Asset Swaps

An asset swap comes up when a bank that holds fixed-rate bonds wants to match the rates on its assets and liabilities. It is also used to judge whether a government bond is cheap or expensive by its rate gap to interest rate swaps.

Combining a bond and an interest rate swap

An asset swap combines the purchase of a bond with an interest rate swap of the same maturity¹. The side that buys the bond and enters a swap paying the fixed rate is said to buy the asset swap. The side that sells the bond and enters a swap receiving the fixed rate is said to sell it¹. How an interest rate swap exchanges a fixed rate for a floating rate is covered on the Interest Rate Swaps page.

The buyer receives the fixed coupon on the bond and pays the fixed rate on the swap. As a result, the buyer receives a floating rate instead. The credit risk of the bond's issuer stays with the buyer².

The type in which the bond is bought at par is a par asset swap. The buyer buys the bond from the seller at par and at the same time enters an interest rate swap with that seller. On the swap, the buyer pays a fixed rate equal to the bond's coupon and receives interest calculated at the floating rate plus the asset swap spread. The swap has the same maturity as the bond³.

From the seller's side, the trade is a sale of the bond at par, together with a swap that receives the fixed rate and pays interest at the floating rate plus the spread⁴.

How the spread is set and what it is called

In a par asset swap, the spread is set at the start so that the bond purchase and the swap together have a value of zero³. Consider a hypothetical example in which Bank N buys a corporate bond from Securities Firm O at par in a par asset swap. The bond has a face value of 10 billion yen, 3 years remaining, and a coupon of 2% a year paid annually. The bond's market value is 9.8 billion yen. The par rate of a 3-year interest rate swap is 1% a year, and the discount rate is 1% a year (compounded annually) for all maturities.

Bank N pays the face value of 10 billion yen for a bond worth 9.8 billion yen, so it overpays by 200 million yen. Securities Firm O repays this through the margin added to the floating rate. The discount factors (1/1.01, 1/1.01², and 1/1.01³) sum to about 2.941. A level payment for 3 years with a present value of 200 million yen is therefore 200 ÷ 2.941, or about 68 million yen a year. That is 0.68% a year on 10 billion yen.

There is a second part of the margin. The fixed rate that Bank N pays is 2% a year, the same as the coupon. This is 1 percentage point above the par rate of 1% a year, and a margin of 1.00% a year makes up the difference. The spread is the sum of the two parts: 1.00% + 0.68% = 1.68% a year⁵. If the bond's market value is 10.2 billion yen instead, buying at par gains 200 million yen in value, and the margin is 1.00% minus 0.68%, or 0.32% a year.

The spread can also be found by subtracting the swap rate from the bond's yield. A 2020 paper from the Policy Research Institute, Ministry of Finance, calls the method that uses the difference between the bond yield and the swap rate of the same maturity matched maturity, and says it is the usual method in Japan. It calls the method that exchanges funds at the start so that the bond is priced at par par-par, and says the two methods give different values⁶. The bond in the example yields about 2.70% a year, compounded annually. Subtracting the swap rate of 1% gives about 1.70%, slightly different from the margin of 1.68% found above, so the value depends on how it is calculated.

The Policy Research Institute paper calls the government bond yield minus the swap rate alpha (α). The swap rate minus the government bond yield is also called the swap spread, which has the opposite sign to α⁷.

Cash flows over three years

In the example above, suppose the floating rate is 0.5% in year 1, 1% in year 2, and 1.5% in year 3. The figure below shows Bank N's cash flows.

Figure description

Bank N pays the face value of 10 billion yen at the start (−10). The coupon and the fixed rate offset each other, so what it receives is the floating rate plus the spread as interest, and the redemption in the last year. The 10.318 in year 3 includes the face-value redemption of 10.

The table below shows the payments year by year. A positive net amount is a receipt for Bank N, and a negative amount is a payment.

Suppose Bank N funds the 10 billion yen purchase price at the floating rate with no margin. The funding cost and the floating-rate receipt offset each other, which leaves the spread: 168 million yen a year (10 billion yen × 1.68%).

Default and remaining risks

The bond and the interest rate swap are two separate trades³. If the bond defaults, Bank N loses part of the bond's coupons and redemption amount. The swap either continues until the bond's maturity or is closed out at market value⁸. While it continues, Bank N keeps paying the fixed rate of 200 million yen a year without receiving the bond's coupons.

Consider a case in which the corporate bond defaults right after the trade and the recovery rate is 40% (a recovery amount of 4 billion yen). Assume interest rates do not change after the start of the trade.

Bank N pays the face value of 10 billion yen for a bond that recovers 4 billion yen, so it loses 6 billion yen on the bond. At the start, the market value of the swap is +200 million yen if the bond's market value is 9.8 billion yen, and −200 million yen if it is 10.2 billion yen. The total loss is the difference between the bond's market value and the recovery amount (9.8 − 4 = 5.8 billion yen, and 10.2 − 4 = 6.2 billion yen)⁹.

Bank N bought a bond worth less than par at par, so for the 200 million yen gap between face value and market value it takes on Securities Firm O's credit risk at the start. This amount falls to zero toward maturity¹⁰. Other risks remain too. The interest rate sensitivities of the bond and the swap do not match, which leaves a small interest rate risk. If the cost of funding the purchase rises, the return falls¹¹.

Uses in bond investing

A bank that holds fixed-rate bonds, funded with short-term money whose rate changes like deposits, can use an asset swap to turn the bond's receipts into a floating rate and match the rates on its assets and liabilities (ALM)². If Bank N in the example funds the purchase at the floating rate, 168 million yen a year remains when there is no default. If the bond defaults right after the trade and rates do not change, the loss with a recovery amount of 4 billion yen is 5.8 billion yen.

An asset swap is also used to reduce the effect of interest rates and take on the credit risk of the bond's issuer. For tax or accounting reasons, it can also be used to trade an asset at par when its price is not par¹².

In the yen bond market, traders buy a government bond and pay on an interest rate swap to trade the rate gap between the government bond and the swap. If you expect the government bond's rate, which is too high compared with the swap rate, to come back down, a position that buys the bond and pays on the swap gains when the gap narrows and can lose money when it widens¹³.

Other types and the difference from a CDS

Besides the par asset swap, there is the market asset swap, in which the bond is bought at its market value¹⁴.

A CDS is a trade in which the protection buyer receives the face value minus the recovery amount if the bond defaults. It is covered on the Credit Default Swaps (CDS) page. If an asset swap buyer pays par for a bond whose market value is also par, the maximum loss is likewise the face value minus the recovery amount. O'Kane explains that the spreads of the two should be close in terms of expected loss. He also explains that, because of liquidity, funding costs, supply and demand, and counterparty risk, the actual difference between the spreads is large¹⁵.

Notes

1. Policy Research Institute, Ministry of Finance, "アセット・スワップ（スワップ・スプレッド）入門 ―日本国債と金利スワップの裁定について―" (external site) (Introduction to asset swaps (swap spreads): arbitrage between Japanese government bonds and interest rate swaps, our translation; in Japanese; Finance, September 2020), section 2.1 (pp. 64–65). ↩ ↩²

2. Dominic O'Kane, "Introduction to Asset Swaps" (external site) (Lehman Brothers, Analytical Research Series, January 2000), summary and "Introduction" (pp. 2–3). A 2000 explanation. ↩ ↩²

3. O'Kane, "Introduction to Asset Swaps" (external site), "Mechanics of a par asset swap" (pp. 3–4) and Figure 1. ↩ ↩² ↩³

4. O'Kane, "Introduction to Asset Swaps" (external site), "Summary" (p. 9). ↩

5. O'Kane, "Introduction to Asset Swaps" (external site), Appendix "Computing the asset swap spread" (p. 10). The formula is applied to the example's conditions. ↩

6. Policy Research Institute, Ministry of Finance paper (external site) (in Japanese), "BOX 1 アセット・スワップにおけるαの計算方法" (Calculating alpha in an asset swap), p. 67. ↩

7. Policy Research Institute, Ministry of Finance paper (external site) (in Japanese), "2.2 アセット・スワップのキャッシュ・フロー" (Cash flows of an asset swap), pp. 65–66, and BOX 1 (p. 67). Note 6 (p. 66) says that in a par-par asset swap and similar cases, the "L − T" swap spread can differ from the asset swap spread. ↩ ↩²

8. O'Kane, "Introduction to Asset Swaps" (external site), note to Figure 1 and "Credit considerations" (pp. 3–4). ↩

9. O'Kane, "Introduction to Asset Swaps" (external site), Tables 1 and 2 (p. 5). ↩

10. O'Kane, "Introduction to Asset Swaps" (external site), "Counterparty risk" and "Market asset swap" (p. 7). ↩

11. O'Kane, "Introduction to Asset Swaps" (external site), "Interest rate risk of an asset swap" (pp. 5–6) and "Funding risk" (p. 7). ↩

12. O'Kane, "Introduction to Asset Swaps" (external site), "Uses of asset swaps" (p. 8). ↩

13. Policy Research Institute, Ministry of Finance paper (external site) (in Japanese), "3.1 金利スワップとの裁定取引とは" (Arbitrage against interest rate swaps), pp. 67–68. ↩

14. O'Kane, "Introduction to Asset Swaps" (external site), "Market asset swap" (pp. 7–8) and Figure 3. ↩

15. O'Kane, "Introduction to Asset Swaps" (external site), second half of "Credit considerations" (p. 5). ↩