Lang Gibson, vice president at First Union Capital Markets, offers strategies for depository institutions to manage their balance sheets actively with capital market and derivative instruments.

In recent years, community banks have enjoyed double-digit earnings growth rates. Maintaining that torrid pace in the coming years, however, will be a difficult task. Competitive pressures from lower-cost providers are squeezing fee income and loan/deposit pricing, and an increasingly flat yield curve requires more optionality and leverage to maintain stable initial net interest spreads (NIS). Moreover, there are fewer remaining merger-and-acquisition targets, and those that remain become costlier as banks’ acquisition currency values—such as their price-to-earnings ratios—decline. Year 2000 systems and M&A-related restructuring costs are also continuing to climb.

Community banks tend to be short options written to their customers on both the asset and liability sides of the balance sheet.

Fortunately, the capital markets have kept pace with these challenges, allowing community banks to enter new markets and take advantage of opportunities previously reserved for the regional and money-center banks. The difficulty lies in clarifying these opaque new businesses and exposures.

For the most part, community banks tend to be short options written to their customers on both the asset side of the balance sheet (prepayments, caps and floors embedded in loan contracts, and so on) and the liability side of the balance sheet (such as core deposits). To complicate this exposure, there are often market options written on agency debentures (assets) and on Federal Home Loan Bank (FHLB) advances and certificates of deposit (liabilities). Unlike the continuous nature of customer options, which are repriced marginally as rates change, these one-time, or switch, market options are called away or convert to floating at the very time fixed-rate exposure is needed, thus decreasing NIS.

There are, however, a number of opportunities for improving performance by restructuring a community bank’s securities portfolio, loan portfolio and funding sources—and there are several alternatives for managing exposures via interest rate hedging as well.

Optimizing risk/return in a securities portfolio

Most community banks have significant excess capital above the regulatory tangible capital ratio of 6 percent, and may therefore have opportunities to improve their NIS by leveraging their balance sheets. Moreover, they may be able to achieve a substantial pickup in NIS, return on equity and return on assets with the same or lower risk. For instance, there is an inherent opportunity cost in not accurately measuring the value and duration of core deposits. In fact, a bank may find that its interest rate exposure is actually more asset-sensitive than its traditional gap schedules imply. Although many community banks treat core deposits as short-term funding vehicles priced at par, core deposits actually have substantial premiums and long durations.

In today’s markets, it is possible to engineer a wholesale leverage strategy that provides a static 175-basis-point NIS. Clearly, such a pickup in today’s flat yield curve environment does not come without some degree of risk. One hypothetical asset allocation may involve long-duration AAA bank-qualified callable municipal bonds, trust preferreds, mortgage-backed securities or whole loans, all funded by 75 percent long lockout and 25 percent short lockout callable FHLB advances. Because of the long maturity of the assets, the strategy may suggest that a large portion of the transaction’s funding have long lockouts, but the possibility of an interest rate mismatch past the model’s horizon date may still exist.

In this hypothetical allocation, even when the minimum point-in-time spread is maximized (using reasonable price and sector constraints), the NIS may shrink 25 basis points in 200-basis-point shifting-rate scenarios. There may also be a significantly larger price decline in an up-200-basis-point scenario than a price increase in a down-200-basis-point scenario. This negative convexity means that the cash flow available for reinvestment increases when rates fall and decreases when rates rise. On the funding side, in a rising rate environment NIS may be compromised over time if and when the FHLB converts funding from fixed to floating. One possible solution is the use of out-of-the-money interest rate caps, which can be purchased to hedge losses in rising-rate scenarios.

For banks with a lower appetite for risk, better interest rate matching with less optionality can still provide attractive earnings enhancement. It is important, in either case, for a bank to understand and achieve a comfort level with the strategy’s NIS and price performance over a three- to five-year time horizon. Moreover, management should ensure that complex instruments with customer prepayments and one-time options are modeled adequately using acceptable assumptions for prepayments and credit losses.

Restructuring the loan portfolio

On the asset side of the balance sheet, a bank’s core competence in evaluating loans—that is, its insider strategy—will help to determine its franchise value. Although securities are critical for managing liquidity, diversifying the asset mix and serving as a surrogate when loan demand is inferior to funding opportunities, loans provide the most attractive yield and total-return opportunities. That said, a closer look at the cost structure for underwriting, monitoring and servicing a lending business can be frightening, and these expenses should be viewed in relation to the relative costs of managing a securities portfolio.

Examining creative investment alternatives can provide insight into such a cost/benefit analysis. Mortgage whole loan investments and commercial and industrial syndication participations may be ideal venues to enhance returns, complement the existing loan portfolio, and diversify credit and duration risk, while avoiding the marginal costs of entering a new business or increasing underwriting and servicing efforts. As a comparison, the outsourced underwriting costs for purchasing jumbo whole loans, which yield 25 basis points to 30 basis points more than identical collateral agency pass-throughs, are only $100 per loan (3 basis points for an average-size loan of $300,000), whereas typical bank underwriting costs can be as much as 10 basis points.

Although the securities portfolio has been the traditional tool used by community banks to adjust interest rate risk bank-wide, hedging represents a significantly more efficient tool.

In addition, as an emerging asset class, collateralized loan obligations represent an alternative to underwriting commercial and industrial loans to gain comparatively high-yielding exposure and diversify into new credits. Certain CLO structures backed by 100 percent senior-secured leveraged bank loan collateral have multiple classes (for example, Standard & Poor’s ratings ranging from AAA to BB-), and yield 60 basis points to 600 basis points over the Treasury curve. These structures can withstand average annual defaults of up to 10 percent before suffering any yield loss as a result of credit losses in the expected base case.

Another opportunity available for obtaining commercial-and-industrial-type yields without the associated costs of entering a commercial and industrial loan business would be retail property-backed real estate investment trust bonds and commercial mortgage-backed securities. In some cases, it may be possible to place higher-yielding promissory notes that are the mirror image of the issuer’s public investment-grade debt in the loan portfolio (where price volatility will not affect a bank’s book equity), and attain the diversification benefit of expanding into uncorrelated markets.

Broker-dealers can also offer valuable services when evaluating restructuring opportunities in bank loan portfolios. Such consultation can often be used to identify loan securitization and loan trading alternatives. Community banks, for example, have traditionally sold conforming mortgages to the agencies to meet customer loan demand and reduce undue collateral concentrations. Similarly, nonmortgage assets (that is, asset-backed collateral) may be securitized to obtain an alternative source of funds, to free up capital and/or to de-lever the balance sheet. Deal structuring can be performed to meet specific investor demand and gain optimal distribution in the capital markets. State-of-the-art structuring requires sophisticated multifactor modeling, which can be provided by some broker-dealers, to clarify precise prepayment and default scenarios based on an investor’s assumptions.

Hedging interest rate exposure

Hedging allows a bank to mitigate risk and protect against spread compression without the use of balance-sheet items. Although the securities portfolio has been the traditional tool used by community banks to adjust interest rate risk bank-wide, hedging represents a significantly more efficient tool and has been successfully implemented by regional and money-center banks for years. To the extent that a bank closely hedges existing balance-sheet exposures on a macro basis and this risk reduction is clearly explained to the board of directors, a bank can comfortably adjust interest rate risk with interest rate swaps, caps and floors, Treasury locks and other instruments.

Cash flows from hedges are considered fairly reliable and are far more clearly delineated in the bank’s underlying balance sheet than exposures such as customer options. After a bank determines a desirable bank-wide interest rate exposure from both a cash-flow and market-value standpoint, interest rate swaps can adjust the existing exposure dynamically over time by locking in fixed cash flows on either the asset or liability side. If a bank determines its exposure is overly asset-sensitive, for instance, a receive-fixed swap contract can convert the exposure to a more liability-sensitive position.

To the extent that a bank is uncomfortable with floating-rate funding exposure, out-of-the-money caps indexed to Libor can be purchased cheaply to protect downside scenarios of drastically rising rates and yet maintain upside exposure if rates fall. Alternatively, banks can hedge the downward repricing of prime-based loans with interest rate floors. Similarly, banks with significant mortgage-servicing portfolios can purchase interest rate floors indexed to constant-maturity Treasury rates to hedge their interest-only-like exposure to falling rates. As mortgage prepayments vary from projections, these losses can only be written down for bookkeeping purposes. Moreover, the true economic-value benefit from rising rates can only be recouped if and when the servicing portfolio is sold. And for some banks, servicing counts as a significant source of Tier 1 capital.

For the loan portfolio, Treasury locks (such as forward contracts) can be used to hedge forward rate commitments made to customers—for instance, construction and mortgage borrowers who can lock in fixed rates up to three months or more in the future. By hedging this exposure with Treasury locks, a bank is protected from rates rising when the loan is finally made.

This year’s model

In the past few years, more community banks have implemented sophisticated asset/liability management models, policies, procedures and controls under guidelines and directives issued by the Federal Financial Institutions Examination Council, the Federal Reserve, the Office of the Comptroller of the Currency and the Bank for International Settlements.

For the most part, these new asset/liability management systems are being used strictly to quantify NIS and the market value of equity performance under interest rate shock scenarios. To exploit fully the time and expense involved, managers should use these systems to understand restructuring opportunities and business strategy scenarios. Because most of these models are deficient at pricing options, modeling customer behavior, evaluating core deposits and so on, community banks should rely on outside sources, including broker-dealers, for model inputs such as option pricing and asset-backed securities pricing. Finally, transaction-specific analysis and external advice are helpful in assessing the true risk/return trade-off in pursuing alternative strategies.

Lang Gibson can be reached at lang.gibson@capmark.funb.com.

William Margrabe, president of the William Margrabe Group, dissects put-call disparity.

Dear Dr. Risk,
Recently a colleague related his theory that if an option was at the money, the prices of the put and call options would have to be the same—because of the symmetrical distribution of the stock price returns. This sounds plausible, but I know it’s not true. Unfortunately, I could not explain why my colleague was wrong. Do you have an answer?

Dear Rob,
Better than that! I have two answers:

(1) You’re right! He’s wrong! Although your colleague’s theorem—with its hypothesis, conclusion and hint of a proof—sounds plausible, as you say, we can easily find counterexamples.

(2) Wait a minute. He’s right! If we change a few words or if we don’t question part of his hypothesis—this was a conversation, not a dissertation defense, right?—and we interpret some of his language favorably, the theorem is correct.

The answer depends largely on the meanings of several ambiguous terms: option, at the money, symmetrical and stock price returns. It also depends on whether he was speaking practically or strictly theoretically—and then it depends on the theory. Finally, it depends on whether you’re feeling picky or generous. Let me lay out the arguments, so you can answer your own question.

European Option Theory

One counterexample disproves a theorem. Consider European call and put options with the same expiration date (T) and strike (K), on one share of the same stock with spot price S and continuous dividend yield d. If that’s the case, the put-call parity theorem says that the value of the call, less the value of the put, equals the present value of the excess of the forward price over the common strike price,

C - P = (F-K) x PV,

where C is the price today (before expiration) of the call, P is the price of the put, F is the forward price for the underlying share with delivery at T, and PV is the value today of a certain dollar delivered at T. This is true, regardless of the probability distribution of stock price changes.

Your colleague’s theorem refers to at-the-money (ATM) options. The usual definition of ATM is that the strike price equals the spot stock price (K=S). Thus, if the forward price exceeded the spot price (F-S>0), the theorem would imply that

C - P = (F-S) x PV > 0,

which means that the call is worth more than the put. So he’s wrong!

However, if we were in a healing mood, we could easily patch up your colleague’s theorem:

(1) We could allow the put and call to be ATM forward, which means struck at the forward price (K=F).

(2) We could specify that the interest rate equals the dividend yield. This would make the net cost of carry zero, and therefore F=S by a cash-and-carry arbitrage argument. (The proof requires a little math, but the basic idea doesn’t: The forward price equals the cash price, plus the interest on the money borrowed to buy in the cash market, minus the cash that the investment throws off.)

(3) We could let the underlying price be a futures price, and therefore K=F. If your colleague trades equity index futures options, maybe that goes without saying. One could quibble that U.S. regulations forbid any futures contracts on shares of a single company, allowing only equity index futures, but theory and Russia allow such contracts. One could quarrel that a futures price is not the same as a forward price, but if the interest rate is not stochastic, the two prices are the same.

With any of these fixes, the put-call parity theorem implies that the price of the call and put are equal. So he’s right!

However, the crucial condition had nothing to do with the distribution of stock price returns, and certainly didn’t require symmetry, as he stated. So he’s wrong!

American option Theory

Your colleague didn’t say that the options were European, so you could argue that the above fixes don’t work for American options. Even if the put and call options are ATM forward, their values may differ, because the put-call parity theorem doesn’t apply to American options. Consider two cases in which ATM forward European call and put options will still be worth the same according to the put-call parity theorem:

(1) Let the dividend yield equal zero and the interest rate exceed zero. Now early exercise of the call makes no sense, while early exercise of the put would make sense at a sufficiently low spot price. Thus, the value of the American put will exceed that of the American call.

(2) Let the dividend yield exceed zero and the interest rate equal zero. Now early exercise of the put makes no sense, while early exercise of the call would make sense at a sufficiently high spot price. Thus, the value of the American call will exceed that of the American put.

In either case: He’s wrong!

If the dividend yield and the interest rate are equal, the spot, forward and futures prices are equal, so an option is ATM spot if and only if it is ATM forward. In a Black-Scholes-Merton equity market—with constant volatility, dividend yield and interest rate—the ATM American call and put will have equal value. Why? The put and call prices are equal, because of a sort of symmetry between the events that lead to exercise for the call and the put. This was difficult to prove, but I’ll outline the proof. For more details, see the mathematical appendix at www.margrabe.com.

Each event that can lead to value for the call—that is, payoff or early exercise at a specific time and underlying price—has its counterpart of equal value for the put. You can see this easily by pricing the call and put in a Cox-Ross-Rubinstein binomial model in a spreadsheet. (In this model, if the price jumps up and then down, it ends up where it started. In the Jarrow-Rudd model, the log of the price drifts over time at the rate r – d – 1/2s2.) If you do, you’ll see that when the dividend yield equals the interest rate, ATM European and American call and put options have equal values, for any number of binomial periods, hence also in the continuous time limit. So he’s right!

Problems with his “proof”

If his “proof” is wrong, then one could argue that his theorem isn’t up to snuff. The justification he presents is open to attack on a couple of grounds.

(1) Do stock price returns have a symmetrical distribution? Consider three definitions of stock price returns: (A) change in price, (B) change in price / initial price, and (C) change in the natural log of the price. All three definitions appropriately ignore the return from dividends that many shares pay, because the option payoff depends on the underlying price movement, not including dividends paid through expiration.

European option traders are extremely conscious of the put-call parity theorem and are ready to arbitrage any violation.

The usual Black-Scholes-Merton assumption about price movements under a risk-neutral probability distribution is log normality, so the distribution of changes in the logarithm of the spot price is symmetrical. The probability distributions of change in price and (change in price) / initial price are clearly not symmetrical—for example, the probability of the price dropping from S to zero is zero, but the probability of it increasing the same amount to 2 x S is positive.

(2) Is a symmetrical distribution crucial for the result? It was crucial for American options, but irrelevant for European options.

He’s right? Wrong? It depends on the standard to which you hold him.

Reality Check

The histogram of observed stock price returns is not symmetrical, no matter how you define returns. Large negative returns have occurred more often than equally large positive ones. My theory is that it’s much easier to suddenly wreck an economy—as with tariffs, taxes or war—than to suddenly nurture it.

The market prices of equity options imply a risk-neutral probability distribution for changes in log price that isn’t symmetrical. Again, the downside has too much weight.

Stock dividends don’t come in a continuous proportional flow but in lumps, such as at the end of the quarter or year. Thus, dividend yield is either zero or infinite, and doesn’t equal the interest rate. That complicates the theory, particularly for American options, which tend to see more exercise just before (for calls) or after (for puts) the stock pays a dividend.

So we can question the reality of your colleague’s assumptions. He’s wrong!

The acid test

Most people, however, will care mainly about whether his theorem’s conclusions seem to describe market reality. Do ATM—spot or forward—call and put options have the same market price? Here we face some practical problems. Exchange-traded options don’t have strikes at every possible spot level, so our chances for observing ATM options precisely are limited. Over-the-counter options are available at any strike you want, but the larger bid/ask spreads may distort the put/call relationship.

My conclusion: European option traders are extremely conscious of the put-call parity theorem and are ready to arbitrage any violation, so I would expect to see corresponding ATM forward call and put options sell at nearly the same prices. For American options, we don’t have put-call parity and we don’t have the theoretical symmetry I described, so I wouldn’t count on the put and call selling for the same price. Nevertheless, they’re often close.

So, tell me. What do you think? He’s right? He’s wrong?

If you have a question for Dr. Risk, send it to DoctorRisk@margrabe.com.

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