How to think about swaps

Swaps is one of those topics that is perceived to be basic, easy, and intuitive. But not really. We study them briefly in business school and in the CFA curriculum, but that happens in a vacuum. We cannot see the thing*.

Later on in life, we find ourselves in meetings with financial advisors discussing swaps. “Of course we know swaps”, we think.

We enter into various swap contracts: fixed-to-floating, floating-to-fixed, cross-currency. And life goes on. No big deal. No one questions us because “of course we all know swaps.”

But… do we see the thing?

Fundamental concepts

Okay, I’m not going to dwell here, but there are a couple of fundamentals that I want to mention. These are really intuitive:

risk return tradeoff

This fundamental principle of finance (and of life) states that if an investor wants to achieve a higher return on an investment, then the investor must assume more risk. There’s no free lunch is a derivation of this principle.

Simple example: bonds vs. stocks. Stocks outperform bond over time but have a higher degree of volatility. This makes sense because bondholders are placed higher than stockholders in the capital structure of a company. Bondholders get paid first, thus they are taking less risk. Bondholders also typically demand a fixed coupon, which practically caps their return, while stockholders can have unlimited returns (but can also be left with nothing, if the company doesn’t perform).

U.S. stocks vs. U.S. bonds comparison over the long run
18 years of stocks vs. bonds (excludes dividends)

duration of fixed- and floating-rate bonds

Bond duration estimates the sensitivity of bond prices to changes in interest rates. The higher the duration of a bond, the higher its expected volatility.

Simple example: two 5% fixed-coupon bonds with different maturities and all else equal. Bond A matures in 1 month, Bond B matures in 10 years.

Bond B is way more sensitive to changes in interest rates than Bond A. If market rates increased from 5% to 10%, my investment in Bond A would hardly suffer a price decline because I just need to wait 1 month to receive the principal back and I’m free to reinvest at the new going rate of 10%.

Bond A, on the other hand, suffers. I’d have to wait 10 years to receive the principal or, if I want to liquidate my position, I would be selling a bond that pays 5% in a market that expects 10%.

Floaters have very short duration

Floating-rate bonds can have different maturities, but they have very short duration. For example, a 10-year floater that pays a coupon of 6-month LIBOR (or SOFR). Since the coupon resets every six months to the market rate, the bond’s price sensitivity to changes in interest rates is low, even though its maturity is long.

The traditional swap diagram is confusing and incomplete

I say this because swaps are typically described in the presence of a bond: “company A issues bond X and wants to transform its coupon by entering into swap Y”.

What happens next is that we have a hard time thinking about the swap in isolation. Our minds add the underlying bond that the swap is modifying.

But they are two separate products.

Sometimes we even want to match the coupon of a swap with that of the underlying bond. For this to make economic sense, we have to modify both legs of the swap and end up with this.

what’s missing

There’s also a missing piece. The traditional diagram depicts the “mechanics”, but fails to give us the “mental map” for valuing this product.

A complementary and more intuitive diagram

What I find useful is to draw the cash flows of the swap on a timeline. I include the final notional exchange even if the contract states that there will be no final notional exchange (for instance, in interest rate swaps).

Here’s an example of a cross-currency swap in which we receive EUR fixed at 5% and pay USD fixed at 7%. Notional is €1000 and $1000 respectively.

If you look at each stream of cash flows separately, they look like the cash flows of two individual bonds. From our perspective, we are long the EUR bond and short the USD bond.

Well, this simplifies things tremendously, and now I can “see the thing”. The value of this swap is the value of the EUR bond minus the value of the USD bond.

After inception, what factors drive value from the perspective of a USD investor?

  1. EUR interest rates (lower rates increase the value of my long position —> good for my swap)
  2. EURUSD exchange rate (a stronger Euro increases the value of my long position —> good for my swap)
  3. USD interest rates (higher rates reduces the value of my short position —> good for my swap)

We can apply the same technique to interest rate swaps. In a fixed to floating swap, the dominant bond is the fixed leg because it is the bond with the longer duration of the two. The floating leg is essentially a floater with very short duration so it’s not very sensitive to interest rate fluctuations.

Conclusion

Thinking in terms of cash flows simplifies complex financial products to a point from which we can reason using fundamental principles. This is not rocket science.

Footnote*

Seeing the thing refers to a learning technique utilized by Richard Feynman. In “Surely you’re joking, Mr Feynman!” he recounts that, when learning, he would imagine a real life example first, and go from there. This would make him go slow at the beginning, and ask basic or “dumb” questions, but shortly after he would be able to understand things in a much more fundamental way and would be capable of spotting errors when other experts couldn’t do it because they were not seeing it.