Conditional market-timing models for mutual fund performance

(1)

Joanna Olbryś

Conditional market-timing models for mutual fund

per-formance evaluation

1

Introduction

Performance evaluation of investment managers is a topic of considerable interest to practitioners and academics alike. Superior performance may be achieved through timing (macro-forecasting) and security selection (micro-forecasting) skills of portfolio managers. Fama suggested that a manager’s fore-casting ability could be split into two separate activities [Fama, 1972]:

– microforecasting, – macroforecasting.

Some researchers have developed models that allow the decomposition of man-ager performance into market-timing and selectivity skills.This began with the work of Treynor and Mazuy [Treynor, Mazuy, 1966] and since then numerous econometric techniques have been applied to this area ([Henriksson, Merton, 1981], [Jensen, 1968], [Henriksson, 1984], [Romacho, Cortez, 2006], [Ferson, Schadt, 1996], [Ferson, Harvey, 1999]).

The main goal of this paper is a performance evaluation using uncondi-tional and condiuncondi-tional models of timing and selectivity. We compare two meth-ods: the unconditional Treynor & Mazuy (T-M) model [Treynor, Mazuy, 1966] and the statistical procedure based on the Ferson & Schadt (F-S) conditional model [Ferson, Schadt, 1996]. The market-timing and selectivity abilities of 15 equity open-end mutual funds have been evaluated for the period January 2003 – April 2009. For comparison, a bear market period from July 4, 2007 to Feb 17, 2009 has been investigated. The overall index of Warsaw Stock Exchange companies (WIG index) fell from 66951.73 (July 4, 2007) to 21274.28 (Feb 17, 2009). It lost 68.22% during this period.

1. Unconditional and conditional models of timing and selectivity

The traditional performance measurement literature has attempted to distin-guish security selection, or stock-picking ability, from market-timing, or the ability to predict overall market returns. However, the literature finds that it is not easy to separate ability into two such dichotomous categories. Traditional unconditional T-M [Treynor, Mazuy, 1966] or H-M [Henriksson, Merton, 1981] models, in addition to their strong assumptions about how managers use their abilities, have taken the view that any information correlated with future market returns is superior information [Ferson, Schadt, 1996, p. 434]. Conditional models of timing and selectivity assume a semi-strong form of market

*

dr, Wydział Informatyki, Politechnika Białostocka, j.olbrys@pb.edu.pl

1

(2)

ciency. The idea is to distinguish “market-timing” based on public information from market-timing information that is superior to the lagged information vari-ables (the F-S model [Ferson, Schadt, 1996] or the F-H model [Ferson, Harvey, 1999]).

1.1. The Treynor-Mazuy (T-M) unconditional model

A classic unconditional market-timing model is the quadratic regression of Treynor and Mazuy (T-M model) [Treynor, Mazuy, 1966]:



Mt



Pt P t M P P t P r r r _,    _,   _, 2  _, (1) where: t F t P t P R R

r _,  _,  _, is the excess return on the portfolio P in period t,

t F t M t M R R

r _,  _,  _, is the excess return on market portfolio M in period t,

t P

R _, is the one-period return on the portfolio P,

t M

R _, is the one-period return on the market portfolio M ,

t F

R _, is the one-period return on riskless securities,

P

 measures selectivity skills of the portfolio’s P manager,

P

 is the systematic risk of the portfolio P,

P

 measures market-timing skills of the portfolio’s P manager,

t P,

 is a residual term, with the following standard CAPM conditions:



_P_,_t



0;E



_P_,_t _P_,_t_₁



0;

E  

If the portfolio manager has the ability to forecast security prices, the in-tercept _P in equation (1) will be positive. On one hand, a passive strategy (random buy-and-hold policy) can be expected to yield a zero intercept. On the other hand, if the manager is doing worse than a random selection buy-and-hold policy, _P will be negative.

If a mutual fund manager increases (decreases) the market exposure of the portfolio prior to a market increase (decrease) then the portfolio return will be a convex function of the market return and _P will be positive. The size of the estimate ˆ informs about the manager’s market skills. _P

Empirical results obtained using the T-M technique do not support the hy-pothesis that mutual fund managers are able to follow an investment strategy that successfully times the return on the market portfolio. The results show neu-tral or negative performance for mutual fund managers for the period January 2003 – January 2008 in the case of 15 Polish equity open-end mutual funds [Olbryś, 2008a]. In general, the fact that Polish managers are not really success-ful as market timers is consistent with most of the literature on mutual fund per-formance ([Henriksson, 1984], [Fletcher, 1995], [Kao, Cheng, Chan, 1998], [Romacho, Cortez, 2006]).

(3)

Conditional market-timing models for mutual fund performance evaluation

1.2. The Ferson – Schadt (F-S) conditional model

Ferson and Schadt derive a conditional version of the Treynor-Mazuy model [Ferson, Schadt, 1996, p 435]:



t Mt



P



Mt



Pt P t M P P t P r z r r r _,    _, '  _₁ _,   _, 2  _, (2) where: t P

r _, is the excess return on the portfolio P in period t,

t M

r _, is the excess return on market portfolio M in period t,

P

 measures selectivity skills of the portfolio’s P manager,

P

 is the systematic risk of the portfolio P,

P

 is the coefficient vector that captures the response of the manager’s beta to the public information Z_t_₁,

1  t

Z is a vector of lagged instrumental variables for the information available at time t1,

 

Z E Z

z_t_₁  _t_₁ is a vector of the deviations of Z_t_₁ from the unconditional means,

P

 is the coefficient that measures the sensitivity of the manager’s beta to the private market-timing signal,

t P,

 is a residual term, with the following standard CAPM conditions:



_P_,_t



0;E



_P_,_t, _P_,_t_₁



0;

E  

The regression (2) may also be interpreted as an unconditional multiple factor model, where the market index is the first factor and the product of the market and the lagged information variables are additional factors. _P is a vec-tor with dimension equal to the dimension of Z_t_₁. The elements of _P are the response coefficients of the conditional beta with respect to the information variables Z_t_₁. The term '_P



z_t_₁r_M_,_t



in equation (2) controls for the public information effect, which would bias the coefficients in the original T-M model (1). The new term in the model (2) captures the part of the quadratic term in the T-M model (1) that is attributed to the public information variables. In the con-ditional model, the correlation of mutual fund betas with the future market turn, which can be attributed to the public information, is not considered to re-flect market-timing ability [Ferson, Schadt, 1996, p 435].

2.

The dataset

We have studied monthly ordinary excess returns for 15 selected open-end equity mutual funds from January 2003 to April 2009 (75 observations). As in the previous studies that used monthly data, we have implicitly assumed that the investors evaluate risk and return, and that mutual fund managers trade using a one-month horizon. Table 1 records the names of the funds, along with sum-mary statistics for the Jan 2003-Apr 2009 period.

(4)

Table 1. Summary statistics for funds’ excess returns from Jan 2003 to Apr 2009

Equity Funds Mean

[%] Standard Deviation [%] Minimum [%] Maximum [%] 1 Arka BZ WBK Akcji FIO 1.10 7.32 -26.88 19.90 2 BPH FIO Akcji 0.46 6.24 -19.47 15.61 3 Aviva Investors FIO Polskich Akcji 0.83 6.97 -24.78 17.31 4 DWS Polska FIO Top 25 Małych

Spółek 0.22 7.33 -23.11 13.79

5 DWS Polska FIO Akcji 0.24 6.33 -24.40 15.81 6 DWS Polska FIO Akcji Plus 0.41 6.33 -23.17 15.40 7 ING FIO Akcji 0.48 6.51 -20.09 17.76 8 Legg Mason Akcji FIO 0.80 6.45 -23.70 14.51 9 Millennium FIO Akcji 0.28 6.16 -21.89 15.46 10 Pioneer Akcji Polskich FIO 0.25 7.61 -27.05 22.35 11 PKO/CREDIT SUISSE Akcji FIO 0.18 6.64 -27.21 14.47 12 PZU FIO Akcji KRAKOWIAK 0.27 6.20 -22.51 15.65 13 SEB 3 – Akcji FIO 0.42 6.63 -25.29 20.20 14 Skarbiec – Akcja FIO 0.79 5.98 -20.75 15.61 15 UniKorona Akcja FIO 0.75 6.31 -19.84 16.58 Income Group Average 0.50 6.60 -23.34 16.69 Source: author’s calculations

The monthly returns on the index of Warsaw Stock Exchange companies (WIG) are used as the returns on the market portfolio. The returns were ob-tained from www.bossa.pl . The monthly average of returns on 52-week Treas-ury bills are used as the riskless asset.

2.1. The predetermined information variables

Ferson and Schadt use a collection of public information variables that previous studies have shown are useful for predicting security returns and risks over time. The variables are: (1) the lagged level of the one-month Treasury bill yield, (2) the lagged dividend yield of the CRSP value-weighted NYSE and AMEX stock index, (3) a lagged measure of the slope of the term structure, and (4) a lagged quality spread in the corporate bond market [Ferson, Schadt, 1996, p 437]. In Poland, the suitable variables are:

1) Z₁_,_t_₁ - the lagged monthly dividend yield of the WSE stock index (WIG), 2) Z₂_,_t_₁ - the lagged monthly level of the 1M WIBOR,

3) Z₃_,_t_₁ - the lagged monthly measure of the slope of the term structure; the term spread is a difference between the average of 2-year Treasury bond yield and the average of 10-year Treasury bond yield.

We assume that the lagged variables are readily available, public information over our entire sample period.

Table 2 presents summary statistics for the lagged information variables. Note that all variables demonstrate high values of variation coefficients.

(5)

Variable Mean Standard Deviation Variation Coefficient Minimum Maximum 1 1 , 1t Z 2.49% 1.07% 42.89% 1.16% 5.83% 2 1 , 2t Z 0.44% 0.07% 16.99% 0.31% 0.56% 3 1 , 3t Z 0.014% 0.043% 319.88% -0.09% 0.09%

Source: author’s calculations

Figure 1. The lagged monthly dividend yield of the WSE stock index (WIG) from Jan 2003 to Apr 2009

Figure 2. The lagged monthly level of the 1M WIBOR from Jan 2003 to Apr 2009

(6)

Figure 3. The lagged monthly measure of the slope of the term structure from Jan 2003 to Apr 2009

In fact, the additional exogenous variables used in the conditional model (2) are:

 z₁_,_t_₁r_M_,_t 



Z₁_,_t_₁E

 

Z₁



r_M_,_t,  z₂_,_t_₁r_M_,_t 



Z₂_,_t_₁E

 

Z₂



r_M_,_t,  z₃_,_t_₁r_M_,_t 



Z₃_,_t_₁E

 

Z₃



r_M_,_t.

Fig. 4, Fig. 5 and Fig.6 present this data in the form of charts, respectively. We have detected (based on Dickey – Fuller test) that the analysed series are sta-tionary.

(7)

Figure 5. The lagged exogenous variable z2,t1rM,t from Jan 2003 to Apr 2009

(8)

3.

Empirical results

Table 3 presents the results of the OLS estimates for the T-M parametric tests. The DW-statistic values indicate that we have encountered some autocor-relation problems. Autocorrelated disturbances are present in the case of the following funds: BPH FIO Akcji, Aviva Investors FIO Polskich Akcji, DWS Polska FIO Top 25 Małych Spółek and Skarbiec – Akcja FIO. The critical val-ues of the DW-test are:

d

_L



1

.

571

,

d

_U



1

.

680

.To detect for heteroskedastic-ity we have used White’s test. The results show that the residuals are het-eroskedastic only in the case of SEB 3 Akcji FIO. The LM-statistic of this fund

67 . 33



LM is higher than the critical value



_*2



11

.

07

.

Table 3. Unconditional T-M model (1) (period from Jan 2003 to Apr 2009) Equity Funds

P ˆ

P

ˆ ˆP R2 DW LM AIC

1 Arka BZ WBK Akcji FIO 0.006* 0.943* -0.460 0.929 2.03 1.57 -373.3 2 BPH FIO Akcji -0.0003 0.815* -0.314 0.949 1.63 10.21 -421.5 3 Aviva Investors FIO

Pol-skich Akcji 0.004* 0.908* -0.614* 0.957 1.44 0.70 -417.6 4 DWS Polska FIO Top 25

Małych Spółek -0.002 0.850* -0.508 0.756 1.29 3.25 -279.9 5 DWS Polska FIO Akcji -0.001 0.820* -0.613* 0.950 2.32 2.45 -420.4 6 DWS Polska FIO Akcji

Plus 0.0005 0.814* -0.557* 0.935 1.87 3.63 -401.6 7 ING FIO Akcji -0.003 0.859* 0.145 0.954 2.10 4.41 -422.8 8 Legg Mason Akcji FIO 0.005* 0.830* -0.679* 0.941 1.72 7.78 -405.4 9 Millennium FIO Akcji -0.0013 0.788* -0.428 0.917 1.98 1.83 -386.6 10 Pioneer Akcji Polskich -0.005* 1.005* -0.074 0.962 2.13 7.31 -412.9

(9)

FIO

11 PKO/CREDIT SUISSE

Akcji FIO -0.0007 0.856* -0.822* 0.952 1.81 4.39 -417.0 12 PZU FIO Akcji

KRAKO-WIAK -0.0007 0.799* -0.577* 0.941 1.75 4.87 -412.0 13 SEB 3 – Akcji FIO -0.0002 0.861* -0.475* 0.946 2.42 33.67 -408.1 14 Skarbiec – Akcja FIO 0.0037 0.766* -0.367 0.918 2.53 4.60 -391.8 15 UniKorona Akcja FIO 0.0015 0.827* -0.136 0.951 2.31 3.08 -422.2

*Significant at 5%

Source: author’s calculations (using Gretl)

The new, improved models have been estimated using the Cochrane – Or-cutt procedure [Osińska, 2005], [Kufel, 2004]. The new model for SEB 3 Akcji FIO has been evaluated using the WLS procedure [Kufel, 2004, p.121] to re-ceive heteroskedasticity – corrected estimates. We have tested the normality of the residuals in this case. Table 4 presents final results of the T-M parametric tests.

The evidence is that all of the funds present significant estimates of the sys-tematic risk (ˆ ) at 5% level. Almost every coefficient (except for that of Pio-_P

neer Akcji Polskich FIO) lies between 0 and 1. The mean estimate of this coef-ficient is 0.835. During the period investigated, the mean value of R-squared was quite high: 0.934. Table 4 provides the evidence of negative market-timing (ˆ_P 0). The mean value of this coefficient is –0.426.

The empirical results show no statistical evidence that Polish equity funds’ managers have outguessed the market. We have also observed that only three funds present significantly positive estimates of selectivity (ˆ_P 0).The mean value of this coefficient is 0.001.

Table 4. Unconditional T-M model (1); heteroskedasticity- and autocorrelation-corrected estimates using the observations from the period Jan 2003 - Apr 2009

Equity Funds

P ˆ

P

ˆ ˆP R2 1 Arka BZ WBK Akcji FIO 0.006* 0.943* -0.460 0.929 2 BPH FIO Akcji -0.0004 0.811* -0.288 0.951 3 Aviva Investors FIO Polskich Akcji 0.004 0.886* -0.632* 0.961 4 DWS Polska FIO Top 25 Małych Spółek -0.0001 0.693* -0.483 0.809 5 DWS Polska FIO Akcji -0.001 0.820* -0.613* 0.950 6 DWS Polska FIO Akcji Plus 0.0005 0.814* -0.557* 0.935 7 ING FIO Akcji -0.003 0.859* 0.145 0.954 8 Legg Mason Akcji FIO 0.005* 0.830* -0.679* 0.941 9 Millennium FIO Akcji -0.0013 0.788* -0.428 0.917 10 Pioneer Akcji Polskich FIO -0.005* 1.005* -0.074 0.962 11 PKO/CREDIT SUISSE Akcji FIO -0.0007 0.856* -0.822* 0.952 12 PZU FIO Akcji KRAKOWIAK -0.0007 0.799* -0.577* 0.941 13 SEB 3 – Akcji FIO 0.0006 0.817* -0.402 0.931 14 Skarbiec – Akcja FIO 0.004* 0.777* -0.378 0.925 15 UniKorona Akcja FIO 0.0015 0.827* -0.136 0.951 The Group Average 0.001 0.835 -0.426 0.934

(10)

Table 5 presents summary results received based on the conditional model (2). The elements of '_P 



₁_P ₂_P ₃_P



are the response coefficients of the conditional beta with respect to the lagged regressors: X₁z₁_,_t_₁r_M_,_t,

t M t r

z

X₂  ₂_,_₁ _, , X₃ z₃_,_t_₁r_M_,_t.

Table 5. Conditional F-S model (2); heteroskedasticity- and autocorrelation-corrected estimates using the observations from the period Jan 2003 - Apr 2009

Equity Funds ˆ_P P ˆ ˆ₁_P ˆ₂_P ˆ₃_P ˆP R2 DW AIC (OLS) 1 Arka BZ WBK Akcji FIO 0.006* 0.940* 1.770 48.71 -61.11 -0.223 0.931 2.16 -369.4 2 BPH FIO Akcji 0.0001 0.791* 1.442 -89,6 5.563 -0.621* 0.957 1.98 -426.4 3 Aviva Investors FIO Polskich Akcji 0.005 0.861* 1.367 -87.7* 1.010 -0.942* 0.966 2.16 -418.5 4 DWS Polska FIO Top 25 Małych Spółek 0.001 0.648* -0.932 -108.5 156.5 -1.014* 0.821 2.39 -274.6 5 DWS Polska FIO Akcji -0.0005 0.798* 3.258 -3.24 -86.05 -0.557* 0.956 2.02 -421.2 6 DWS Polska

FIO Akcji Plus 0.001 0.792* 3.060 -38.75 -13.19 -0.700* 0.939 1.90 -400.5 7 ING FIO Akcji -0.003 0.861* -1.094 -24.56 33.89 0.023 0.955 2.13 -418.0 8 Legg Mason Akcji FIO 0.006* 0.805* 1.887 -99.43 96.87 -1.160* 0.952 1.83 -414.5 9 Millennium FIO Akcji -0.001 0.795* -2.250 -62.31 -121.2 -0.507 0.918 2.04 -382.0 10 Pioneer Akcji Polskich FIO -0.005* 0.957* 12.64* 161.9* 187.6* 0.328* 0.977 1.98 -442.5 11 PKO/CREDIT SUISSE Akcji FIO -0.0004 0.831* 7.241* 136.7* 29.94 -0.396 0.961 1.89 -425.9

12 PZU FIO Akcji

KRAKOWIAK -0.0002 0.780* 2.440 -41.14 -16.29 -0.721* 0.945 1.77 -410.4 13 SEB 3 Akcji FIO -0.0001 0.839* 6.311* -18.42 -60.59 -0.413* 0.964 2.02 -425.9 14 Skarbiec Akcja FIO 0.004* 0.776* -0.344 -34.51 -98.61 -0.373 0.926 2.04 -386.9 15 UniKorona Akcja FIO 0.001 0.856* -2.532 -22.77 -8.81 -0.202 0.955 2.06 -416.5 The Group Average 0.001 0.822 2.284 -18.90 3.04 -0.490 0.942 - - *Significant at 5%

The evidence regarding the mean value of R-squared is similar to that from the model (1) in Table 4. During the period investigated, the mean value of the R-squared was slightly higher and equal to 0.942. All of the funds present

(11)

sig-Conditional market-timing models for mutual fund performance evaluation nificant estimates of the systematic risk (ˆ ) at 5% level. Each coefficient lies _P

between 0 and 1. The mean value of this coefficient is equal to 0.822.

We have used Cochrane – Orcutt procedure to correct autocorrelated error terms in the case of eight funds, and Table 5 reports final empirical results from the conditional F-S models. To detect for heteroskedasticity we have used White’s test. Although not reported in the paper, the results show that for all of the funds the LM-statistics have been lower than the critical value



_*2



21

.

03

, so we have no grounds for rejecting the null hypothesis that the residuals are homoskedastic.

Additionally, we have used the VIF test to detect for multicollinearity. The major undesirable consequence of multicollinearity is that the variances of the OLS estimates of the parameters of the collinear variables are quite large. The inverse of the correlation matrix is used in detecting for multicollinearity. The diagonal elements of this matrix are called variance inflation factors

VIF

_i. One interpretation is that it is a measure of the amount by which the variance of the ith coefficient estimate is increased (relative to no collinearity) due to its linear association with the other explanatory variables. As a rule of thumb, for standardized data, a

VIF

_i



10

indicates harmful collinearity. In the investigat-ed sample of equity funds’ F-S models, no multicollinearity has been found.

For selected equity funds, the factors X₁ z₁_,_t_₁r_M_,_t, X₂ z₂_,_t_₁r_M_,_t and X₃ z₃_,_t_₁r_M_,_t included in equation (2), do not seem to have an important role in explaning mutual fund excess returns. In fact, only one fund (Pioneer Akcji Polskich FIO) exhibits significant estimates of ˆ₁_P,ˆ₂_P,ˆ₃_P coeffi-cients. We have used Akaike Information Criterion (AIC) to compare T-M models (see Table 3) and F-S models (see Table 5). Lower values of the AIC index indicate the preferred model, that is, the one with the fewest parameters that still provides an adequate fit to the data. The evidence is that only in the case of seven funds, the regressors addition caused a little decrease in the AIC index. To sum up, the lagged variables Z₁_,_t_₁,Z₂_,_t_₁,Z₃_,_t_₁ are not very useful for improving the quality of the market-timing models for Polish equity open-end mutual funds.

4.

Empirical results in a bear market period

The period from July 4, 2007 to Feb 17, 2009 was a bear market period. The overall WIG index fell from 66951.73 (July 4, 2007) to 21274.28 (Feb 17, 2009). It lost 68.22% during this period (Fig. 7). We have studied monthly ordi-nary excess returns for 15 selected open-end equity mutual funds in this period (20 observations).

(12)

Table 6 reports final empirical results of the unconditional T-M tests in the bear market period. Although not reported in the paper, the values of DW-statistic show evidence that residuals are autocorrelated in the case of five funds: Arka BZ WBK Akcji FIO, BPH FIO Akcji, DWS Polska FIO Akcji, PZU FIO Akcji KRAKOWIAK and SEB 3 – Akcji FIO. To detect for het-eroskedasticity we have used White’s test. The results have shown that the re-siduals are heteroskedastic in the case of BPH FIO Akcji and Millennium FIO Akcji. Hence, we have used the Cochrane – Orcutt procedure to correct autorelated error terms and the WLS procedure to receive heteroskedasticity – cor-rected estimates. We tested the normality of the residuals in this case.

Table 6 provides the evidence of negative, but not significant market-timing (ˆ_P 0), in the case of 14 funds (except BPH FIO Akcji). The mean value of this coefficient is -0.361. All of the funds present significant estimates of the systematic risk (ˆ ) at 5% level. The mean estimate of this coefficient is _P

0.843 and it is almost equal to this in Table 4. Note that the poor quality of the models can be attributed to small sample size.

Table 6. Unconditional T-M model (1) in a bear market period from July 2007 to Feb 2009

Equity Funds ˆ_P

P

ˆ ˆP R2 1 Arka BZ WBK Akcji FIO 0.006 0.911* -1.310 0.942 2 BPH FIO Akcji -0.004* 0.955* 0.740* 0.982 3 Aviva Investors FIO Polskich Akcji -0.003 0.986* -0.107 0.987 4 DWS Polska FIO Top 25 Małych Spółek -0.036* 0.694* -0.479 0.765 5 DWS Polska FIO Akcji 0.006 0.972* -0.289 0.953 6 DWS Polska FIO Akcji Plus -0.008* 0.828* -0.393 0.950 7 ING FIO Akcji -0.014* 0.629* -0.724 0.943 8 Legg Mason Akcji FIO 0.005 0.857* -0.545 0.965

(13)

9 Millennium FIO Akcji -0.007* 0.848* -0.056 0.998 10 Pioneer Akcji Polskich FIO -0.008* 1.053* -0.067 0.977 11 PKO/CREDIT SUISSE Akcji FIO -0.007 0.851* -0.931 0.954 12 PZU FIO Akcji KRAKOWIAK -0.005* 0.878* -0.107 0.984 13 SEB 3 – Akcji FIO -0.005 0.786* -0.930 0.965 14 Skarbiec – Akcja FIO -0.0015 0.710* -0.621 0.874 15 UniKorona Akcja FIO -0.002 0.864* 0.123 0.959 The Group Average -0.004 0.843 -0.361 0.957 *Significant at 5%

Conditional F-S models (2) have not been estimated in the bear market pe-riod from July 2007 to Feb 2009 because of their low quality (see Table 5) and small sample size. Misspecifying the timing function may cause violations of regression assumptions in unknown and possibly time-varying ways, so that standard corrections for heteroskedasticity and serial correlation may not fully capture the effect of these violations on the standard errors of regression coeffi-cients. Such models may generate false evidence of market-timing abilities.

Conclusion

In this paper we have examined the usefulness of the unconditional T-M and the conditional F-S models for the investment managers’ performance evaluation. While Ferson’s and Schadt’s empirical investigations of conditional market-timing models are adequate to illustrate that the use of conditioning in-formation is important, they do not advocate using them to evaluate managers in practice [Ferson, Schadt, 1996, p.453]. The evidence on Polish market shows that the quality of the conditional models is rather low (Table 5). Probably the selected lagged variables are not very appropriate for timing and selectivity modelling and it seems to be the main reason why these models are not better in comparison with the unconditional versions.

References

1. Admati A., Bhattacharya S., Pfleiderer P., Ross S., (1986), On timing and selectivity, “The Journal of Finance”, 41 (July), pp. 715-730.

2. Becker C., Ferson W.E., Myers D., Schill M. (1999), Conditional market timing with benchmark investors, “Journal of Financial Economics”, 52, pp. 119-148.

3. Bollen N. P. B., Busse J. A. (2001), On the timing ability of mutual fund managers, “The Journal of Finance”, Vol. LVI, No. 3, pp. 1075-1094. 4. Brown S.J., Goetzmann W.N. (1995), Performance persistence, “Journal of

Finance”, 50, pp. 679-698.

5. Chang E., Lewellen W. (1984), Market timing and mutual fund investment performance, “Journal of Business”, 57, pp. 57 - 72.

6. Chen C.R., Stockum S. (1986), Selectivity, market timing and random beta behaviour of mutual funds: a generalized model, “The Journal of Financial Research”, Vol. IX, No. 1, Spring 1986.

(14)

7. Cheng-few Lee, Rahman S. (1990), Market timing, selectivity, and mutual fund performance: an empirical investigation, “Journal of Business”, 63, No. 2, pp. 261-276.

8. Czekaj J., Woś M., Żarnowski J. (2001) Efektywność giełdowego rynku akcji w Polsce, PWN, Warszawa.

9. Fama E., (1972), Components of investment performance, “The Journal of Finance”, 27, No. 2, pp. 551-567.

10. Ferson W.E., Harvey C.R. (1999), Conditioning variables and the cross section of stock returns, “The Journal of Finance”, 54 (August), pp.1325-1360.

11. Ferson W.E., Schadt R.W. (1996), Measuring fund strategy and perform-ance in changing economic conditions, “The Journal of Finperform-ance”, 51 (June), pp.425-461.

12. Fletcher J. (1995), An examination of the selectivity and market timing per-formance of UK unit trusts, “Journal of Business Finance & Accounting”, 22, pp. 143 - 156.

13. Grinblatt M., Titman S. (1994), A study of monthly mutual fund returns and performance evaluation techniques, “Journal of Financial and Quantitative Analysis”, 29, pp. 419-444.

14. Henriksson R., Merton R. (1981), On market timing and investment per-formance. II. Statistical procedures for evaluating forecasting skills, “Jour-nal of Business”, 54, No. 4, pp. 513-533.

15. Henriksson R. (1984), Market timing and mutual fund performance: an em-pirical investigation, “Journal of Business”, 57, pp. 73-96.

16. Jensen M. (1968), The performance of mutual funds in the period 1945-1964, “Journal of Finance”, 23, pp 389-416.

17. Kao G., Cheng L., Chan K. (1998), International mutual fund selectivity and market timing during up and down market conditions, “The Financial Review”, 33, pp. 127 - 144.

18. Kufel T. (2004), Ekonometria. Rozwiązywanie problemów z wykorzysta-niem programu Gretl, PWN, Warszawa.

19. Lehmann B., Modest D.M. (1987), Mutual fund performance evaluation: A comparison of benchmarks and benchmark comparisons, “Journal of Fi-nance”, 42 (June), pp 233-265.

20. Maddala G.S. (2008) Ekonometria, PWN, Warszawa.

21. Merton R. (1981), On market timing and investment performance. I. An equilibrium theory of value for market forecasts, “Journal of Business”, 54, No. 3, pp. 363-406.

22. Olbryś J. (2008a), Parametric tests for timing and selectivity in Polish mu-tual fund performance, „Optimum. Studia Ekonomiczne”, Wydawnictwo Uniwersytetu w Białymstoku, 3(39)/2008, str. 107-118.

23. Olbryś J. (2008b), Parametryczne testy umiejętności wyczucia rynku – po-równanie wybranych metod na przykładzie OFI akcji, [w:] Z. Binderman

(15)

Conditional market-timing models for mutual fund performance evaluation (red.) Metody ilościowe w badaniach ekonomicznych IX, Wydawnictwo SGGW w Warszawie, Warszawa, str. 81-88

24. Olbryś J. (2008c), Ocena umiejętności stosowania strategii market-timing przez zarządzających portfelami funduszy inwestycyjnych a częstotliwość danych, Studia i Prace Wydziału Nauk Ekonomicznych i Zarządzania Nr 10, Uniwersytet Szczeciński, Szczecin, str. 96-105.

25. Olbryś J., Karpio A. (2009), Market-timing and selectivity abilities of Pol-ish open-end mutual funds managers, [w:] P.Chrzan, T.Czernik (red.) „Me-tody matematyczne, ekonometryczne i komputerowe w finansach i ubezpie-czeniach 2007, Wydawnictwo AE im. K. Adamieckiego w Katowicach, str.437-443.

26. Osińska M. (2006) Ekonometria finansowa, PWE, Warszawa.

27. Osińska M. (red.) (2005) Wybrane zagadnienia z ekonometrii, Wydawnic-two WSIiE TWP w Olsztynie.

28. Prather L.J., Middleton K.L. (2006), Timing and selectivity of mutual fund managers: An empirical test of the behavioral decision-making theory, “Journal of Empirical Finance”, 13, pp. 249-273.

29. Rao S. (2000), Market timing and mutual fund performance, “American Business Review”, 18, pp. 75 – 79.

30. Rao S. (2001), Mutual fund performance during up and down market condi-tions, “Review of Business”, 22, pp. 62 - 65.

31. Romacho J. C., Cortez M. C. (2006), Timing and selectivity in Portuguese mutual fund performance, “Research in International Business and Fi-nance”, 20, pp. 348-368.

32. Sharpe W. (1992), Asset allocation: Management style and performance measurement, “The Journal of Portfolio Management” Winter 1992, pp. 7-19.

33. Treynor J., Mazuy K. (1966), Can mutual funds outguess the market?, “Harvard Business Review”, 44, pp. 131-136.

Zastosowanie warunkowych modeli market-timing do oceny wyników fun-duszy inwestycyjnych

Streszczenie

Pierwszy parametryczny model market-timng (tzw. wyczucia rynku) zaproponowali w 1966 roku Treynor i Mazuy (model T-M). Technika market-timing zarządzania portfe-lem polega na wyborze momentu dokonania inwestycji oraz czasu jej trwania w oparciu o krótkoterminowe oczekiwania cenowe, na podstawie obserwacji całego rynku (prze-widywanie w skali makro). W odpowiedzi na zapotrzebowanie praktyków pojawiły się w literaturze przedmiotu modele wspomagające ocenę jakości zarządzania portfelem pod kątem analizy umiejętności w zakresie stosowania technik market-timing. Celem artykułu jest porównawcza analiza empiryczna umiejętności wyczucia rynku przez za-rządzających portfelami OFI akcji z wykorzystaniem parametrycznego modelu T-M oraz warunkowego modelu F-S Ferson’a i Schadt’a (1996). Badaniem objęto grupę 15 funduszy akcji na rynku polskim w okresie styczeń 2003 – kwiecień 2009.

(16)

Conditional market-timing models for mutual fund performance evalua-tion

Performance evaluation of investment managers is a topic of considerable interest to practitioners and academics alike. Superior performance may be achieved through tim-ing (macro-forecasttim-ing) and security selection (micro-forecasttim-ing) skills of portfolio managers. The main goal of this paper is a performance evaluation using unconditional and conditional models of timing and selectivity. We compare two methods: the uncon-ditional Treynor & Mazuy (T-M) model [Treynor, Mazuy, 1966] and the statistical pro-cedure based on the Ferson & Schadt (F-S) conditional model [Ferson, Schadt, 1996]. The market-timing and selectivity abilities of 15 equity open-end mutual funds have been evaluated for the period January 2003 – April 2009.