Short and intermediate Treasury yields rose sharply in 2022 to the highest levels in 15 years. One clear impact to depository institutions was higher unrealized losses on their AFS portfolios, but at the same time, reinvestment yields were significantly higher as well. However, higher rates have an impact on other fixed-income concepts beyond just the bond’s stated yield to maturity (that too is impacted by higher discount rate assumptions). Some bankers and portfolio managers have only known the ultra-low rates of the post-crisis era thanks to a heavy Fed presence, but in this article, we summarize several bond concepts impacted by the absolute level of rates.
#1 Compounding Matters More
Higher interest rates shine a light on the impact of compounding. When rates are low, as they were for much of the post-crisis era, differences between compounded and non-compounded rates are de minimis. But now that Fed Funds is north of 4% the difference is much more meaningful. Exhibit 1 shows the difference between a daily-compounded rate and non-compounded rate at various rate levels. As the graph shows, when rates are at 0.25% compounding makes little difference. But as rates rise the difference between a non-compounded and compounded rate grows; at 5% there’s a 13-bps difference between the two.
Additionally, the frequency of compounding becomes more meaningful as rates rise. Exhibit 2 helps demonstrate this idea. When rates are at 2%, the difference between a rate that is compounded daily and one that is compounded semi-annually is only 1 bp, but with rates at 5% that difference is 7 bps. This is a critical concept to understand when evaluating interest rate swaps, where counterparties have the option of deciding on such conventions.
#2 Yield to Maturity and Reinvestment Assumptions
A key assumption in a yield to maturity (YTM) calculation is that all periodic cashflows are reinvested at the security’s purchase YTM. However, when yields move sharply in either direction, realized holding period returns can deviate notably from original YTM estimates due to different reinvestment rates. This effect is amplified in the current environment given the sharp increase in market rates in a relatively short timeframe.
Consider the following example: Three different investors bought the five-year US Treasury on July 31, 2020, at a yield of 0.20%. One purchased a zero-coupon bond; one purchased a par bond, and one purchased a 6% coupon bond at a dollar price of $128.84, all three to yield 0.20% to maturity. In a hypothetical scenario, the following day cash rates jumped to 4%, taking the reinvestment rate from 0.20% to 4%. The zero-coupon bond does not benefit from higher interest rates because it does not have periodic cash flows to reinvest. The coupon-paying bonds both benefit from higher interest rates because the realized reinvestment rate for the coupon payments is now significantly higher than the original assumption in the YTM calculation, as well as the compounding effect. Additionally, the higher 6% coupon bond benefits significantly more than the par bond because more of its original dollar price was derived from the larger periodic interest payments from the much higher coupon. On a $1mm investment, the cumulative pick-up with the 6% bond is approximately $30k, as illustrated in the tables below.
#3 Durations are Lower on Non-Callable Assets as Rates Rise
Fixed income portfolio managers rely on duration estimates to measure a bond’s price sensitivity to interest rates. However, the relationship between price and yield is not linear, but rather a convex curve. The curvature, typically referred to as convexity, highlights how changes in yields can influence duration.
Exhibit 4 exemplifies this concept using a 10-year debenture across various yields. When underlying interest rates increase, the duration of non-callable bonds declines and can pose challenges for longer liabilities structures that require a higher price volatility to offset. The reverse holds true for the opposite scenario: as yields decrease, the duration of a bond or portfolio will extend. Compounding the effect in the example, is the coupon rate. While weighted average life (WAL) of principal cashflows remains constant, a bond’s duration is reduced when proportionately more interest is received before maturity, all else constant.
#4 ROE Hurdle Rates for Asset Returns are Higher
Traditional asset profitability models (ROE/RAROC) share a unique feature that keeps them tied to modern notions of expected equity returns and equity risk premiums. Financial theory tells us that expected equity returns must be higher when risk-free rates rise since investors need to be appropriately compensated over their risk-free alternatives. If the risk-free opportunity cost rises, assuming equity risk premiums stay constant, so should the required return on equity.
Because all assets are capitalized on the balance at a certain capital target, an asset’s return incorporates the funding benefit of equity. As interest rates rise, expected equity returns rise and the funding benefit of equity to capitalized assets becomes increasingly valuable. Because an asset’s target ROE, or hurdle rate of return, incorporates the funding benefit of equity, those hurdle rates must also follow higher. If the target ROE stays static when interest rates are increasing, asset spreads will increasingly tighten, thereby underpricing risk exposure.
Exhibit 5 demonstrates this visually with an asset priced at a 200-bps option adjusted spread (OAS) versus Treasuries capitalized to a 10% target. Hurdle ROE rates move up linearly right along the risk-free rate due to the funding benefit of equity. The main takeaway is that one cannot fall asleep at the wheel when pricing assets while interest rates are on the rise, or one will end up with overpriced assets and underpriced risks.
#5 Shorter Payment Delays are Worth More
A variety of payment delays exist in the bond market, and how quickly an investor receives principal back matters more when rates are higher. Exhibit 6 illustrates this concept. The table compares the price of two par floaters that were valued using a 50 OAS and a constant speed of 15 CPR. The main difference between the two is the payment delay, the Freddie KF has a 0-day payment delay while the SBA pool has a 54-day delay. These two bonds were run as of 12/31/20 and 12/31/22 to show the impact that the level of rates has on the value of two similar bonds that have different payment delays. As the table shows, in the low-rate environment of 2020 the price difference is roughly 10/32nds in favor of the SBA floater, but at the end of 2022 that difference is close to 28/32nds in favor of FHMS KF141 AS. This should make intuitive sense as the opportunity cost of receiving principal back is lower when rates are lower and is higher when rates are higher.
#6 No Need for Settlement Fail Charges
In the wake of the Great Financial Crisis when the Fed lowered the fed funds rate to the zero bound, sellers had less incentive to deliver bonds on time because cash returns were so low. In response, the Treasury Market Practices Group headed by the New York Federal Reserve introduced charges for delayed delivery of sold securities, specifically for Treasuries, Agency debt, and Agency mortgage-backed securities (MBS). For Treasuries and Agency debt, the penalty is 2% minus the fed funds rate, and for MBS, the penalty is 3% minus the fed funds rate. In other words, when the fed funds rate moves above 2-3%, fail charges no longer apply because there is appropriate incentive for sellers to deliver bonds and receive proceeds from the sale when prevailing reinvestment rates are much higher.
#7 Higher Value on Death Puts in Brokered CDs, Munis and Corporates
Higher rates have increased the value of the estate option, colloquially known as the death put, that is a common feature in certificates of deposit (CDs) as well as some retail-oriented municipal and corporate bonds. Because issuing depositories must honor these contracts, this can become a rising cost to the institution. The death put allows for full redemption of principal at par, plus accrued interest, in the event of death or declaration of incompetence of the security holder. This is particularly important if the fair value of the asset is eroded by a sharp increase in interest rates, as was the case in 2022. If an owner of a 3yr CD sees 3yr rates rise by 300bps, he or she can expect to see the fair value of their investment fall by approximately 9% to 91 cents on the dollar. Consequently, the value of the put option rises to about 9 points*, which is large relative to where they have been over the past decade. Exhibit 7 demonstrates the increase in put option value as rates rise in this example.
*this is a simplified calculation and assumes the put option can be exercised immediately
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