THE VOLATILITY OF EQUITY MUTUAL FUND RETURNS

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. THE VOLATILITY OF EQUITY MUTUAL FUND RETURNS Central Connectcut State Unversty, USA. E-mal: BelloZ@mal.ccsu.edu ABSTRACT I nvestgated both the volatlty and the level of dversfcaton of domestc equty mutual funds from 1988 to 008. I also nvestgated the Market Model s explanatory power for domestc equty funds durng that 0 year perod. The volatlty of equty mutual funds dd not change sgnfcantly from Aprl 1988 to March 1998, but t ncreased apprecably from Aprl 1998 to March 003, and then declned n the followng fve-year perod from Aprl 003 to March 008. Ths trend seems to dffer from a prevous study of common stock prces that found no trend n the stock market or ndustry volatlty from 196 to 1997. Moreover, the volatlty of mutual fund portfolos vared wth the aggressveness of the nvestment objectve, and the porton of total volatlty that remaned undversfed tended to be hgher durng perods of hgh market volatlty. Consstent wth the prevous studes of common stocks, the explanatory power of the Market Model declned from Aprl 1988 to March 003. However, the explanatory power of the Market Model ncreased substantally from 003 to 008. Fnally, stock mutual funds lead the expansonary phase of the busness cycle, but do not appear to predct recessons three months ahead of tme. Key Words: Mutual Funds, Volatlty, Idosyncratc Rsk, and Portfolo Dversfcaton JEL Codes: C13, C3, C5, and G3 I. INTRODUCTION The volatlty of common stock returns exhbted a sgnfcant change durng the last half of the 0 th Century. Campbell, Lettau, Malkel, and Xu (001) found that volatlty at the frm level more than doubled from 196 to 1997. Campbell et al. also found that ndustry and market volatlty dd not exhbt a sgnfcant trend durng the 196 to 1997 perod, contrary to Offcer (1973), Schwert (1989), and Hamlton and Ln (1996), who found that the volatlty of the stock market was sgnfcantly hgher durng perods of economc recesson, Further, Campbell et al. found that frm, ndustry, and market volatlty were negatvely correlated wth the GDP growth, suggestng that dversfcaton s more mportant durng economc downturns. Moreover, Campbell et al. (001) found that the ncrease n frm level volatlty relatve to market volatlty from 196 to 1997 mples that the correlatons among ndvdual stocks and the explanatory power of the market for a typcal stock tended to 4

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. declne over tme, suggestng that the benefts of portfolo dversfcaton had ncreased. They argued that the ncrease n frm level volatlty over tme suggested that the number of randomly selected stocks needed to acheve relatvely complete dversfcaton had also ncreased. The behavor of stock prces over the phases of the economc cycle was documented by Moore (1975), Moore and Cullty (1988), Mlls (1988), Schwert (1990), and McQueen and Roley (1993). Moore and Cullty (1988) observed that there were few substantal swngs n stock prces, over tme that were not assocated wth the swngs n the busness cycle. But whereas stock prces tended to rse durng expanson and to declne durng recessons, bond prces moved n the opposte drecton. Durng economc expansons, bond prces declned as nterest rates rose. However, bond prces rose durng economc recessons as nterest rates declned. Typcally, stock prces lead the alternatng expansons and contractons n busness actvty, and bond prces tended to lead stock prces. In other words, bond prces and stock prces are leadng ndcators of economc actvty, but bond prces lead s sgnfcantly longer than that of stock prces. Moreover, Schwert (1990) found a strong postve relaton between real stock returns and producton growth for the next several quarters. Accordng to Moore and Cullty (1988), the stock prces lead ranges from two to 15 months. Generally, good tmes are good for stock prces and bad for bond prces. Conversely, perods of economc recesson are good for bonds and bad for stocks. Interest rates and profts are the major lnk between securty prces and economc cycle, as observed by Moore and Cullty (1988), and Bolten and Wegand (1998). Accordng to Ewng, Payne, and Forbes (1998), securty prces are more senstve to short term nterest rates such as the Treasury bll rates. They found that past changes n the certfcate of deposts rates and the Prme Rate helped to explan changes n current stock returns. The purpose of the present study s to nvestgate (1) the volatlty of mutual fund portfolos over a 0 year perod, from 1988 to 008, () to nvestgate the level of resdual rsk nherent n equty mutual fund portfolos, and (3) to nvestgate the Market Model s explanatory power for domestc equty portfolos durng that 0 year perod. II. DATA The sample conssts of 1065 domestc equty mutual funds drawn from fve nvestment objectve categores, ncludng Aggressve Growth, Growth, Growth and Income, Equty Income, and Small Company. Mutual funds that have more than 15% of ther portfolo nvested n ether bonds or non-u.s. stocks are not ncluded, nether are mutual funds that have an average net assets of less than $500 mllon. Monthly returns for 0 years, from Aprl 1988 to March 008, for the mutual fund sample were obtaned from the Mornngstar Prncpa database. Monthly returns on three month Treasury blls, the Federal Reserve s Index of Industral Producton (seasonally adjusted), and the Lehman Brothers Aggregate Bond Index were also obtaned from the Mornngstar 43

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. Prncpa database. And, fnally, monthly excess market returns were obtaned from Kenneth R. French s data lbrary 1. III. METHODOLOGY To determne the explanatory power of the Market Model for a typcal mutual fund portfolo, I ran a regresson of the form: r r e (1) t mt t, where: rt = the excess return for fund, n month t; rmt = the excess market return n month t; et = the random error term for fund, n month t; α = the Jensen s alpha for fund ; and β = the market beta for fund. The total varance of fund s portfolo,, s measured as: 1 m e, () n where: s the varance of returns on the market portfolo, n s the number of stocks n m portfolo, and e s the varance of portfolo s resdual terms. The resdual varance (RV) s therefore estmated as follows: m RV 1, (3) I also examned the lnear relaton between mutual fund returns and selected economc varables as follows: IDI t 3 1r mt r t 3ABI t 4 Tbll t et, (4) where: rt and rmt are the excess fund return and excess market return, respectvely, as defned n Equaton (1). IDIt+3 s the monthly growth rate of the Index of Industral Producton n perod t+3, Tbll s the monthly return on three month Treasury blls, and ABI s the rate of return on the Lehman Brothers Aggregate Bond Index. The sgnfcance of estmated parameters, 1 and, ndcate the extent to whch the stock market and mutual fund portfolos, respectvely, predct economc actvty, wth a lead of three months. IV. THE RESULTS Panel A of Table1 shows the average standard devatons of return for the market and for mutual funds. From Aprl 1988 to March 1998 the volatlty of mutual fund return dd not change sgnfcantly. However, over the followng fve-year perod, from Aprl 1 Mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_lbrary.html 44

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. 1998 to March 003, volatlty ncreased apprecably from 3.643% per month to 6.178%, and then declned substantally to the level of prevous years. In other words, a downward trend from 1988 to early 003 was evdent, followed by a jump n the followng fve years, before the downward trend contnued n the 003 to 008 perod. Ths trend of mutual fund volatlty s reflectve of the stock market trend as a whole, as shown n the Table, and seems to dffer from a prevous study of common-stock volatlty by Campbell et al. (001), who found no trend n volatlty of the market or ndustry from 196 to 1997. However, my results are consstent wth Offcer (1973), Schwert (1989), and Hamlton and Ln (1996), who found that volatlty of the stock market was sgnfcantly hgher durng economc recessons. Table 1 The Volatlty of Mutual Fund Returns (Aprl 1988 March 008) Sub-Perod #Funds RV R m Panel A: Sub-Perod Volatlty 4/88-3/93 706 3.894 3.379 0.179 0.786 4/93-3/98 1054 3.643 3.3 0.31 0.705 4/98-3/03 1065 6.178 5.588 0.91 0.654 4/03-3/08 1065 3.305.87 0.155 0.800 Average 1065 4.657 --- --- --- Market --- 4.069 --- --- --- Panel B: Volatlty by Investment Objectve (1988-008) Inv. # Funds σ RV RMSE --- Objectve AG 36 6.56 0.75 3.435 --- SC 186 5.166 0.374 3.13 --- G 49 4.801 0.34.71 --- GI 90 3.916 0.196 1.6 --- EI 61 3.4 0.301 1.854 --- Note: RV s the porton of total return varance that has not been elmnated through dversfcaton, as shown n Equaton (3): RV m 1 RMSE s the standard devaton of the error varance from the same Equaton. Is the standard devaton of mutual fund returns measured ndvdually for each fund and then averaged across funds. #Funds s the number of mutual fund portfolos n each nvestment 45

Standard Devaton % North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. (nv.) objectve category, and R s the cross-sectonal squared estmated usng the Market Model --Equaton (1). The porton of total volatlty of return that has not been elmnated by portfolo dversfcaton, RV, ranges from 0.155% to 0.91% and s reflectve of the total volatlty,. Campbell et al. found that the total number of stocks needed to acheve a gven level of portfolo dversfcaton ncreased durng ther 196 to 1997 sample perod. Fgure 1 graphcally compares the level of both the market and mutual fund volatlty wth the level of resdual varance, RV, the porton of total fund volatlty that remans undversfed. Resdual varance s shown to be hgher from Aprl 1998 to March 003, the same perod n whch both the stock market and mutual fund portfolos experenced the hghest levels of volatlty. It appears that the more volatle the market, the greater the need to dversfy a portfolo. Fgure 1 Volatlty of Mutual Fund Returns (Aprl 1988-March 008) 7.00 6.00 5.00 4.00 3.00.00 1.00-4/88-3/93 4/93-3/98 4/98-3/03 4/03-3/08 Funds Market RV Fve Year Sub-Perods To determne f, for stock mutual funds, the explanatory power of the Market Model has changed over tme, I estmated the regresson R-squared of Equaton (1). As shown n Panel A of Table 1, the R declned for each fve-year sub-perod from Aprl 1988 to March 003. These results are n lne wth Campbell et al. (001) who found that, for a typcal common stock, the explanatory power of the Market Model declned durng ther 196 to 1997 sample perod. However, ths trend obvously has not extended to later perods as suggested by the sgnfcant ncrease n R from 0.654 to 0.800 durng the Aprl 003 to March 008 perod. Further, as shown n Panel B of Table 1, the volatlty of mutual fund returns tends to vary wth the aggressveness of ts nvestment objectve. Aggressve Growth funds exhbt the hghest volatlty of 6.56% per month and Equty Income (EI) funds exhbt the lowest return volatlty of 3.4%. The average volatlty for the overall 46

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. sample of 1065 stock mutual funds was 4.657% per month and that for the market was 4.069%. However, although total volatlty s lowest for the EI group, the level of dversfcaton as judged by resdual varance s second poorest for the EI group. Table shows regressons of economc actvty usng four predctors: the stock market, stock mutual funds, long-term bond returns as represented by the Lehman Brothers Aggregate Bond Index, and short-term nterest rates as represented by the monthly return on three-month-treasury blls (RF). As shown n the Table, the stock market appeared to be a very good leadng ndcator of economc actvty. For the overall sample perod, from 1988 to 008, the coeffcent on the market s 0.007 and s sgnfcant at the 5% level. Moreover, durng both the expansonary and the recessonary perods, the stock market sgnfcantly predcted the busness cycle. These results are consstent wth Schwert (1990, page 146) who found a strong postve relaton between common stock returns and producton growth. Table. Equty Mutual Fund Returns as Predctor of the Economc Cycle (Aprl 1988 March 008) Regressor Overall Data Expanson Recesson Intercept 0.185 0.53-0.548 (67.13)* (91.53)* (-105.1)* Market 0.007 0.003 0.009 (13.86)* (5.54)* (8.4)* Funds -0.003-0.00 0.001 (-6.35)* (-3.66)* (0.55) Bond Index 0.05 0.039 0.039 (3.09)* (36.45)* (14.67)* RF 0.065-0.006 0.195 (8.65)* (-0.84) (1.48)* Note: The response varable s the growth rate of the Federal Reserve s Industral -Producton Index, seasonally adjusted. In all cases, the condton number s less than 5. T-statstcs are n parentheses. Parameter estmates as defned n Equaton (4): IDI t 3 1r mt r t 3ABI t 4Tbll t et All varables are as defned earler. *Sgnfcant at the 5% level. Surprsngly, equty mutual fund returns do not sgnfcantly predct recessonary perods, and although fund returns predct economc expansons, the coeffcent on fund returns turns out negatve, suggestng that news about forthcomng economc growth s bad news for stock mutual funds. Ths result s counterntutve but s consstent wth McQueen and Roley (1993, pages 694-695) who found a negatve coeffcent on common stocks and arrved at the concluson that good news about economc actvty s bad news for [common] stocks. Moreover, bond returns are also strong predctors of the economc cycle, as shown n Table, but short-term nterest rates as represented by Treasury blls tend to 47

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. predct recesson qute well but are not good predctors of upturns n economc actvty the coeffcent on RF beng negatve and nsgnfcant. V. SUMMARY AND CONCLUSIONS The purpose of the present study s to nvestgate (1) the volatlty of mutual fund portfolos over a 0 year perod, from 1988 to 008, () to nvestgate the level of resdual rsk nherent n equty mutual fund portfolos, and (3) to nvestgate the Market Model s explanatory power for domestc equty portfolos durng that 0 year perod. The volatlty of equty mutual funds dd not change sgnfcantly from Aprl 1988 to March 1998, but t ncreased apprecably from Aprl 1998 to March 003 and then declned n the followng fve-year perod from Aprl 003 to March 008. Ths trend seems to dffer from a prevous study of stock prces that found no trend n the stock market or ndustry volatlty from 196 to 1997, but s consstent wth prevous studes that found that stock prces were more volatle durng economc recessons. The porton of total volatlty that remans undversfed tended to be hgher durng perods of hgh market volatlty and that dversfcaton appeared to be more urgent durng perods of economc recesson. The explanatory power of the Market Model declned from Aprl 1988 to March 003, consstent wth prevous studes of common stocks. However, volatlty experenced a jump from Aprl 1998 to March 003, a perod that has not been covered by those prevous studes, before contnung the downward trend from Aprl 003 to March 008. Moreover, the volatlty of mutual fund portfolos vared wth the aggressveness of the nvestment objectve, but level of portfolo dversfcaton dd not vary wth nvestment objectve. Fnally, stock mutual funds lead the expansonary phase of the busness cycle wth a lead of three months but they dd not appear to sgnfcantly predct recessons three months ahead of tme. REFERENCES Bolten, S. E., and R. A. Wegand, 1998. The generaton of stock market cycles, Fnancal Revew 33, 77-84. Campbell, J. Y., M. Lettau, B. G. Malkel, and Y. Xu, 001. Have stocks become more volatle? An emprcal exploraton of dosyncratc rsk, Journal of Fnance 56, 1-43. Ewng, B. T., J. E. Payne, and S. M. Forbes, 1998. Co-movements of the prme rate, CD rate, and the S&P Fnancal Stock Index, The Journal of Fnancal Research 1, 469-48. Fama, E. F., and K. R. French, 1989. Busness condtons and expected returns on stocks and bonds, Journal of Fnancal Economcs 5, 3-49. Hamlton, J. D., and G. Ln, 1996. Stock market volatlty and the busness cycle, Journal of Appled Econometrcs, 11, 573-593. 48

North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. McQueen, G., and V. V. Roley, 1993. Stock prces, news, and busness condtons, The Revew of Fnancal Studes 6, No. 3. (Fall), 683-707. Menns, E. A., 1995. Securty prces and busness cycles, Fnancal Analysts Journal 51, No. 1 (January/ February), 44-50. Mlls, L., 1988. Can stock prces relably predct recessons? Busness revew Federal Reserve Bank of Phladelpha, 3-14. Moore, G.,1975. Stock prces and the busness cycle, The Journal of Portfolo Management 1, No. 3 (Sprng), 59-64. Moore, G., and Cullty, J. P., 1988. Securty markets and busness cycles, The Fnancal Analysts Handbook, 45-69. Offcer, R. A., 1973. The varablty of the market factor of New York Stock Exchange, Journal of Busness, 46, 434-453. Schwert, G. W., 1989. Why does market volatlty change over tme? Journal of Fnance, 44, 1115-1153. Schwert, G. W., 1990. Stock returns and real actvty: A century of evdence, Journal of Fnance, 45, 137-157. 49