save some time and don't have to calculate each of the discounted Coupon cash flows for each Re-Investment period...?

 

[ShaktiRathore]

Future value of coupons reinvested at 5% semiannually for 5 years.
Future value=(coupon(PMT)/2.5%)*((1.025)^10-1)=(2.5/.025)*((1.025)^10-1)=28.0085 which is same as coming from calculator gargi.I think you did some calculation error.
thanks

 

[gargi.adhikari]

HI @ShaktiRathore
My apologies- I should have included a screenshot for reference...Please refer the screenshot below..the Discounted Coupon Cashflows add upto $44.81...
I understand the calculation if we calculate each Discounted Coupon cash flow and add them up....I was trying to see if I could directly do it on the calculator...?
Thanks for all your help in advance

 

[David Harper CFA FRM]

Hi @gargi.adhikari Your inputs are correct except the coupon payments are $4.00 not $2.50; ie, the bond has a coupon rate of 8.0% per annum payable semi-annually. So if you want the future value of only the coupons: N=10, I/Y = 2.5, PV =0, PMT = 4 and then CPT FV = 44.81. I hope that helps!

 

[gargi.adhikari]

@David Harper CFA FRM Thanks a bunch again for coming to the rescue. .
Needless to say that am indebted..