<p>I find it hard to believe the professor never discussed any of these formulas but expects you to compute it - unless it is a Matlab course where teh professors expects you to search Mathworks a bit (e.g. for &quot;select CTD bond&quot;) where there are plenty of resources (everything related to a BondFuture instrument object: like convfactor, bndfutprice, and bndfutimprepo).</p>
<p>For example, the implied repo rate is the return you get from selling the future and buying the CTD bond. The formula:</p>
<p><span class="math-container">$$IR = \frac{DP + ACC_D - (P + ACC_S) + C}{(P_{B_{flat}} + ACC_S )\times (D_1/360)) - C \times (D_2/360)}$$</span></p>
<p>where <span class="math-container">$DP$</span> is the delivery price (factor * futures quote for factor contracts), <span class="math-container">$ACC_S$</span> is the accrued at spot date, <span class="math-container">$ACC_D$</span> is the accrued at the delivery date, <span class="math-container">$P$</span> is the flat bond purchase price, <span class="math-container">$D_1$</span> refers to the days from purchase settlement to futures delivery and <span class="math-container">$D_2$</span> are the days from interim coupon receipt to futures delivery.</p>
<p>If you have access to Bloomberg (via a university lab or library for example), you can look up <code>CTD</code>:</p>
<p><a href="https://i.sstatic.net/KiV3b.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/KiV3b.png" alt="enter image description here" /></a></p>
<p>The implied repo of -31.925 is computed as such (using <a href="https://julialang.org/" rel="nofollow noreferrer">Julia</a>:</p>
<pre><code>p_flat = 98.3828125
acc_s = 1.2230663
D1 = 64
interim_coupon = 1.375 # from CSHF in BBG 
D2 = 44
P_delivery = 119.59375
factor = 0.7718
acc_d = 0.32880435 # from YAS for delivery date 
(P_delivery*factor + acc_d-(p_flat + acc_s) + interim_coupon)/(((p_flat + acc_s)*(D1/360))-(interim_coupon*(D2/360)))*100
</code></pre>
<p><a href="https://i.sstatic.net/X4kMU.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/X4kMU.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2023-03-29T22:01:48.920Z
2023-03-29T22:01:48.920Z
AKdemy
<p>I'm trying to solve an exercise with Eurodollar and deliverable bonds.
This is the text in matlab <a href="https://i.sstatic.net/kpfYq.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/kpfYq.jpg" alt="enter image description here" /></a></p>
<p>Basically there are two Bonds A and B and I need to find a few things about them. I use the formula with the yield to maturity (and notional = 1) to compute the Conversion factors at point 5a (the formula for Price of the bond with yield to maturity equal to 6%) and I find that CF_A = <span class="math-container">$0.98$</span> and CF_B = <span class="math-container">$1.12$</span>.</p>
<p>However now I'm stuck after point a, since I don't understand how can i compute the different points:</p>
<p>5b. How  can I get the number of deliverable bonds from the CF? Is there a formula? I tried asking the professor he just told me it depends on the CF itself...</p>
<p>5c. How can I compute the Implied Repo rate? What do I need ?</p>
<p>5d/5e. I know that we need to have a minimization problem with the notes basis in order to find the CTD, but I don't understand how I can do it in matlab.</p>
<p>If someone can help, even with only point 5b. it would be amazing! This is just a quick exercise the professor gave us to practice, nothing too serious!</p>

CC BY-SA 4.0
2023-03-26T14:05:23.813Z
Eurodollar futures have no cheapest to delivery (the underlying is not a bond). I am sure the professor provided formulas for bond futures in the lecture notes.
AKdemy
CC BY-SA 4.0
2023-03-26T16:21:30.963Z
The last lecture was on Eurodollar futures, so I assumed the homework was also on that, but I think you are right... in older notes there are no formulas for CTD or for number of bonds to be delivered, I even tried asking him and he just said that the number of bonds depends on the CF only. Do you know what he means? I couldn't find anything neither in the notes, nor the book/internet
Blipo
<self-study><bonds><eurodollar>
Eurodollar exercise
Blipo
# Eurodollar exercise

(Asked by: username_0 on 2023-03-26)

I'm trying to solve an exercise with Eurodollar and deliverable bonds.
This is the text in matlab [![enter image description here](https://i.sstatic.net/kpfYq.jpg)](https://i.sstatic.net/kpfYq.jpg)

Basically there are two Bonds A and B and I need to find a few things about them. I use the formula with the yield to maturity (and notional = 1) to compute the Conversion factors at point 5a (the formula for Price of the bond with yield to maturity equal to 6%) and I find that CF\_A = $0.98$ and CF\_B = $1.12$.

However now I'm stuck after point a, since I don't understand how can i compute the different points:

5b. How can I get the number of deliverable bonds from the CF? Is there a formula? I tried asking the professor he just told me it depends on the CF itself...

5c. How can I compute the Implied Repo rate? What do I need ?

5d/5e. I know that we need to have a minimization problem with the notes basis in order to find the CTD, but I don't understand how I can do it in matlab.

If someone can help, even with only point 5b. it would be amazing! This is just a quick exercise the professor gave us to practice, nothing too serious!

**Tags:** self-study, bonds, eurodollar

> **Comments:**
> **username_1**: Eurodollar futures have no cheapest to delivery (the underlying is not a bond). I am sure the professor provided formulas for bond futures in the lecture notes.  
> **username_0**: The last lecture was on Eurodollar futures, so I assumed the homework was also on that, but I think you are right... in older notes there are no formulas for CTD or for number of bonds to be delivered, I even tried asking him and he just said that the number of bonds depends on the CF only. Do you know what he means? I couldn't find anything neither in the notes, nor the book/internet  

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## 1 answers

### Answer by username_1 on 2023-03-29. Score: 1 | Accepted answer

I find it hard to believe the professor never discussed any of these formulas but expects you to compute it - unless it is a Matlab course where teh professors expects you to search Mathworks a bit (e.g. for "select CTD bond") where there are plenty of resources (everything related to a BondFuture instrument object: like convfactor, bndfutprice, and bndfutimprepo).
For example, the implied repo rate is the return you get from selling the future and buying the CTD bond. The formula:
$$IR = \frac{DP + ACC_D - (P + ACC_S) + C}{(P_{B_{flat}} + ACC_S )\times (D_1/360)) - C \times (D_2/360)}$$
where $DP$ is the delivery price (factor * futures quote for factor contracts), $ACC_S$ is the accrued at spot date, $ACC_D$ is the accrued at the delivery date, $P$ is the flat bond purchase price, $D_1$ refers to the days from purchase settlement to futures delivery and $D_2$ are the days from interim coupon receipt to futures delivery.
If you have access to Bloomberg (via a university lab or library for example), you can look up CTD:

The implied repo of -31.925 is computed as such (using Julia:
p_flat = 98.3828125
acc_s = 1.2230663
D1 = 64
interim_coupon = 1.375 # from CSHF in BBG 
D2 = 44
P_delivery = 119.59375
factor = 0.7718
acc_d = 0.32880435 # from YAS for delivery date 
(P_delivery*factor + acc_d-(p_flat + acc_s) + interim_coupon)/(((p_flat + acc_s)*(D1/360))-(interim_coupon*(D2/360)))*100


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