While equity swaps typically use a variable notional, fixed notional swaps are possible as well. So it's important to understand the mechanics of both variable and fixed notional equity swaps.

Let's begin with variable notional equity swaps in a variable notional equity swap, the notional amount is adjusted at each reset based on the price performance of the underlying index.

This approach simulates holding an equity portfolio with a constant number of shares, meaning the value of the position grows or shrinks with the markets. At each reset, accumulated obligations are exchanged between the two parties.

This is akin to terminating the existing swap and entering a new one with the notional adjusted for index performance.

Let's explore this with an example, using a three month equity swap with monthly resets, and let's start with an initial notional of 100 million and an initial index level of 2,605.

Over the first month index rises by 2.3608%.

Taking the new index level to 2,666.50.

This performance increases the notional to 102.36 million reflecting the 2.36% gain.

Now, consider the cash flows.

The equity payer owes the equity receiver, the 2.3608% gain, which is approximately $2.36 million.

At the same time, the equity receiver owes the equity payer interest on the notional. Using the examples one month rate of 5.315%.

The interest payments is approximately 443,000, calculated ads 100 million times 5.315%, and then de-annualized down to a one month time period by multiplying by 30 over 360.

Knitting these flows, the equity receiver receives about 1.92 million for the first month.

This process repeats each month with a notional recalculated to reflect the latest index performance.

For example, the payments to be made at the second reset will be calculated on the adjusted notional at the end of the first month, the 102,360,844.53.

This means the equity leg cash flow for month two is calculated as the 102.36 million adjusted notional times the 2.0559% equity return to give 2,104,414 and an interest cash flow of 102.36 million times the one month rate for the second month of 5.328% times 30 over 360.

One question that often arises is why the interest in a variable notional swap is paid on the increased notional after each reset.

To understand this, let's compare it to a direct equity investment. In a regular share position, if you initially invested 100 million, you would only borrow 100 million, and any capital appreciation would remain unrealized until you sold the shares.

However, in a variable notional equity swap, the equity returns including any gains that would be unrealized in the direct equity investments, those returns are settled at each reset because the gains are realized and received at the reset, the equity receiver effectively has more capital at their disposal, which they could reinvest into the equity markets, but could also invest elsewhere.

Paying interest on the increased notional accounts for the fact that the realized gains provide immediate liquidity, ensuring the swap remains fair and balanced for both parties.

Let's move on to fixed notional equity swaps.

In contrast, fixed notional swaps maintain a constant notional throughout the swaps life.

This approach simulates a fixed investment value where an investor implicitly buys or sells shares at the end of each reset period to return their equity portfolio back to its initial value.

Taking the same initial setup as the variable notional swap that we looked at previously, there will be no difference in the first month's cash flow since the opening notional onto both approaches would be 100 million.

However, under a fixed notional swap, the logic is that the investor liquidates The 2.36 million gain from their equity position.

Meaning the equity position for month two would start again back at 100 million.

This leads to a lower equity leg cash flow in month two.

Since the return of 2.0559% is applied to 100 million rather than on 102.36 million.

The same goes for the interest payment giving 444,000 for the fixed notional rather than 454,482 for the variable notional swap interest leg in month two.

The key takeaway is that variable notional swaps mimic a position of holding a constant number of shares, allowing the position to grow or shrink with the markets. Fixed notional swaps, on the other hand, simulates a fixed investment value where the notional remains stable regardless of market performance.

While variable notional swaps are more common due to their natural alignments with typical equity exposure, fixed notional swaps can be useful for investors seeking to maintain a constant capital allocation.