# Does prepayment risk of mortgages affect excess returns of bank stocks? The evidence suggests that it does.

This paper explores the relationship between the prepayment risk embedded in conventional, fixed-rate residential mortgages and excess returns for bank stocks. There are two interesting findings in this study. First, commercial banks traded in the Nasdaq market are more mean-variance efficient than the other seven groups of industrial stocks. Second, the prepayment risk factor is significant for these banks. The prepayment risk mainly reflects a call option embedded in a mortgage plus foreclosure costs associated with a mortgage put option. This risk is measured by a remaining part of mortgage rates after excluding the influence of real estate market, maturity, and default risks on mortgage rates. The results of this study suggest that the prepayment risk factor does significantly affect excess returns for bank stocks in the period with high levels of mortgage refinancing activities.**********

Compared with other types of loans, mortgage loans embed a unique risk, prepayment risk, in addition to maturity (term) and default risks. In the case of residential mortgages, a homeowner may exercise either a call option (refinancing) to prepay the loan balance without paying any financial penalties if new mortgage rates are lower, or a put option to default--the homeowner is to "put" the house to the bank and let the bank foreclose the property--if the net worth is negative (i.e., if the market value of the property is less than the mortgage loan balance).

In either case, the mortgage is closed before its maturity. The prepayment risk mainly reflects the first case, however. When the homeowner prepays (calls back) the mortgage, the lender faces a reinvestment problem: lower interest rates on new mortgages. In order to compensate the loss on interest revenue, a prepayment risk premium must be included in mortgage interest rates. It is similar to a call premium embedded in a call price for a callable corporate bond. Essentially, a mortgage is a callable bond issued by a home buyer (borrower). There are two different risks contained in a put option. The first is the probability of defaulting on a mortgage, which is measured by the default risk--the chance of losing some interest and possibly losing some principal. The second is the probability of a foreclosure. Only the possible foreclosure costs, in the case of negative net worth, are reflected in the prepayment risk premium, because the bank is responsible for the foreclosure costs. (1) Therefore, prepayment risk is an additional risk for banks engaged in mortgage lending.

Fratantoni and Schuh (2002) note that the "prepayment risk is generally more important empirically than the default risk in most economic environments, since single-family mortgages have very low credit risk relative to other types of loans." Furthermore, according to Bennet, Peach, and Peristiani (2001), homeowners' propensity to prepay or refinance increased in the 1990s relative to 1980s, due to some structural changes in the mortgage market discussed below. In order to compensate lenders for taking prepayment risk, mortgage rates--the required returns on mortgage loans--should contain a premium for this risk. However, the prepayment risk premium is not easy to quantify because it is not observable. In many previous studies, estimation of the prepayment risk premium is included in the context of mortgage pricing (Hendershott and Order, 1987). Other studies try to use more direct methods to quantify the prepayment risk premium. For instance, Bennet et al. (2001) use option values on ten-year U.S. Treasury note futures contracts as a proxy for the prepayment premium. This measure may not be accurate enough to reflect the option values embedded in mortgages. Unlike the option on Treasury notes, mortgage refinancings can be the result of different motivations, ranging from lowering monthly mortgage payments to shortening the maturity of mortgages (Lekkas, 1993). Therefore, a better alternative measure of prepayment premium needs to be developed based on mortgage rates and real estate markets.

Obviously, changes in real estate markets have an immediate impact on the demand for mortgages and mortgages interest rates. Mortgage rates are affected by not only the real estate market risk factor, but also by the term, default, and prepayment risk factors. Theoretically, a reasonable measure of prepayment premium is a component of the mortgage rate that is not explained by the real estate market, term, and default risk factors.

Mortgage loans are one of the major asset classes for banks, and prepayment risk represents an additional unique risk to those banks. Therefore, required returns on bank stocks should contain a unique prepayment risk premium. Evidence from stock price indexes presented in Table 1 for the relatively small and medium-sized banks represented in Nasdaq seems supportive. Over the period of January 1972 through December 2002, the average monthly "excess return"--the monthly percentage changes in stock prices less the rates on one-month T-bills--on the Nasdaq Bank Index (0.39 percent) was higher than for any other Nasdaq sectors: the composite, industrial, insurance, financial institutions, transportation, telecommunication, and utilities. The standard deviation of bank stock returns (3.92 percent) was lower than any other indexes. For the same period, the mean of monthly excess returns in Standard & Poor's 500 stock index was 0.13 percent and the standard deviation was 3.66 percent. Apparently, the average monthly return rate for the Nasdaq Bank Index outperformed many other indexes over a 31-year period. Results of this study also indicate that the prepayment risk factor plays a significant role in determining excess returns for bank stocks in periods with high levels of refinancing activities.

The relationship between the prepayment risk and excess returns of bank stocks is important to the banking industry for various reasons. First, mortgage lending is an important business for many commercial banks, and it is beneficial for managers of those banks to understand the prepayment risk involved in their daily business operations. Second, the measure of the prepayment risk developed in this paper provides a tool for bank managers to quantify the prepayment risk premium. Finally, the tradeoff relationship between the prepayment risk and bank stock returns is important to bank stock investors. The significant influence of the prepayment risk on bank stocks can shape many financial decisions of investors as well as top bank managers. This paper is an effort to explore this interesting and important trade-off relationship.

Estimation Models for the Effect of Prepayment Risk on Excess Returns of Bank Stocks

Early studies on market performance of banks use changes in the stock market and interest rates to explain bank stock returns. The results reported by these studies are not always consistent. Some studies find only weak relationships between bank stock returns (equity appreciation) and interest rates--see Stone (1974), Lloyd and Shick (1977), Chance and Lane (1980), and Sweeney and Warga (1986). Other studies--such as Lynge and Zumwalt (1980), Booth and Officer (1985), Scott and Peterson (1986), and Chaudry and Reichert (1999)--suggest that the stock returns of banks or financial institutions are highly sensitive to changes in interest rates. Flannery and James (1984) and Kwan (1991) find that the maturity composition of the bank's balance sheet may be relevant to the interest rate sensitivity of its stock returns. In addition to the equity and bond market factors, several studies include real estate as an additional explanatory factor in explaining stock returns for banks. For example, Eisenbeis and Kwast (1991) find that banks that specialize in real estate outperform typical banks in terms of both increased earnings and reduced risk. In their study of the sensitivity of bank stock returns to the real estate market, He, Myer, and Webb (1996) report that real estate is indeed a relevant factor in explaining both bank stock returns and risk. Results of He and Reichert (2003) further indicate that three real estate measures--changes in new housing prices, excess returns on equity real estate investment trusts (REITs), and excess returns on mortgage REITs have similar effects on bank stock returns. (2)

Bank stocks may also be sensitive to other general risk factors, such as spreads. Two types of spreads have been widely used as measures of maturity (term) risk and default risk premiums in previous studies. Fama and French (1993) find that a combination of maturity risk (measured by the difference between long-term government bond returns and one-month T-bill rates) and default risk (measured by the difference between long-term corporate bond returns and long-term government bond returns) can explain a significant portion of variation in stock and bond returns.

When banks make mortgage loans, they face maturity and default risks; and the two spreads should help explain excess returns for bank stocks. Unlike other industries, banks also face prepayment risks. (3) Although there is no direct measure for the prepayment risk premium, residuals from a regression model that uses real estate, maturity, and default risk factors to explain variations in risk premiums contained in mortgage rates may be able to quantify the prepayment risk premiums. This prepayment risk factor can serve as an independent variable, with other risk factors as control variables, to explain excess returns on different industrial portfolios. It is hypothesized that only the bank stock portfolio is sensitive to the prepayment risk factor, because it is the only portfolio, among all eight industrial portfolios, fully (all banks) engaged in mortgage lending. This unique risk facing banks may justify higher excess returns and lower variance of excess returns for bank stocks, compared with other industries.

The following is the first of three estimation models:

(1) Mor[t.sub.t] = [alpha] + [[beta].sub.R]Rei[t.sub.t] + [[beta].sub.T]Ter[m.sub.t] + [[beta].sub.D]Defaul[t.sub.t] + [[epsilon].sub.t]

Mor[t.sub.t] represents risk premiums contained in mortgage rates and are measured by differences between the monthly mortgage rates and one-month T-bill rates. Rei[t.sub.t], the proxy for real estate markets, is the difference between monthly stock returns for equity real estate investment trusts (REITs) and one-month T-bill rates. Ter[m.sub.t] is maturity risk premium as defined by Fama and French (1993): differences between monthly returns on long-term government bonds and one-month T-bill rates. Defaul[t.sub.t] is the default risk premium defined by Fama and French (1993): differences between monthly returns on long-term corporate bonds and long-term government bonds, which are default risk free. The sum of the constant term and residuals of Equation 1 represents prepayment risk premiums (Prepa[y.sub.t]).

In order to find out whether the prepayment risk is significant for bank stocks, a second, more complete, model is applied to more accurately examine the impact of prepayment risk on bank stock returns:

(2) Ban[k.sub.t] = [alpha] + [[beta].sub.M][MKT.sub.t] + [[beta].sub.C]Mor[t.sub.t] + [[beta].sub.R]Rei[t.sub.t] + [[beta].sub.I][PPI.sub.t] + [[beta].sub.L]Leas[e.sub.t] + [[beta].sub.T]Term + [[beta].sub.D]Defaul[t.sub.t] + [[beta].sub.P]Prepa[y.sub.t] + [[epsilon].sub.t]

where Ban[k.sub.t] represents excess returns on bank stocks--monthly percentage changes in the bank stock index minus one-month T-bill rates; MK[T.sub.t], represents differences between monthly percentage changes in the S & P 500 Index and one-month T-bill rates; CMor[t.sub.t] is the percentage change in monthly mortgage rates; [PPI.sub.t] is the monthly change in the producer price index; Leas[e.sub.t] represents percentage changes in banks' total leases, another major revenue resource for banks; other variables are defined the same as in Equation 1.

Data Description

This study uses monthly data on excess returns over a period of January 1972 through December 2002-372 months. The availability of data determines this sample period, since January 1972 is the earliest month for which there are observations on the total return index for equity REITs. The descriptions of basic variables in the empirical analysis are as follows (data source in parentheses):

Bill = One-month Treasury bill rates (Ibbotson Associates).

Bank = Percentage changes in NASDAQ Bank Index (533 banks) -- Bill.

MKT = Percentage changes in S & P 500 Index (Yahoo) -- Bill.

Reit = Percentage changes in the Equity REIT Total Return Index (National Association of REITs) -- Bill.

Long = Returns on long-term government bonds (Ibbotson Associates).

Corp = Returns on long-term corporate bonds (Ibbotson Associates).

Mort = Mortgage rates on 30-year fixed-rate conventional mortgages (Federal Reserve).

Leas = Percentage changes in total leases: (Total loans & leases -- Real estate loans--Commercial & industrial loans--Consumer loans) (Federal Reserve).

PPI = Change in the Producer Price Index (Bureau of Labor Statistics).

Term = Long -- Bill.

Default = Corp -- Long.

Prepay = Sum of the constant and residuals from Equation 1.

Results

Mean-variance efficiency of bank stocks

Monthly excess stock returns for banks traded in Nasdaq were 0.39 percent over the period of January 1972 through December 2002, as shown in Table 1. This portfolio generated higher excess returns, with lower variance in returns (0.15 percent), than any other Nasdaq index. The two closest indexes were the Nasdaq Financial 100 and Insurance Indexes. Monthly excess returns for these two indexes were 0.36 percent and 0.37 percent, and variances were 0.25 percent and 0.19 percent, respectively. Both of them also shared the highest correlations with the Bank index, 73 percent and 72 percent. Nasdaq Telecommunications and Utility Indexes had the smallest excess returns (0.23 percent), highest variances (0.47 percent), and lowest correlations (37 percent) with the Bank index. The t-statistics in Table 1 suggest that excess returns for banks are not significantly higher than the other seven Nasdaq sector indexes or the composite index. However, variations in bank stock excess returns are significantly lower than variances for the other seven sectoral indexes, as the Bartlett-statistics and F-statistics indicate. All differences in variance are at the one percent significance level, except for the Insurance Index, which is at about the five percent level. The results unequivocally suggest that the bank portfolio is more mean-variance efficient than other industrial portfolios in Nasdaq. That is, compared with other portfolios, given the similar or slightly higher excess returns, the bank portfolio experiences less volatility in stock prices.

A cross exchange comparison shows no evidence for higher mean-variance efficiency for Nasdaq bank stocks. Monthly excess returns for stocks in the S & P 500 Index were only 0.13 percent, but they were not significantly lower than excess returns for Nasdaq banks as evidenced by the small t-statistic of 0.92 (Table 1). Furthermore, although the variance for the S & P 500 Index was 0.13 percent, it was not significantly lower than that for Nasdaq banks.

The higher level of mean-variance efficiency for Nasdaq banks may be explained by some unique or "hidden" risk factors facing banks that are actively involved in mortgage lending. Given the fact that the prepayment options (call and put) contained in mortgage loans represent a risk factor unique to mortgage lending, stocks of these banks must be very sensitive to the prepayment risk factor, a factor that is missing from other sectors, although each sector faces its own unique risks.

Important risk factors to bank stocks

In addition to maturity, default, and prepayment risk factors, five other risk factors may also play important roles in explaining excess returns for bank stocks, as described in Equation 2. Summary statistics of variables used in the estimation model are provided in Table 2. The monthly maturity and prepayment risk premiums are similar and sizable (0.25 percent and 0.28 percent), while the size of default risk premium is as low as -0.01 percent. All three risk premiums have similar correlations with excess returns of bank stocks, ranging from 12 percent to 15 percent.

Table 2 also presents the OLS regression results of Equation 2. All three risk premiums have positive coefficients. The result is consistent with the basic finance concept: higher risk should be compensated by a higher return. The large size of the prepayment coefficient (3.19 with a t-value of 2.59) suggests that among the three risk factors the prepayment is the most important risk involved in mortgage lending activities. The second important risk factor is the default risk. It has a coefficient of 0.25 and a t-value of 1.69. This coefficient is significant at the ten percent level. However, the OLS results indicate that the maturity risk is not an important factor in determining excess returns of bank stocks. The coefficient of Term, a measure of maturity risk, is only 0.06, and its t-value is as small as 0.95. This insignificant Term coefficient is not surprising. If a large number of people prepay their mortgages through refinancing or defaulting, as reflected in the significant Prepay coefficient, the effective maturities of many mortgages are in fact shortened. It means that some amount of maturity risk is transferred into prepayment risk when mortgages are prepaid. Therefore, the increase in mortgage prepayment may be responsible for the highly significant Prepay coefficient and the insignificant Term coefficient.

All other five control variables have significant coefficients and meaningful signs. Excess returns on the stock market and on the real estate market and changes in total leases have positive effects on bank stock returns. On the other hand, changes in mortgage rates and inflation may adversely influence bank stock prices.

In order to correct the potential heteroskedasticity problem, the White's heteroskedasticity-consistent covariance matrix is used in the OLS estimation. The results are basically as same as the OLS results. Table 2 also reports results from the least absolute error (LAE) estimation, which suggest an even more important impact of prepayment risk on excess returns of bank stocks.

Prepayment risk and mortgage rates

Figure 1 clearly shows variations in the linear relation between prepayment risk premiums and monthly mortgage rates. The relation is negative over periods of 1/1972-12/1979 and 1/1990-12/2002. Monthly mortgage rates in these periods were relatively low. The relation turns positive over the period of 1/1980-12/1989 with higher mortgage rates. The summary statistics in Table 3 indicate that the average monthly mortgage rate is 0.71 percent (about 8.5 percent annual) for the periods of 1/1972-12/1979 and 1/1990-12/2002, and the correlation between prepayment risk premiums and mortgage rates is -20.1 percent; while for the period of 1/1980-12/1989 the correlation becomes 26 percent and the average monthly mortgage rate is one percent (12 percent annual).

When mortgage rates are high, there may be a greater tendency for homeowners to exercise their put options and place their houses into foreclosure due to large payments. In order to compensate for foreclosure costs, lenders demand higher prepayment risk premiums. Therefore, the correlation between mortgage rates and prepayment risk premiums is positive. On the other hand, when mortgage rates are low, demand for homes is strong, and the probability of negative net worth and foreclosure is low. However, more homeowners may exercise their call options for refinancing if mortgage rates fall further. As a result, the correlation between mortgage rates and prepayment risk premiums is negative.

Compared to foreclosure, refinancing is less costly to lenders. In fact, the cost of refinancing to a bank may be offset by the revenue of originating a new mortgage. The large volume of refinancing has become an increasing revenue resource for many banks in recent years. The lower effective refinancing cost to banks determines lower prepayment risk premiums in the period with lower mortgage rates. The average monthly prepayment risk premium is 0.25 percent for period with lower mortgage rates and 0.33 percent for the higher rate period.

Structural change and the prepayment sensitivity of bank stocks

During the sample period of this study, the banking and mortgage markets experienced important structural changes that may have caused alterations in bank sensitivity to prepayment risk. The inflationary environment of the late 1970s not only undermined the traditional structure of housing finance, which is more sensitive to credit availability than to interest rates, but also "led to a significant deregulation of mortgage markets in the late 1970s and early 1980s," according to Sellon (2002). The two important deregulations were the elimination of deposit-rate ceilings over a period of time and the legalization of adjustable-rate mortgages. Securitization of mortgages and improvements in information-processing technology became more prominent in the 1980s (Bennett, Peach, and Peristiani, 2001). As a result of these structural changes, mortgage lending turned out to be more sensitive to interest rates than previously.

The Financial Institutions Reform, Recovery, and Enforcement Act of 1989 (FIRREA) also shaped lending activities of depository institutions after the collapse of S & Ls and thrifts in the 1980s, contributing further to structural changes. The result of a Chow test, shown in Table 3, supports a hypothesis of structural change between the pre- and post-FIRREA periods. In the pre-FIRREA period (January 1972-July 1989), the housing finance system was generally more sensitive to credit availability rather than to interest rates; and as a result, bank stocks were not very sensitive to prepayment risk. When the housing finance system became more sensitive to interest rates, the prepayment sensitivity of bank stocks increased. Table 3 shows that the coefficient of Prepay is as high as 9.06 in the post-FIRREA period. It is significant at the one percent level, as suggested by t-statistics (3.35 and 3.37) from the OLS estimations with and without using the White's heteroskedasticity-consistent covariance matrix. The result is consistent with the finding that homeowners' propensity to refinance their mortgages increased in the 1990s relative to 1980s (Bennet et al., 2001).

Conclusions

This paper reports two interesting findings. Banks traded in the Nasdaq market are more mean-variance efficient than the other seven groups of industrial stocks. Those banks are mainly medium and small commercial banks that are actively involved in mortgage lending. Mortgage loans carry a unique risk, the prepayment risk, in addition to normal maturity and default risks. The prepayment risk mainly reflects a call option embedded in a mortgage and the foreclosure costs associated with a mortgage put option. A part of mortgage rates should reflect the prepayment risk after excluding the influence of the real estate market, maturity, and default risks on mortgage rates. In an efficient market, the higher mean-variance efficiency should be explained by some unique risks. Prepayment risk is indeed unique to commercial banks, compared to other sectors in the Nasdaq market; and this study finds evidence that it does affect excess returns for bank stocks. Nonetheless, the prepayment sensitivity of bank stocks varies over time. In the pre-FIRREA period, when the housing finance system was more sensitive to credit availability than to interest rates, prepayment risk did not significantly affect excess returns of bank stocks. In the post-FIRREA period, bank stocks have been highly sensitive to the prepayment risk factor due to high levels of refinancing activities and interest rate sensitivities of mortgage lending.

In an eight-factor model, the coefficient of the maturity risk factor becomes insignificant. This result may suggest that prepayments of mortgage can effectively shorten mortgage maturities. That is, some amount of maturity risk may be transferred into prepayment risk when mortgages are prepaid.

ACKNOWLEDGEMENT

I would like to acknowledge the helpful comments and suggestions of the referees and the editor in the preparation of this paper

REFERENCES

Bennett, P., R. Peach, and S. Peristiani. 2001. "Structural Change in the Mortgage Market and the Propensity to Refinance." Journal of Money, Credit, and Banking. 33, pp. 955-975.

Booth, J.R. and D.T Officer. 1985. "Expectations, Interest Rates, and Commercial Bank Stocks." Journal of Financial Research. 8, pp. 51-58.

Chance, D.M. and W.R. Lane. 1980. "A Re-Examination of Interest Rate Sensitivity in the Common Stocks of Financial Institutions." Journal of Financial Research. 3, pp. 49-55.

Chaudhry, M. and A. Reichert. 1999. "The Impact of Off-Balance Sheet Derivatives and Interest Swaps on Bank Risk." Research in Finance. 17, pp. 275-300.

Eisenbeis, R.A. and M.L. Kwast. 1991. "Are Real Estate Specializing Depositories Viable? Evidence from Commercial Banks." Journal of Financial Services Research. 5, pp. 5-24.

Fama, E. and K. French. 1993. "Common Risk Factors in the Returns on Stocks and Bonds." Journal of Financial Economics. 33, pp. 3-56.

Flannery, M.J. and C.M. James. 1984. "The Effect of Interest Rate Changes of Common Stock Returns of Financial Institutions." Journal of Finance. 39, pp. 1141-1153.

Fratantoni, M. and S. Schuh. 2003. "Monetary Policy, Housing, and Heterogeneous Regional Markets," Journal of Money, Credit, and Banking. 35, pp. 557-589.

He, L.T., N. Myer, and J. Webb. 1996. "The Sensitivity of Bank Stock Returns to Real Estate," Journal of Real Estate Finance and Economics. 12, pp. 203-220.

He, L.T. and A. Reichert. 2003. "Time Variation Paths of Factors Affecting Financial Institutions and Stock Returns." Atlantic Economic Journal. 31, pp. 71-86.

Hendershott, P.H. and R.V. Order. 1987. "Pricing Mortgages: In Interpretation of the Models and Results." Journal of Financial Services Research. 1, pp. 19-55.

Kwan, S.H. 1991. "Re-examination of Interest Rate Sensitivity of Commercial Bank Stock Returns Using a Random Coefficient Model." Journal of Financial Services Research. 5, pp. 61-76.

Lekkas, V. 1993. "Comparing Refinance Booms." Secondary Mortgage Market. 10, pp. 15-18.

Lloyd, W.P. and R.A. Shick. 1977. "A Test of Stone's Two-Index Model of Returns." Journal of Financial and Quantitative Analysis. 12, pp. 363-368.

Lynge, M.J. and J.K. Zumwalt. 1980 "An Empirical Study of the Interest Rate Sensitivity of Commercial Bank Returns: A Multi-Index Approach," Journal of Financial and Quantitative Analysis. 15, pp. 731-742.

Scott, W.L. and R.L. Peterson. 1986. "Interest Rate Risk and Equity Values of Hedged and Unhedged Financial Intermediaries." Journal of Financial Research. 9, pp. 325-329.

Sellon, G.H. 2002. "The Changing U.S. Financial System: Some Implications for the Monetary Transmission Mechanism." Economic Review. Federal Reserve Bank of Kansas City, First Quarter, pp. 5-35.

Stone, B.K. 1974. "Systematic Interest Rate Risk in a Two-Index Model of Returns." Journal of Financial and Quantitative Analysis. 9, pp. 709-721.

Sweeney, R.J. and A.D. Warga. 1986. "The Pricing of Interest-Rate Risk: Evidence from the Stock Market." Journal of Finance. 41, pp. 393-410.

Ling T. He is Professor of Finance and Carmichael Professor at the University of Central Arkansas. He received his DBA in Finance from Cleveland State University. His research includes real estate investment, financial institutions, international finance, and forecasting.

(1) Costs of foreclosure--aside from costs captured in default risk--include litigation and the costs of reselling the foreclosed property.

(2) Equity REITs are those which take equity positions and whose income comes from rentals and capital gains. Mortgage REITs are those which are lenders and whose income comes from interest.

(3) Of course, other industries face risks not faced by banks--e.g., exchange rate and raw materials price risks by manufacturers and fuel cost risks in transportation.

TABLE 1 SUMMARY STATISTICS OF EXCESS RETURNS FOR DIFFERENT INDUSTRIAL STOCKS JANUARY 1972-DECEMBER 2002 BANK COMP INDU FIN INSU TRAN Mean (percent) 0.39 0.32 0.25 0.36 0.37 0.25 Variance (percent) 0.15 0.34 0.34 0.25 0.19 0.24 Correlation Matrix (percent) Bank Comp Indu Fin Insu Tran Bank 100 50 57 73 72 65 Comp 100 93 79 56 62 Indu 100 77 59 74 Fin 100 70 62 Insu 100 62 Tran 100 Tele Util MKT Mean and Variance Comparisons: Banking vs. Other Industries Bank vs. Comp Indu Fin Insu Tran T-statistic 0.19 0.38 0.09 0.07 0.44 F-statistic 2.20 2.20 1.60 1.22 1.55 Bartlett-statistic 55.9 55.6 20.4 3.77 17.9 TELE UTIL MKT Mean (percent) 0.23 0.23 0.13 Variance (percent) 0.47 0.47 0.13 Correlation Matrix (percent) Tele Util MKT Bank 37 37 66 Comp 89 89 79 Indu 75 75 81 Fin 69 68 77 Insu 41 41 71 Tran 44 44 72 Tele 100 100 65 Util 100 65 MKT 100 Mean and Variance Comparisons: Banking vs. Other Industries Tele Utll MKT T-statistic 0.40 0.40 0.92 F-statistic 3.08 3.07 1.15 Bartlett-statistic 111.5 111.2 1.71 All variables are as defined in the text. T-statistic tests the null hypothesis of equality of means of excess returns between bank and another industrial stock portfolio without the assumption of equal population variances. F-statistic tests the null hypothesis of equality of variances of excess returns between bank and another industrial stock portfolio. Bartlett-statistic tests the null hypothesis of homogeneity of variances of excess returns between Bank and another industrial stock portfolio. TABLE 2 SUMMARY STATISTICS (IN PERCENT) OF VARIABLES AND REGRESSION RESULTS OF MODEL 2 Term Default Prepay MKT Reit Cmort PPI Mean (percent) 0.25 -0.01 0.28 0.13 0.52 -0.02 0.34 Variance (percent) 0.09 0.01 0.00 0.13 0.15 0.08 0.01 Lease Bank Mean (percent) 0.61 0.39 Variance (percent) 0.02 0.15 Correlation Matrix (percent) Term Default Prepay MKT Reit Cmort PPI Lease Bank Term 100 -49 -0 12 17 -29 -20 1 15 Default 100 -0 13 9 1 9 -14 12 Prepay 100 4 -0 -13 -21 -14 13 MKT 100 47 -30 -19 -12 66 Reit 100 -31 -13 -10 52 CMort 100 17 -5 -38 PPI 100 10 -22 Lease 100 -2 Bank 100 OLS Regression Results with the Dependent Variable of Bank (1/72-12/02) Constant Term Default Prepay MKT Reit CMort PPI -0.01 0.06 0.25 3.19 0.53 0.23 -0.16 -0.32 (-1.85) (0.95) (1.69) (2.59) (11.85) (5.60) (-2.83) (-1.70) [-1.66] [1.14] [1.63] [2.33] [8.59] [5.33] [-2.88] [-1.65] OLS Regression Results with the Dependent Variable of Bank (1/72-12/02) Constant Lease [R.sup.2] -0.01 0.23 0.54 (-1.85) (2.48) [-1.66] [2.27] Least Absolute Error (LAE) Estimation Results with the Dependent Variable of Bank Constant Term Default Prepay MKT Reit CMort PPI -0.01 0.07 0.20 3.96 0.57 0.17 -0.17 -0.43 {-1.65} {1.20} {1.39} {3.35} {13.28} {4.18} {-3.19} {-2.38} Least Absolute Error (LAE) Estimation Results with the Dependent Variable of Bank Constant Lease -0.01 0.07 {-1.65} {0.74} All variables are as defined in the text. t-statistics from the OLS estimation are in parentheses. t-statistics from the OLS estimation of using White's heteroskedasticity-consistent covariance matrix are in brackets. t-statistics from the LAE estimation are in curly brackets. TABLE 3 SENSITIVITY OF BANK STOCK EXCESS RETURNS TO PREPAYMENT RISK IN TWO PERIODS 1/72-12/79 AND 1/90-12/02 1/80-12/89 SUMMARY STATISTICS (%) Prepay Mortgage Prepay Mortgage Mean 0.25 0.71 0.33 1.00 Standard Deviation 0.11 0.14 0.12 0.21 Correlation -20.10 26.00 Structural Beak between 1/72-7/89 and 8/89-12/02 Chow-test Statistic 2.489 P-value 0.009 OLS Regression Results with the Dependent Variable of Bank (1/72-7/89) Constant Term Default Prepay MKT Reit CMort PPI -0.00 0.03 0.21 1.53 0.63 0.16 -0.13 -0.17 (-0.88) (0.50) (1.57) (1.22) (12.81) (3.52) (-2.17) (-0.87) [-0.77] [0.51] [1.42] [1.00] [9.04] [3.46] [-2.10] [-0.87] OLS Regression Results with the Dependent Variable of Bank (1/72-7/89) Constant Lease [R.sup.2] -0.00 0.22 0.68 (-0.88) (1.97) [-0.77] [1.94] OLS Regression Results with the Dependent Variable of Bank (8/89-12/02) Constant Term Default Prepay MKT Reit CMort PPI -0.02 0.20 0.77 9.06 0.43 0.32 -0.26 -0.84 (-2.82) (1.14) (1.77) (3.35) (5.14) (4.14) (-2.11) (-2.11) [-2.69] [1.25] [1.56] [3.37] [4.80] [3.88] [-2.33] [-2.19] OLS Regression Results with the Dependent Variable of Bank (8/89-12/02) Constant Lease [R.sup.2] -0.02 0.32 0.43 (-2.82) (2.06) [-2.69] [1.92] All variables are as defined in the text. t-statistics from the OLS estimation are in parentheses. t-statistics from the OLS estimation of using White's heteroskedasticity-consistent covariance matrix are in brackets.

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Comment: | Does prepayment risk of mortgages affect excess returns of bank stocks? |
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Author: | He, Ling T. |

Publication: | Business Economics |

Geographic Code: | 1USA |

Date: | Jan 1, 2007 |

Words: | 5394 |

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