# FRM Fun 16 (P1 only): Comparative advantage

Discussion in 'Today's Daily Questions' started by David Harper CFA FRM, Aug 9, 2012.

1. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

For P1 FRM only.

In my tweetstream, @jdportes writes, "Astonishing. WSJ prints article whose first sentence defines comparative advantage - and gets it completely wrong."

The article is here, and this is the mistaken first paragraph from yesterday's Wall Street Journal:
In regard to Hull's (Chapter 7) swaps, our AIM is "Describe the comparative advantage argument for the existence of interest rate swaps ..."

If we were to mistakenly assume the above definition with respect to interest rate swaps, a comparative advantage would mistakenly refer to a bank (FI) which can borrow at a lower rate, or earn a higher investment return, than another bank. But a comparative advantage in borrowing/lending markets is more subtle than this.

Questions:
1. What is a comparative advantage in borrowing/lending capital markets which enables the utility of an interest rate swap (something brief and memorable would be great)?
2. If we assume a market maker as the swap intermediary who charges (X) bps to intermediate a vanilla fixed-for-floating interest rate swap, what is the simple mathematical condition that justifies an IRS; i.e., that implies both counterparties can improve their position via an IRS?

2. ### ShaktiRathoreWell-Known Member

Comparative Advantage means that parties entering into contract are in advantage than when they are not entering into the contract. In interest rate swap either party can change their liability or an investment from fixed to floating or from floating to fixed. For e.g. X has liability of paying fixed interest on Bonds but are facing risk of volatile interest rates and wants to minimize this risk. Y on the other hand has floating rate liability and want to minimize risk of interest rates than it can enter into IRS with X by paying fixed rate and receiving floating rate. IN this way X pays its fixed rate liability at the same time minimizing the floating rate risk which is advantageous to X and similarly Y pays its floating rate liability by paying fixed rate which is advantageous to Y.

Part2:
X receives fixed rate x and pays floating rate y. While Y pays fixed rate x and receives floating rate y. With Intermediary charges X.
X pays y+X and receives x that y+X<x
x-y>X…1
and on other hand
Y pays x+X and receives y so that y>x+X
y-x>X….2
from 1 and 2,
mod(x-y)>X

3. ### Turtle KingNew Member

Comparative advantage in the context of borrowing/lending markets exists in the form of interest rate differentials across the fixed rate and floating rate markets. This interest rate differential exists due to the difference in default risk premium priced in both these markets (generally default risk premium in fixed markets is higher than that of floating rate markets). Accordingly, companies and financial institutions might leverage this competetive advantage to enjoy an incentive by swapping cash flows from one market into the other in their borrowing/lending activities by entering into an IRS.

4. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

ShaktiRathore and Turtle King, thank you for your participation, you each win a star!

In regard to (2), if X pays fixed rate of f(x) and floating rate of l(x) where l(x) = rate above LIBOR or any floating rate index that is common to both as it washes out, and Y pays fixed rate of f(y) and floating rate of l(y), and where:
a = f(x) - f(y),
b = l(x) - l(y)

then according to Hull, and as demonstrated by several of the practice questions, the total net gain (before intermediary) is (a - b) and with intermediary, total gain distributed to both counterparties, where F = intermediary fee, is given by (a-b) - F, such that gain is possible i.i.f.: a - b > F

or, put equivalently, where F = fee, total net gain is given by:
[f(x) - f(y)] - [l(x) - l(y)] - F, or
[f(x) - l(x)] - [f(y) + l(y)] - F

in this way, comparative advantage occurs when
• fixed rate differential <> floating rate differential, between X and Y, or equivalently
• fixed rate premium of X (i.e., fixed rate - floating rate) <> fixed rate premium of Y
and the total net gain among the two counterparties is given by:
• MAX[ABS(a - b) - F, 0]
• where a = f(x) - f(y) = fixed rate difference and b = l(x) - l(y) = floating rate difference

• Like x 1
5. ### Aleksander HansenWell-Known Member

An interesting corollary is what this means in terms of:
1) Free trade and restrictions on voluntary exchange,
2) The whining about manufacturing jobs being moved "overseas" and outsourcing and the division of labor.