Actuarial Outpost Intrest Rate swap question
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 Financial Mathematics Old FM Forum

#1
07-07-2017, 12:14 PM
 nickeisenberg Non-Actuary Join Date: May 2017 College: UNLV Posts: 16
Intrest Rate swap question

I have a question on #11 from the interest rate swap online reading (https://www.soa.org/Files/Edu/2016/e...rate-swaps.pdf) for the FM exam.

ABC Life Insurance Company enters into a one-year interest rate swap with a notional value of 10 million. Under this swap, ABC will pay a variable interest rate each quarter and in return will receive a fixed interest rate each quarter. The variable interest rate will adjust each quarter to be the three-month spot interest rate at the start of each quarter.

Part d) is having me find the net interest payment after the first quater.

The definition for the net interest payment is (amount of interest owed)+(net swap paid)-(net swap received)

In this problem the original loan of 10 million has a fixed rate and we are swapping it for a variable rate. So the amount of interest owed should be based on the fixed rate. The fixed rate in the problem was found to be .0033555 so the interest we owe on the loan at the first quarter is 33555. We also found that the first quarter variable rate that we are swapping to is .0024907 which means that we pay the counter party 24907 but receive 33555 from the counter party which means we receive a net swap payment of 33555-24907=8648.

So the interest owed on the loan = 33555
our net swap payment received is 8648
we have no net swap payment
so our net interest payment is 33555-8648=24907.

This isnt the answer given. They say the interest owed on the load is 24907 and we make a net swap payment of 8648 which means the net interest payment is 24907 + 8648 = 33555.

I feel like this answer doesn't make sense because we are not paying the 8648, we are receiving it from the counter party. Also 24907 isn't the interest owed on the loan for the first quarter, that is what we are paying after we agree on a swap, the interest on the loan is 33555.

I was hoping someone could explain this problem to me.
#2
07-07-2017, 01:45 PM
 CrunchinNumbers Member CAS SOA Join Date: Jul 2016 Studying for MFE? IDK Yet College: University of Missouri - St. Louis Favorite beer: Urban Chestnut: Zwickel Posts: 30

I will be watching this thread because I hate this portion of this exam, and I too believe it is a typo because ABC should be receiving the $8,700 (rounding) and not paying it out. #3 07-07-2017, 02:01 PM  nickeisenberg Non-Actuary Join Date: May 2017 College: UNLV Posts: 16 Quote:  Originally Posted by CrunchinNumbers I will be watching this thread because I hate this portion of this exam, and I too believe it is a typo because ABC should be receiving the$8,700 (rounding) and not paying it out.
If you look at the study note at example 9 and exercise 13 you can see they found the net interest payment by the way I reasoned above which makes me think it might be a typo for their answer in exercise 11. In example 9 and exercise 13 they take the interest owed to the lender (before a swap was arranged) and then add the swap payment if we make a payment to the counter party or they subtract the swap payment if the counter party makes a payment to us.
#4
07-07-2017, 10:31 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,416

Where is the information on the original loan?
#5
07-09-2017, 02:18 AM
 NattyMo Member Non-Actuary Join Date: Nov 2016 Posts: 606

Quote:
 Originally Posted by Academic Actuary Where is the information on the original loan?
Seconded. I downloaded that pdf the OP linked to and I'm not seeing the problem as described.
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#6
07-09-2017, 06:40 PM
 nickeisenberg Non-Actuary Join Date: May 2017 College: UNLV Posts: 16

Quote:
 Originally Posted by Academic Actuary Where is the information on the original loan?
heres the original problem

http://imgur.com/Szg48ay
#7
07-09-2017, 07:27 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,416

The problem gives the terms of the swap. It says nothing about an "original loan" or even if there is one.
#8
07-09-2017, 09:30 PM
 NattyMo Member Non-Actuary Join Date: Nov 2016 Posts: 606

Quote:
 Originally Posted by CrunchinNumbers I will be watching this thread because I hate this portion of this exam, and I too believe it is a typo because ABC should be receiving the \$8,700 (rounding) and not paying it out.
I agree, this section is a PITA. I'm going over the OP's most recent link (in post #6) and the terminology usage is irregular (and somewhat confusing, consequently).

Example: "The variable rate will adjust each quarter to be the three-month spot rate at the start of each quarter."

Umm... yeah, those sound like forward rates.

I would expect business types to be that sloppy with terminology, but for math professors and/or actuaries to write that problem using loose language like this is appalling.

DEFN: "The t-year spot rate, denoted $s_t$, is the rate of interest between time 0 and time t. Unless stated otherwise, assume that $s_t$ is an effective annual rate."
__________________
Favorite Quote(s):

Spoiler:

“Progress isn't made by early risers. It's made by lazy men trying to find easier ways to do something.”

“Don't handicap your children by making their lives easy.”

“There are no dangerous weapons; there are only dangerous men.”

“A desire not to butt into other people's business is at least eighty percent of all human 'wisdom'...and the other twenty percent isn't very important.”

“Belief gets in the way of learning.”

“The first principle of freedom is the right to go to hell in your own handbasket.”

“Does history record any case in which the majority was right?”

#9
07-10-2017, 01:03 AM
 NattyMo Member Non-Actuary Join Date: Nov 2016 Posts: 606

OK, so I finally managed to dissect this problem. What a royal PITA! Even worse than I thought.

\begin{align}
\textrm{LET:}
* &= \textrm{designate "effective quarterly rate" (EQR)}
\textrm{"forward rate"} &= f^*_{0,0.25}
&= (1.01)^{0.25}-1
&= 0.0024907\dots
\textrm{"ABC interest paid"} &= 10^7 f^*_{0,0.25}
&= 24,907 &\textrm{[part d]}
\textrm{"swap rate"} &= R^*
&= 0.0033555\dots &\textrm{[part a]}
\textrm{"ABC interest received"} &= 10^7 R^*
&= 33,555
\textrm{"net swap payment"} &= \textrm{"interest received"} - \textrm{"interest paid"}
&= 33,555 - 24,907
&= +8,648 &\textrm{[part b]}
\textrm{"Conclusion"} &=\textrm{"ABC will receive the net swap}
&= \textrm{payment from [part b]."} &\textrm{[part c]}

\end{align}
__________________
Favorite Quote(s):

Spoiler:

“Progress isn't made by early risers. It's made by lazy men trying to find easier ways to do something.”

“Don't handicap your children by making their lives easy.”

“There are no dangerous weapons; there are only dangerous men.”

“A desire not to butt into other people's business is at least eighty percent of all human 'wisdom'...and the other twenty percent isn't very important.”

“Belief gets in the way of learning.”

“The first principle of freedom is the right to go to hell in your own handbasket.”

“Does history record any case in which the majority was right?”

#10
07-10-2017, 02:29 AM
 NattyMo Member Non-Actuary Join Date: Nov 2016 Posts: 606

I think this edit of the problem is much more clear and precise.

Also, when learning a topic, the answers required by the problem writer should flow in a natural order designed to hint at an approach.

(11)

ABC Life Insurance Company enters into a one-year interest rate swap with a notional value of 10 million. Under this swap, ABC will pay a variable interest amount rate each quarter and in return will receive a fixed interest amount rate each quarter quarterly. The variable interest rate will adjust each quarter to be the three-month spot interest rate at the start of each quarter.

The spot interest rates at the time of the purchase of the swap are below: those in Table 1 but are repeated here for your convenience:

Table 1:

\begin{align}
&\textrm{t} &\textrm{|} &\textrm{r_t} &\textrm{||} &\textrm{t} &\textrm{|} &\textrm{r_t}
&\textrm{-----} &\textrm{|} &\textrm{-----} &\textrm{||} &\textrm{-----} &\textrm{|} &\textrm{-----}
&\textrm{0.25} &\textrm{|} &\textrm{ 1.00 %} &\textrm{||} &\textrm{1.75} &\textrm{|} &\textrm{ 2.05 %}
&\textrm{0.50} &\textrm{|} &\textrm{ 1.10 %} &\textrm{||} &\textrm{2.00} &\textrm{|} &\textrm{ 2.40 %}
&\textrm{0.75} &\textrm{|} &\textrm{ 1.22 %} &\textrm{||} &\textrm{2.25} &\textrm{|} &\textrm{ 2.75 %}
&\textrm{1.00} &\textrm{|} &\textrm{ 1.35 %} &\textrm{||} &\textrm{2.50} &\textrm{|} &\textrm{ 3.05 %}
&\textrm{1.25} &\textrm{|} &\textrm{ 1.50 %} &\textrm{||} &\textrm{2.75} &\textrm{|} &\textrm{ 3.30 %}
&\textrm{1.50} &\textrm{|} &\textrm{ 1.75 %} &\textrm{||} &\textrm{3.00} &\textrm{|} &\textrm{ 3.50 %}
\end{align}

(i)
Determine the
net interest payment made by ABC at the end of the first quarter.

(ii)
a.
Determine the swap interest rate per quarter.

(iii)
b.
Determine the net swap payment that will be made at the end of for the first quarter.

(iv)
c.
State whether ABC will make or receive the payment in (iii). b.or be required to make the payment in b.

d.
Determine the net interest payment made by ABC at the end of the first quarter.
__________________
Favorite Quote(s):

Spoiler:

“Progress isn't made by early risers. It's made by lazy men trying to find easier ways to do something.”

“Don't handicap your children by making their lives easy.”

“There are no dangerous weapons; there are only dangerous men.”

“A desire not to butt into other people's business is at least eighty percent of all human 'wisdom'...and the other twenty percent isn't very important.”

“Belief gets in the way of learning.”

“The first principle of freedom is the right to go to hell in your own handbasket.”

“Does history record any case in which the majority was right?”

 Tags interest rate swap, net interest payment