Bond Fund Returns

which suggests that a few easily identifiable factors/indices are enough to explain the returns of bond portfolios (Blake, Elton and Gruber, 1993; Elton, Gruber and Blake, 1995). In order to address this issue, in our sample of European bond funds, we also consider a multi-index model as a performance benchmark.

The conditional approach can easily be extended to multiple index models, by including the cross products of each factor with the predetermined information variables. That is, we replace equation [5.2] with a similar equation for each of the K factor-betas of the managed portfolio. Thus, the regression equation of our conditional K-factor model will have (L+1)*K+1 regressors: a constant, the K factor-portfolios and the product of the L information variables in Z_t−1 with the K factor-portfolios. In the case of the conditional model with time-varying alphas (expressed in equation [5.5]) it will have more L regressors corresponding to the variables in Z_t−1 resulting in a model with (L+1)*(k+1) regressors.

We select bond funds that invest mainly in the domestic market and/or in the European market, with monthly data at least since January 1994. We evaluated the performance of these bond funds for the period February 1994 to December 2000. For Portugal we considered a shorter period, from January 1995 to December 2000, as previously (Chapter 4), due to the availability of the index used as benchmark. The funds are grouped according to the type of bonds held by the fund and the classification varies from country to country, as we can see in Table 5.1. The main differences are:⁷¹

• Corporate bond funds, which constitute a separate category only in the UK;

although in the other European countries we may find bond funds with a significant percentage of corporate bonds, they are not classified as corporate⁷²;

• the classification of bond funds according to the maturity of the held bonds;

while for some countries we have bond funds classified as either short-term bond funds or long-term bond funds, for others this distinction is not done;

• Portugal is an exception in classifying bond funds according to the type of coupon rate: fixed rate or floating rate.

The data on Portuguese bond funds was obtained from the Portuguese Mutual Fund Association, APFIN. The information on Spanish and French bond funds was collected from Micropal.⁷³ The data on bond funds for Germany, UK and Italy were obtained from Datastream. As this database does not classify the funds, we previously

71 These differences make some comparisons difficult. We think it is necessary to move towards a more homogeneous classification, in order to have a single European bond fund market.

72 We think that this fact is related to the development of the corporate bond segment, which is clearly superior in the UK.

73 “Source Standard & Poor`s Fund Services SARL © [2001]”. We are extremely grateful to Jorge O´Neill, from Difdata (Standard & Poor`s Fund Services Exclusive Representative in Portugal) for his efforts in providing the data on French and Spanish bond funds.

contacted the domestic associations of investment funds⁷⁴ in order to obtain the list and respective classification of bond funds. With that information, we then collected the end of month total return index for each of the funds. Since Datastream, however, does not have historical records for all funds, our sample is composed by bond funds with available data (both in Datastream and Micropal) and with historical series, at least, since January 1994. Thus, our sample may be affected by survivorship bias, as we do not have data on nonsurviving funds. Notwithstanding, previous research suggests that survivorship bias has less impact upon inferences about bond fund performance compared to stock fund performance (Blake, Elton and Gruber, 1993; Dahlquist, Engström and Söderlind, 2000).⁷⁵ According to Blake, Elton and Gruber (1993) this may be due to the stability of the performance of bond funds.

All fund returns are monthly continuously compounded returns, with dividends and income distributions reinvested, and in local currency. These returns are net of management expenses but not of load charges. The monthly continuously compounded return for fund p at time t is calculated as:

⎟⎟

⎟

⎠

⎞

⎜⎜

⎜

⎝

⎛ +

=

−

∑

1 t , p

i

* t

, p t

,

p NAV

D NAV

ln

r ⁱ [5.6]

where:

t ,

r = total return of fund p for the period t; p

i =1,…, n represents the number of fund’s distributions during period t;

74 The associations are: BVI for Germany, INVERCO for Spain, AUTIF for UK, AFG-ASFFI for France, and ASSOGESTIONI for Italy.

75 Blake, Elton and Gruber (1993) found a survivorship bias of 1,02% for a sample of US bond funds, over the period of 1979-1988, considering alpha estimates based on a six-index model. An even lower bias is reported for other markets. Dahlquist, Engström and Söderlind (2000) estimate a bias of only 0.10% (-0.09%) per year on Swedish bond funds over the period of 1993-1997 using average excess returns (or a conditional risk-adjusted performance measure).

t ,

NAV and p NAV_p,t−1 = net asset value of fund p at the end of period t and t-1, respectively;

i i , p t

, p

*

i (NAV /NAV )*D

D = = value of income distribution (D) paid per unit by fund p at time i reinvested at the NAV up to the end of period t. _p,i

In order to obtain excess returns the risk free rate is subtracted from this return.

The risk free rate is proxied by the 3-month Interbank offered rate⁷⁶.

Due to the different taxation principles, mentioned in Chapter 2, the comparison of bond fund performance, across the different countries that constitute our sample, must be done with caution. In particular, for Italian bond funds, it should be pointed out that since June 1998 the NAV is reported after-tax. Also, in some countries, the interest received by the bond funds are on a net basis (as it is the case for Portuguese and UK bond funds), thus having impact on the reported NAV used to calculate fund returns.

76 Alternatively, we also used the 1-month Euro rate for each country, and the results were similar.

Table 5.1 – Summary statistics for equally-weighted portfolios of bond funds

Bond funds are grouped according to the classification used by the domestic associations (BVI, Assogestioni, Autif, APFIN, AFG-ASFFI and Inverco) and also by Micropal. For Germany there are bond funds that invest mainly in Euro securities (Renten Euro), bond funds that invest mainly in European securities (Renten Europa), bond funds that invest mainly in short term and near money market Euro securities (Renten kurz.) and bond funds investing in Euro securities, funds with limitation of duration (Renten IZB). Italian funds are grouped as follows: bond funds that invest in Euro short-term securities (Short-term Euro), bond funds that invest in medium and long-term Euro securities (M/L Euro) and bond fund that invest in European securities (Europa). In the UK there are “Gilt” funds that invest mainly in UK Government securities, “Corporate” bond funds that invest mainly in investment grade securities (BBB rated or above) and UK “Other Bond” funds that invest at least 20% in non-investment grade securities (below BBB). In the case of Portugal there are two types of funds: funds that invest mainly in fixed-rate Euro securities and funds that invest in floating rate Euro securities. For France there are bond funds investing in Euro securities: short term bonds (Obbl.Euro CT), medium term bonds (Obbl.Euro MT) and long-term bonds (Obbl.Euro LT) and also bond funds investing in the European market. For Spain we have bond funds that invest mainly in short term Euro securities (RentaFija CP Euro) and bond funds that invest mainly in long-term Euro securities (RentaFija Euro). Average size in million Euros and management fees in annual percentage of assets invested as of 31/12/00. Mean excess returns and standard deviations are statistics for the period February 1994 to December 2000.

*** Statistically significant at 1% ** Statistically significant at 5% * Statistically significant at 10%

(1) The average size for France includes mainly French SICAVs as we could not obtain the information on the majority of the French FCPs that compose our sample.

(2) The management fees are average fees for the categories of Italian funds as reported by Assogestioni.

Nº. of Average Size Management Mean Excess Return St. Deviation Funds (Millions Euro) Fees (annual %) (Monthly %)

Germany

Renten Euro 59 209 0.46 0.118 0.887

Renten Europa 14 518 0.56 0.198 1.276

Renten Kurz. 11 288 0.44 0.042 0.402

Renten IZB 6 463 0.36 0.013 0.492

All Funds 90 284 0.46 0.115 0.833

France ⁽¹⁾

Obl.Euro CT 60 136 0.99 -0.019 0.337

Obl.Euro MT 83 273 1.11 0.013 0.715

Obl.Euro LT 114 222 0.99 0.067 1.062

Obl.Europe 9 95 0.85 0.047 1.125

All Funds 266 128 1.01 0.030 0.776

UK Gilt 26 65 0.92 -0.059 1.558

Corporate 13 409 0.92 -0.012 1.462

Other Bond 6 459 1.20 0.142 1.522

All Funds 45 236 0.95 -0.019 1.437

Spain

RentaFija CP Euro 108 87 1.38 -0.125^*** 0.373

RentaFija Euro 49 117 1.41 -0.047 0.639

All Funds 157 96 1.39 -0.101** 0.454

Italy ⁽²⁾

Short-Term Euro 26 960 0.82 -0.151*** 0.387

M/L Euro 25 1157 1.03 -0.106 0.786

Europa 7 505 1.10 -0.125 0.776

All Funds 58 990 0.98 -0.129** 0.586

Portugal

Euro Fixed Rate 6 80 0.79 0.033 0.621

Euro Floating Rate 16 188 0.43 -0.114^*** 0.062

All Funds 22 159 0.53 -0.074^*** 0.194

All Sample 638

Table 5.1 above presents the summary statistics and main characteristics of our European bond fund sample. The average of monthly excess returns is positive for all types of bond funds in Germany, for almost all in France (the exception is “Obl.Euro CT”) and for the funds classified as “Other Bond” funds in the UK (respectively 0.12 and 0.03 percent considering all the funds and 0.14 percent). However, none of these positive excess returns are statistically significant. In all other countries, bond funds present negative mean excess returns and most are statistically significant (particularly for short-term bond funds). Italian and Spanish bond funds present the most negative mean excess returns: –0.13 and –0.10 percent, respectively. With respect to the variability of the monthly excess returns, UK bond funds present clearly the highest standard deviation.

As it can be observed, the average bond fund size is highest in Italy, with a value of about 990 million Euros, and far distant from that of the other countries. At the bottom we have Spain with an average bond fund size of about 96 million Euros. With respect to management fees, the countries with the lowest average fees are Germany and Portugal, deducting about 0.5 percent annually. This value rises to almost 1 percent for bond funds in Italy, UK and France and to about 1.4 percent for Spanish bond funds.

In Appendix 5.2 we present the main statistics for each individual fund. One can see that for a large number of funds we do not reject, at the 5 percent level, the hypothesis of a normal distribution (372 funds, which represent 58 percent of our sample). Although it is commonly advocated that, given the dynamics of the term structure of interest rates and the finite live of bonds, bonds often exhibit non-normal and autocorrelated returns, this does not seem to be an obvious problem in our sample.