Interest Rate Risk

Interest rate risk is the risk to the earnings or market value of a portfolio due to uncertain future interest rates. Discussions of interest rate risk can be confusing because there are two fundamentally different ways of approaching the topic. People who are accustomed to one often have difficulty grasping the other.

The two perspectives are:

• a book value perspective, which perceives risk in terms of its effect on accounting earnings, and
• a market value perspective – sometimes called an economic perspective – which perceives risk in terms of its effect on the market value of a portfolio.

The first perspective is typical in banking, insurance and corporate treasuries, where book value accounting prevails. The latter is typical in a trading or investment management context.

Interest rate risks can be categorized in different ways, and there is usually some overlap between categories. One approach – that is well suited for a book-value perspective – is to break interest rate risk into three components:

• term structure risk,
• basis risk,
• options risk.

Term structure risk (also called yield curve risk or repricing risk) is risk due to changes in the fixed income term structure. It arises if interest rates are fixed on liabilities for periods that differ from those on offsetting assets. One reason may be maturity mismatches. Suppose an insurance company is earning 6% on an asset supporting a liability on which it is paying 4%. The asset matures in two years while the liability matures in ten. In two years, the firm will have to reinvest the proceeds from the asset. If interest rates fall, it could end up reinvesting at 3%. For the remaining eight years, it would earn 3% on the new asset while continuing to pay 4% on the original liability. Term structure risk also occurs with floating-rate assets or liabilities. If fixed-rate assets are financed with floating rate liabilities, the rate payable on the liabilities may rise while the rate earned on the assets remains constant.

In general, any occasion on which interest rates are to be reset – either due to maturities or floating rate resets – is called a repricing. The date on which it occurs is called the repricing date. It is this terminology that motivates the alternative name “repricing risk” for term structure risk.

If a portfolio has assets repricing earlier than liabilities, it is said to be asset sensitive. This is because near term changes in earnings are going to be driven by interest rate resets on those assets. Similarly, if liabilities reprice earlier, earnings are more exposed to interest rate resets on those liabilities, and the portfolio is called liability sensitive.

For example, a bank that is supporting fixed-rate liabilities with floating-rate assets is asset sensitive. Earnings risk is posed by the floating rate on the assets. This example is only meaningful from a book value standpoint – which focuses on earnings risk. From a market risk standpoint, the floating rate assets pose little risk – floaters have stable market values. It is the long-dated liabilities that pose a market risk. Their market values fluctuate with changes in long-term interest rates. From an economic perspective, it would be reasonable to call the bank “liability sensitive!” Of course, that is not how the terminology is used. However, our example highlights how fundamentally different the book-value and market-value perspectives are.

It should be emphasized that this discussion uses the terms “asset” and “: liability” loosely, and not in any strict accounting sense. We include among assets and liabilities both derivatives and other off-balance sheet instruments that may behave like assets or liabilities. A pay-fixed interest rate swap might be considered a combination of a floating rate asset with a fixed-rate liability. On a stand-alone basis, it poses considerable term structure risk.

Basis risk is risk due to possible changes in spreads. In fixed income markets, basis risk arises from changes in the relationship between interest rates for different market sectors. If a bank makes loans at prime while financing those loans at Libor, it is exposed to the risk that the spread between prime and Libor may narrow. If a portfolio holds junk bonds hedged with short Treasury futures, it is exposed to basis risk due to possible changes in the yield spread of junk bonds over Treasuries. Basis risk is another name for spread risk.

As with term structure risk, book-value and market-value perspectives differ with respect to basis risk. As always, the book value perspective focuses on risk to earnings. If the spread between interest earned on assets and interest paid on liabilities narrows, those earnings will suffer. The economic perspective considers the risk to the portfolio’s market value. If a spread narrows or widens, the market values of assets and liabilities may be affected differently—and the net market value of the overall portfolio could suffer.

Options risk, as a component of interest rate risk, is risk due to fixed income options – options that have fixed income instruments or interest rates as underliers. Options may be stand-alone, such as caps or swaptions. They may also be embedded, as with the call feature of callable bonds or the prepayment of mortgage-backed securities (MBS). In some respects, options risk is just another component of term structure risk. This argument needs to be explored differently for the book value and market value perspectives.

From the book value perspective, the distinction between term structure and options risk has historical roots. Payoffs of options depend upon changes in interest rates, which would seem to make options one more source of term structure risk. However, by shorting embedded options, a depository institution can enhance short-term earnings at the expense of long-term earnings. This is what happened during the 1980s, when the MBS market was just emerging. Dealers found US thrifts and other depository institutions to be eager buyers of MBSs. Because of their short embedded prepayment options, the MBSs offered very high yields – and those high yields flowed immediately to earnings. Because MBS pricing was far from transparent, dealers could charge exorbitant prices for the MBS – they priced them to have yields much higher than Treasury notes, but not high enough to fully compensate for the short options. From an economic standpoint, thrifts incurred a loss every time they purchased an MBS, but the thrifts didn’t see that. Perceiving the world from a purely book-value/earnings perspective, all they saw was an immediate jump in earnings. Only later, when interest rates dropped and prepayments on the MBS surged, did the thrifts realize their mistake. Loses were staggering and were a primary contributor to the ensuing crisis in the US thrift industry.

Part of the thrifts’ problem was due to being cheated by the dealers who sold them the MBS at inflated prices. That is a risk distinct from interest rate risk. It is as old as Wall Street – caveat emptor. However, another significant issue was the emerging problem that derivatives and new structures with embedded options made it possible to do an “end-run” around traditional book value accounting. Increasingly, earnings could be manipulated for the short-term, with consequences pushed into the future. Traditional techniques of asset-liability management – which focused on term structure and basis risk – were ill-equipped to address this emerging risk. Hence, the new risk was given a name – options risk – and managers came under pressure to supplement old tools with new ones that could assess this new risk.

The economic perspective on options risk is very different. From that standpoint, options pose an immediate risk in the form of changes in their market value. While shorting embedded options can generate income that immediately flows to earnings, it does nothing for market value – the option premiums are offset by the negative market value of the newly shorted options. If the options are shorted at fair prices, the two cancel – and there is no immediate market value impact.

Market risk of fixed income options arises primarily from two sources:

• Changes in underlying interest rates, and
• Changes in applicable implied volatilities.

The first of these, from a market value standpoint, is no different from term structure risk – the portfolio’s value rises or falls with interest rates in a fairly predictable manner. The latter isn’t a form of interest rate risk – it is implied volatility risk. Accordingly, from an economic perspective, it is more reasonable to identify just two components of interest rate risk:

• Term structure risk, and
• Basis risk.

where a term structure includes a component of what we previously called options risk, and the balance of options risk is a new, non-interest rate risk:

• volatility risk.

There are many techniques for assessing interest rate risk. Some focus on the earnings impact of interest rate risk. Others focus on the market value impact. Accordingly, the choice of tools will be motivated by your perspective.

Investors with a book value perspective tend to address interest rate risk with the tools of asset-liability management – cash matching, gap analysis, earnings simulation, earnings at risk and duration. Those with an economic perspective use some of these – especially gap analysis and duration – but they also use tools that focus on economic value – delta, PV01 and value-at-risk.

Tools such as earnings simulation and earnings-at-risk quantify risk in terms of its earnings impact, so they are only applicable from a book-value perspective. Tools like PV01 and value-at-risk quantify risk in terms of market value impact, so they are only applicable from a market-value perspective. Gap analysis and duration are interesting because they can be used with either perspective. Let’s look at why.

Gap analysis doesn’t consider the consequences of the risk it assesses, so it doesn’t lock the user into one perspective or the other. It simply identifies interest rate gaps. The book-value and market-value perspectives may see differing implications in those gaps, but they both see risk. Accordingly, gap analysis is useful for both.

Duration is different. Rather than avoid describing the consequences of the risks it identifies, it offers two alternative interpretations of those risks. Based on the Macaulay formula, duration is the average weighted maturity of a portfolio. From the book-value perspective, a portfolio that has positive duration is liability sensitive. One that has negative duration is asset sensitive. From the economic perspective, duration describes the sensitivity of the portfolio’s market value to parallel shifts in the spot curve (see the article Duration and Convexity). Accordingly, the single notion of duration is perceived in fundamentally different ways.

As mentioned earlier, there is no particular need from an economic perspective to consider a separate options risk. Standard tools, including delta, vega, PV01 and value-at-risk—if correctly implemented—easily capture the risks of options. From a book value perspective, traditional tools, including cash matching and gap analysis, simply cannot incorporate options. This necessitated a search for new tools. One was earnings simulation. If implemented to assess risk over a long-enough horizon—in the past, it often wasn’t— it can easily incorporate the effects of options over time. Another is option-adjusted duration. Abandoning the somewhat limited Macaulay formula, investors would use option pricing models to accurately calculate duration as a factor sensitivity. To clarify terminology, from the book value perspective, duration is Macaulay duration and option-adjusted duration is what, from an economic perspective, is called duration. Yes, interest rate risk can be confusing. Blame it on the two competing perspectives.

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