Interest Rate Risk and the Stock Prices of Financial Institutions

Interest Rate J3isk and the Stock Prices of Financial Institutions

G. .1. Santoni

OST discussions of the effects of interest rate FINANCIAL INSTITUTIONS AND movements on the portfolios of financial institutions INTERMEDIATION typically conclude that the relatively high and volatile interest rates of the past 15 years have placed many of Financial institutions intermediate many transac- these institutions in jeopardy of failing. The consensus tions between borrowers and lenders. In doing so, of many of these discussions is that institutions with banks and savings and loans do not act merely as credit “unbalanced” portfolios and low capital are partic- brokers, negotiating ct-edit transactions between bor- ularly susceptible to interest rate movements.’ rowers and lenders. Rather, they borrow directly from The purpose of this paper is to analyze the effect of some individuals and lend directly to others. These interest rate changes on the relative value of financial transactions make up the portfolio of the financial firm. institutions.’ This issue is important not only to the In large part, the market value of the firm is determined owners, managers and employees of financial institu- by the net present value of its portfolio of assets and tions but to monetary policvmakers as well. Monetary liabilities. Changes in the interest rate affect the firm’s policy actions affect interest rates. If the viability of market value because they influence the present value financial institutions is particularly sensitive to interest of the assets and liabilities in the firm’s portfolio. rate changes, monetary policymakers will want to take this effect into account. INTEREST HATE CHANGES AND THE RELATIVE PRICE OF FINANCIAL INSTRUMENTS

Since the interest rate is the price of the earlier 0. J. Santoni is a senior economist at the Federal Reserve Bank availability of dollars, a change in the interest rate of St Louis. Thomas A. Pollmann provided research assistance. 3 means that this price has changed. For example, if the ‘See, for example, Maisel and Jacobson (1978), p. 688; Kaufman (1984); Bierwag, Kaufman, and Toevs (1983); Hopewell and Kauf- man (1973); Flannery (1981); and Samuelson (1945). ‘More correctly, it is unexpected changes in the interest rate that affect relative values. Any future change that is expected is reflected ‘Since this paper is mainly concerned with changes in the whole in current prices. Long-term interest rates are important determi- complex of interest rates (i.e., changes that leave the term structure nants of stock prices, and changes in these interest rates can be unaltered), “the” interest rate is used as a shorthand method of characterized as unexpected (see footnote 15). referring to the complex of interest rates,

12 FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984

interest rate rises from a level of 10 percent to 12 per- last column shows the percentage change in present cent, the price (or valuel of present dollars rises in value that occurs when the interest rate rises. terms of future dollars. Before the change in the in- Theexample is constructed so that the present value terest rate, borrowing a dollar today necessarily meant of each instrument is $100 at an interest rate of 10 giving up 1.10 dollars one year from now or- 1.21 dollars percent. Because each is worth $100 at this interest two years from now, etc. After the increase in the in- tate, each will exchange one-for--one in the market. An terest rate, borrowing a dollar today requires the sac- increase in the interest rate, however, will completely rifice of 1.12 dollars one year from now or 1.25 dollars alter this set of relative prices. two years from now, etc. The increase in the interest rate from 10 percent to 11 percent causes the present value of each instrument Since financial instruments represent claims to dol- that promises future dollars to fall. Those that repre- lars at different points in the future, changes in the sent earlier- claims to dollars, however, become rela- interest rate affect the relative values of financial assets tively more valuable compared with those that promise and liabilities. A rise in the interest rate has two impoi- dollars in the more distant future as indicated by the tant effects on financial claims. First, it reduces the smaller percentage reductions in the present values of present value of all such instruments in terms of present dollars. Second, and equally important, the present these instruments. values of various instruments will change in terms of Interest Elasticity: ~4Fundamental each other; the prices of claims to dollars in the more distant future will fall relative to the prices of claims to Measure of Interest Rate Risk dollars in the near future. Discussions of the impact of an interest rate change on the prices of financial assets have a long history in Table I presents an example that illustrates the economic litei-ature and are typically referred to as the effect of an interest rate change on the present “elasticity of capital value with respect to the interest 4 values of four different financial instruments. The rate.” instruments are similar in that each promises a single future dollar receipt (payment) of a given amount; they This “elasticity” is simply the percentage change in differ in both the amount to be received (paid) and the present value of an asset (liabilityl divided by the timing of the receipt payment). The fiist column of the percentage change in the inteiest rate. The number’ table indicates when each receipt will occur. The that results approximates the percentage change in second column shows the amount to be received. Col- umns three and four- give the present values of the 4 various instruments at two different interest rates. The See Hicks (1939), pp. 184—88, and, more recently, Alchian (1955).

13 FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984

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/ N i,~’, the present value that will occur for a 1 percent change percent increase in the interest rate reduces the pres- 5 in the interest rate. ent value of the asset by slightly more than .27 percent.

Interest elasticity measures the sensitivity of the present value of an asset (liability) to interest rate changes. The larger the absolute value of the elasticity, Duration: Another Measure of Interest the greater is the percentage change in present value Bate Risk for a given percentage change in the interest rate and, consequently, the more sensitive is the value of the More recently, the concept of interest tate elasticity has been applied in the area of financial management asset to interest rate changes.” where it has appeared in the guise of the “duration of 7 the financial portfolio and interest rate risk.” Usually, Table 2 uses the data in table I to calculate the different names are used to identi[v different things. In approximate interest elasticities of the various instru- this case, however, there seems to be a distinction with ments. The larger elasticity (in absolute value) for the no real difference. more distant receipts indicates that their present values are more sensitive to interest i-ate changes. Like elasticity, duration is a number that ranks the interest rate sensitivity ofvarious assets. Unlike elastic- The examples in tables t and 2 consider’ only assets ity, however, which is a “pure” number (i.e., is not that consist of single receipts at different dates in the dimensioned in any particular unit), duration is ex- future. The same procedure, however, works for assets pressed in units of time. The duration of an asset is the that yield any conceivable stream of future receipts. All “average” length of time that receipts are deferred from that is required to calculate an interest elasticity is the the present. In calculating the avet’age, the time period ability to calculate present values at different interest that each receipt is defen’ed is weighted by the dis- rates. This is comparatively easy, provided that present counted value of the receipt.’~As the duration of an value tables and ahand calculator- are readily available. asset increases (as the average length of time one must For’ example, table 3 shows how to use the present wait for’ payment rises), the interest rate sensitivity of value table (shown at the bottom of table 3) to compute the asset also increases. the interest elasticity of an asset yielding a varying stream of receipts (one of which is negative) over a Interest rate elasticity and duration are closely re- five-year period when the interest rate is around 10 lated concepts. In fact, for given interest rates. the percent. The elasticity is — .275, indicating that a 1 duration of any asset is simply its interest elasticity

7 “It is an approximation because the calculation holds only for small ”Duration has now emerged as an important tool for measuring and changes in the interest rate. managing interest rate risk,” Bierwag, Kaufman, and Toevs, p. 15. See, as well, Hopewell and Kaufman, “Since present values and interest rates are inversely related, the 8 elasticity measure will always be negative. Hicks, p. 186.

14 FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984

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multiplied by the factor — (1 + i)/i.°Consequently, the rankings of assets and liabilities in terms of their in- duration and interest rate elasticity produce identical terest rate sensitivity or risk.

lfthe interest rate elasticity ofan asset is known (and it is always relatively simple to estimate), its duration 9The elasticities of the present values of various types of assets (liabilities) with respect to the interest rate are given by: can be immediately obtained. Forthe examples used in A, In thecase of asingle receipt (payment) of Adollars n years in table 1, the approximate durations ofthe various assets the future, the present value is: are 0.00, 0.99, 1.97 and 2.95 years, respectively. The An P ~ (1±i)” and dPi The duration of this instrument is measured by the term in brackets, Duration = ~ ajtMj _ n. i.e., the “averagelength oft/me for which the variouspayments are di P n( l) El— 1 deferred from the present, when the times of deferment are In this case, duration is equal to n, the number of years one must weighted by the discounted valuesof the payments (emphasis in wait before receipt (payment) of A. the original).” Hicks, p. 186. B. In the case of a stream of receipts (payments) of various C, In the case of a perpetual stream of receipts (payments) of expected amounts, A~,at the end of each year for n years, the equal annual amounts, A, present value is: present value is:

P = ~ and

P = ~ (lti)’ ~ ~Jtt±)±~ ~ Lii±!) diP i (1+i) i di PL i dPI/~[n. tA, A ~i /9 1 Theduration of this instrument is (1 + i)/i and the percentage change ~di~i’ [~±~(l’t.i)t/ t=1 (l+i)tj (~•,-f~’) in its price is equal to the percentage change in the interest rate. Note that in each of the three cases duration is always equal to ‘ ‘‘ dPi ,, interest rate elasticity, -~- ~, multiplied by — (1 + 1)/i. and Duration ~ f [— il.jL~j

15 FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984

approximate duration of the asset shown in table 3is is such that the ratio of assets to liabilities (leverage) is 1 3,02 years. ° initially the same for’ each firm. An increase in the interest rate from 10 percent to 11 The Effect of Interest Rate Changes on percent causes the net present value of the firm in “Unbalanced” PorU’olios panel A to fall by $3.62, rise by $1.19 in panel B and remain unchanged in panel C. The explanation for’ this Changes in the rate of interest generally will change differential effect is that the increase in the interest rate the present value of a firm’s assets relative to its liabili- lowers the present value offirm A’s assets relative to the ties. When this occurs, the market value of the firm will present value of its liabilities, causing its net worth to change. If the firm’s shares are publicly traded, the fall. The reverse is true for firm B, while for firm C the change in the firm’s value will be reflected by a change present values of assets and liabilities fall proportion- in the price of its shares. Thus, the market value of a ally, leaving its net worth unchanged. firm is sensitive to interest rate changes, and this sensitivity generally will differ across firms.

As in the case of par-ticular- assets or liabilities, the DURATION: SOME sensitivity of the value of the flr’m to interest rate COUNTERINTUITIVE ANOMALIES changes can be measured by the elasticity of the pres- Since the duration of an asset or liability is in terms of ent (market) value of the firm with respect to the in- units of time, it may appear to be a more intuitively terest rate.” Unlike the case for a paiticular asset or appealing measure of interest i-ate sensitivity than elas- liability, however, the interest rate elasticity of the pres- ticity, which is a pure number. However, duration has ent value of the firm may be positive~negative or equal some counterintuitive qualities that emerge when it is to zero. If positive, the market value of the firm will rise applied directly to the net flow ofreceipts generated by as interest t’ates rise and fall as interest rates fall. If the firm (i.e., when the firm is treated as a single asset). negative, the reverse is true; if zer’o, the net present value of the firm is unaffected by interest rate changes. There Is Less in Duration Than Meets the Eye Table 4 presents an example of each possibility. In panel A, the interest elasticity of net present value is While duration presumably measures the average negative. Interest elasticity is positive in panel B and length of time that receipts and payments are defer-red equal to zero in panel C. The example is constructed so from the present, the measurement can produce sonic that the net present values are identical when the unusual results. This is apparent in panel A where the interest rate is 10 percent. In addition, the construction duration of the portfolio is approximately 8.76 years, while the durations of the asset and liability are only 5.0 and 1.0 years, respectively. Intuitively, it would seem ‘°Theseare approximatedurations because theelasticities computed that the duration of the portfolio should be no more in thetables areestimates of the trueelasticity (see footnote6)-The than 5.0 years. The asset will mature after five years, so exact durations are 0.00, 1.00, 2.00, 3.00 and 3.10 years (see a measured duration of 8.76 years is somewhat un- footnote 9). usual in terms of the way aver-ages (even weighted “Let A, and C, be, respectively, the dollar value of the firm’s averages) are normally computed. This odd result receipts and thedollar value of its payments in period t. If the life occurs because duration employs an unusual method of thefirm is n years, the marketvalue of thefirm in period t, M, is: in weighting the streams of receipts and payments (see n A, n C, footnotes 9 and 11). M, = ~ (1+0’ ~ (1+0’ t= 1 As a further illustration, notice that the duration of the portfolio in panel B is negative. In a mechanical t’A, _____ /1+0’ (1+0’ sense, this result is not surprising. Duration is always di M, (14-i) A, C, equal to interest elasticity multiplied by —u + U/i. For (1 ~‘0’ (I i—i)’ the firm in panel B, interest elasticity is positive and As long as the market value of the firm is positive, i.e., the —(1 +U/i is negative. So duration, the product of the denominator exceeds zero, positive and negative numbers, is negative. However, a dM, i tA, tC, N portfolio with a negative average life is surely counterintuitive. ‘this result indicates that duration is more See Samuelson, p. 19. appropriately thought of as a proxy for the interest rate

16 FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984

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N’, ‘~ ~N/4- tfr~/////> //// N ‘N ~ N,t/N~~4$1VP’N ////t/ ~a44-/ N,t/NN~~:\N // ~ <~ 4- FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984 elasticity of the portfolio rather than an indicator of the INTEREST RATE RISK AND portfolio’s average life. FINANCIAL INSTITUTIONS Thus, at best, duration produces a consistent rank- There is reason to believe that financial firms are best ing of assets, liabilities and portfolios in terms of in- characterized by the firm shown in panel A of table 4. terest rate risk. The ranking is identical to the one that Notice that in examples B and C, the finn’s asset ma- would be obtained by calculating interest rate elastici- tures in one year, while its liabilities extend beyond ties. Calculating duration, however, requires an extra one year-. Once the asset matures, the net present value computational step and produces a result that reveals of the firm is negative (and will continue negative very little intuitive information about the average life of throughout its remaining life) unless the owners rein- the portfolio. vest the proceeds of the matured asset. Leverage Affects Portfolio Duration What are the incentives for the owners to reinvest? If the firm is a corporation and, hence, creditors have no An increase in the firm’s leverage (an increase in claim on the personal assets of the owners, there is liabilities relative to assets) affects the duration of the relatively little incentive. The wealth of the owners will portfolio. Again, consider panel A of table 4. Suppose be greater if they simply take the proceeds of the ma- that the present values of these particular assets and tured asset ($100) as a dividend and declare the firm liabilities were increased by equal amounts so that the bankrupt. Their wealth will rise by the present value of firm’s net worth remained constant. This increase in the liabilities. The incentive to behave in this fashion is the leverage of the firm would also increase the interest greater the larger the liabilities are relative to assets, elasticity of the portfolio. Since duration is simply the that is, the greater the firm’s leverage. interest elasticity multiplied by —u + U/i and, in this case. interest elasticity is negative, the duration of the Financial institutions tend to be highly levered!’ On average, net worth represents about 5 percent of total portfolio will increase even though the average lives of assets for these firms. Under these conditions, it is the assets and liabilities were not changed. unlikel that financial institutions could attract many depositors if they maintained maturity structures of Matching Asset/Liability Duration Does assets and liabilities similar to those shown in panels B Not Eliminate Interest Rate Risk and C. Public trust makes up much of the capital of financial institutions, both literally and figuratively. Matching asset and liability durations will not insu- These institutions provide assur’ance against the kind late the net worth of the firm (valued at market) against of behavior discussed above by maintaining asset/ interest rate changes. This is particularly apparent in liability maturity structures similar to that shown in panel C of table 4.The duration of the firm’s asset is one panel A rather than those shown in panels B and C. year, while the duration of its liability is two years. Although the firm has a mismatch of asset/liability This implies that the interest elasticity of the present durations, a change in the interest rate leaves its net value of financial institutions will be negative. Positive present value unaffected. changes in the interest rate will be associated with reductions in their market values, while negative Insulating the firm against changes in the interest changes in the interest rate will be associated with rate requires that the interest elasticity of the portfolio increases in their market values. Moreover-, the abso- be zero, If the firm’s net worth is positive, as must be lute value of the interest i-ateelasticity should be lar-ger the case for any viable firm, achieving this result re- for savings and loan associations than for banks, be- quires that the duration of the firm’s liabilities must cause they lend on a much longer-term basis than do exceed the duration of its assets. That is, the weighted average length of time forwhich payments are deferred from the present must exceed the weighted average length of time for which receipts are deferred from the 12 unrealistic, However, the same results would be obtained if a present. more realistic example were employed; all that would be gained by more realism is more complexity.

‘~ example, the ratio of capital to total assets averaged .042 for the 35 banks listed in Salomon Brothers (1983), p. 54, overthe “The above example considers only a single receipt and pay- most recentfive-year period. Theratio for all savings and loans ment, only a single interest rate, and only one type of asset and is .053 over the same period (Savings and Loan Sourcebook, liability. The real world, of course, is considerably more compli- various years). In contrast, the ratio of capital to total assets for cated and, hence, the example used here may appear to be all manufacturing firms averaged .500 over the same period.

18 FEDERAL RESERVE BANK OF ST. LOUIS ST/SEPTEMBE 984

4 banks while both borrow on a short-term basis,’ / N ‘N N 7 ~l’he highly levered:~zm~portfolios of all financial institu- //‘N / / N 7 N /77~ cial institutions will not only decline, but decline rela- live to the share prices of other firms when the interest N /~ rate uses and, conversely, when the interest rate falls, ///~N/ / SN /// NN ‘NNN N / ‘N /

Because of this, the stock prices of financial institu- N /‘N-~ ~N N // / N 4- trons should exhibit gi eatcr variation around their ‘N’N~c N ~ N N-N N. N c ~ N-<-’NN- N N/N ~ 7 mean levels than firms that are less highly levered and / 4- N / NN~~~Nt: NN that maintain more balanced portfolios. / 7N / /NN N / / ‘NN’N- / N4- NN N’ N N N /4-N

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The above discussion implies that, other things N/ / N ~ equal, the owners of financial institutions accept more N~$jj~N>N N / N’ interest rate risk than the owner-s of nonfinancial firms. / r N To what extent does an ana]ysis of share prices for > !/~N-~t’N’N N publicly traded firms support this implication? / N N / / 7 To investigate this issue, quarterly data on the per- 7/ N N 7N 2 / centage change in various indexes of share prices were ~ N ~ 4- N’S regr’essed on the percentage change in the corporate N ‘

Aaa bond rate over the period from 1961 to 1983 to N-N /N N produce estimates of the inter’est i-ate elasticities con- / / ‘ fronting different types of firms.” The share price indexes used are the Standard and Poor’s indexes of 7 / share prices of 400 industrial companies, banks out- N N / / ~/NN N sideofNewyorkCity,NewYorkCitybanks,andsavings C / N - N N ~ N and loan holding companies. The regressions also in- 7 // dude the growth rate of real GNP to control for cyclical ~ N7~ ~ N N/ ‘N 4-4~ N’ factors. rhe results are shown In tableS. ~ <>N~ N 4415 > Ø~-/ ‘N>N-~ N

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4 ‘ All federally insured savings and loan associations are required by 15 law to hold the bulk of their assets in the form of home mortgage loans with remaining maturities of not less than eight years (Federal 4- Home Loan Bank Act of 1932, sec. 2, p. 1). It was not until 1980 that N>-

15 t’Nc~~N~$flFIR~fIJ5~PP!II~!4 The first differences of the corporate Aaa bond rate can be characterized as representing unexpected changes in the interest rate. The hypothesis that the series represents white ~ N/ 4 NNN ~‘N 4- noise cannot be relected. The Chi-square statistic based on 24 N/NN4j~415S%>Slt N4- tags is 30.22. In addition, three sets of initial regressions at- ~ /4-N tempted to control for changes in theterm structure of interest ~ N~ N / N NNN> NN4-~ rates by including the percentage change in the three-month 4- NNN -~ //NN / 7N~N N / 47N ~j~444 T~::~~1~ ~ and the percentage change in thedifference between one plus ~ the three-month Treasury bill rate and the corporate Aaa bond ‘N N N N N N/N N -/47 N rate. However, these variables proved insignificant and were N -77 4- N ~ ~ NN~ ~ dropped from subsequent regressions. / N N-N N SN 4-’N N ///7 N 5 6 N 4- N ‘N ‘ 1n the case of estimates 1, 2 and 4 the procedure used was 5 N - / / N generalized-least-squares regression. Estimates 1 and 4 were N ‘N SN--N- -~—N’ N. N 4-N ~7 N/ aNN 4-N -/7 N’1N~~NN N 4- 19 FEDERAL RESERVE BANK OF ST. LOUIS AUGUST/SEPTEMBER 1984

In each of the regressions reported, the estimated CONCLUSIONS coefficient of the percentage change in the long-term

inter-est rate (corpor-ate Aaa bond rate) — which is an The share prices of financial institutions (and the estimate of the interest elasticity of the stock prices of wealth of their owners) are more sensitive to interest

the firms — is both negative and statistically signifi- rate changes than are the shaie prices of industrial cant. Increases in the long-term interest rate are firms. This is true because financial institutions are associated with reductions in the capital values of both highly levered relative to other firms and because the industrial and financial firms. portfolios of savings and loan associations ar-c com- posed of relatively long-term financial assets and rela- The estimated coefficient of the growth i-ate in real tively short-term financial liabilities. Because the mar- GNP (the proxy for cyclical factors( is positive in each ketvalue ofthese institutions is particularly sensitive to estimate. The positive sign of the coefficient indicates changes in the long-term interest rate, financial finns that expansions in economic activity are associated (parlicularly savings and loan associations) are subject with increases in the stock prices of both industrial to greater interest i-ate risk. and financial firms. The coefficient is statistically significant, however’, only in estimates I and 2. Simply matching asset and liability durations will not insulate the firm against interest rate risk, In fact, Djfferential Interest Rate Elasticities complete insulation is probably undesirable. Interest The results in table 5, as expected, show that a given risk can only be eliminated if these firms wet-c to bor- percentage change in the long-term interest rate pro- row long and lend short, that is, if they were to com- duces differential effects on the share prices of the pletely ieverse their traditional practices. However-, different types of firms. For example, a 1 pci-cent in- structuring portfolios in this way can be costly to finan- crease in the long-term interest rate is associated with cial institutions iL as suggested here, it reduces the an average reduction of 0.4 percent in the net present credibility of the commitments these institutions make value of industrial firms, a 0.9 percent reduction in the to depositor’s. net present value of banks, and a 2.41 per-cent reduction in the net present value of savings and loan associations. REFERENCES

Since the coefficients of the percentage change in Alchian, Armen A. “The Rate of Interest, Fisher’s Rate OverCost the long-term interest rate are estimates of interest rate and Keynes’ Internal Rate of Return,” American Economic elasticity, the results indicate that, on average, the Review (December 1955), pp. 938—43. stock prices of savings and loans are about two and a Bierwag, G. 0., George G. Kaufman, and Alden Toevs, “Dura- tion: Its Development and Use in Bond Portfolio Management,” half times more sensitive to changes in the long-term Financial Analysts Journal (July/August 1g83), pp. 15—35. interest rate than are the stock prices of banks, and Federal Home Loan Bank Act of 1932. Public No. 304,72 Cong., about five times moi-e sensitive to such changes than HR 12280. are the stock prices of industrial firms. These differ- 7 Flannery, Mark J. “Market Interest Rates and Commercial Bank ences are statistically significant.’ Profitability: An Empirical Investigation,” The Journal of Fi- nance (December 1981), pp. 1085—i 02. The i-dative ranking of the various types of firms Hicks, J. R. Value and Capital (Oxford: Clarendon Press, 1939). indicated by these estimates of interest elasticity is Hopewelt, Michael H., and George G. Kaufman, “Bond Price consistent with that suggested by the previous discus- Volatility and Term to Maturity: A Generalized Respecification,” sion: financial firms are more highly levered than other American Economic Review (September 1973), pp. 749—53. firms, and savings and loans maintain asset/liability Kaufman, George G. “Measuring and Managing Interest Rate portfolios that are heavily weighted by long-term assets Risk: A Primer,” Federal Reserve Bank of Chicago Economic and short-term liabilities. Perspectives (January/February 1984), pp. 16—29. Maiset, Sherman J., and Robert Jacobson, “Interest Rate Changes and Commercial Bank Revenues and Costs,” Journal “When the ratio of the index of the prices of bank stock to the of Financial and Quantitative Analysis (November 1978), indexof theprices of industrial stockwasregressed on the same pp.687—700. set of right-side variables as appear in tables, the coefficient of the long-term interest rate was negative and statistically signifi- Salomon Brothers, Inc. A Review of Bank Performance (1983), cant for both of the proxies for the price of bank stock, The test p. 54~ was repeated using the ratio of the indexes of the prices of Samuelson, Paul A. ‘The Effect of Interest Rate Increases on savings and loan stock to the prices of bank stock with the same the Banking System” American Economic Review (March results, In sum, unexpected increases in the long-term interest 1945), pp. 16—27. rate cause the stockprices of savings and loan associations to decline relative to the stock prices of banks, whichdecline rela- Savings and Loan Sourcebook, (United States League of Sav- tive to the stock prices of industrial firms. ings Associations, 1982.)