Dmitrii V. Kandaurov
Influence of return and risk indicators on open-end mutual fund flows.
1) Introduction
As often mutual fund manager income depends on the value of assets under
management, manager primarily interested in fund growth. In order to attract individual
investors and their money managers try to offer them the most wanted product (portfolio with
optimal balance of risk and return).
There are two main directions in contemporary researches dedicated to the problem of
portfolio optimization: portfolio optimization based on the advanced modern portfolio theory
(e.g. Campbell, Huisman, Koedijk, 2001) or direct maximization of the utility function (e.g.
Lan, Wang, Yang, 2013). Thus, different risk measures, from variance to spectral and
coherent measures, are used in studies of both directions. Many researches confirm the
relatively high efficiency of value at risk, as well as coherent and spectral risk measures for a
portfolio optimization (e.g. Adam, Houkari, Laurent 2001; Alexander, Baptista, 2002).
The relationship between the inflow of funds for the performance and profitability and
risk fund was shown by many researchers. One of the first and most comprehensive studies in
this area is the paper of Chevalier and Ellison (1997). Authors confirm the non-linear nature
of the flow-performance relation. This nonlinearity creates risk incentives, which dispose
fund manager to actively operate risk.
In the paper of Sirri and Tufano ( 1998) asymmetric disposition of individual investors
to invest in funds, that very well performed previously explained by the existent of individual
investor’s "search costs", that are compensated by the successful fund manager in exchange
for the investments through the additional advertising.
In this paper, the character of the flow-performance relation for Russian open-end
mutual funds is studied. A model analogous to (Chevalier, Ellison, 1997) is used. We also
consider the flow-risk performance for different risk measures.
2) Flow-performance relation
a) Model
To analyze the flow-performance relationship for Russian open-end mutual funds two
different models for return and risk performance were considered. The first model (flowreturn model) is close to the semiparametric model, considered in (Chevalier, Ellison, 1997):
𝐹𝑙𝑜𝑤𝑖,𝑡+1 = ∑ 𝛾𝑘 𝐴𝑔𝑒𝑘𝑖𝑡 𝑓(𝑟𝑖𝑡 − 𝑟𝑚𝑡 ) + ∑ 𝛿𝑘 𝐴𝑔𝑒𝑘𝑖𝑡
𝑘
𝑘
+𝛼1 (𝑟𝑖,𝑡−1 − 𝑟𝑚,𝑡−1 ) + 𝛼2 (𝑟𝑖,𝑡+1 − 𝑟𝑚,𝑡+1 ) + 𝛼3 𝐼𝐺𝑡+1 + 𝛼4 𝑀𝑆𝑖,𝑡+1 , where
𝐹𝑙𝑜𝑤𝑖,𝑡+1 – net fund 𝑖 flow in period 𝑡 + 1,
(1)
𝑟𝑖,𝑡 – fund 𝑖 return in period 𝑡,
𝑟𝑚,𝑡 – broad-base index (micex) return in period 𝑡 ,
𝐼𝐺𝑡+1 – open-end mutual funds industry grow in period 𝑡 + 1,
𝑀𝑆𝑖,𝑡+1 – fund i market share in the beginning of period 𝑡 + 1,
𝐴𝑔𝑒𝑘𝑖,𝑡 - dummy variable, characterize age category of the fund.
𝐴𝑔𝑒𝑘𝑖,𝑡
1,
2,
={
3,
4,
𝑖𝑓 𝑓𝑢𝑛𝑑 𝑎𝑔𝑒 ≤ 2 𝑦𝑒𝑎𝑟𝑠
𝑖𝑓 4 ≥ 𝑓𝑢𝑛𝑑 𝑎𝑔𝑒 > 2 𝑦𝑒𝑎𝑟𝑠
𝑖𝑓 6 ≥ 𝑓𝑢𝑛𝑑 𝑎𝑔𝑒 > 4 𝑦𝑒𝑎𝑟𝑠
𝑖𝑓 𝑓𝑢𝑛𝑑𝑎𝑔𝑒 > 6 𝑦𝑒𝑎𝑟𝑠
Under the net fund flow we assume relative fund growth ratio, that is
𝐹𝑙𝑜𝑤𝑖,𝑡+1 =
𝑁𝐴𝑉𝑖,𝑡+1 −𝑁𝐴𝑉𝑖,𝑡
𝑁𝐴𝑉𝑖,𝑡
− 𝑟𝑖,𝑡+1 , here
𝑁𝐴𝑉 is net assets value.
The attractiveness of this model lies in the fact that the usage of the coefficients 𝛾𝑘 and
𝛿𝑘 allows us to compare the degree of the elasticity of the flow-performance relationship for
different fund age categories.
Estimation of the model (1) parameters is carried out in three stages.
On the first stage consistent estimates of 𝛼’s were obtained by nonparametric1
partialing-out procedure, described in (Robinson, 1988): obtaining residuals from
nonparametric regression of 𝐹𝑙𝑜𝑤𝑖,𝑡+1 and 𝑋𝑖,𝑡 on 𝑟𝑖,𝑡 − 𝑟𝑚𝑡 , then regress the residuals on the
residuals.
On the next stage 𝛾 and 𝛿 estimates were derived as follows. First of all nonparametric
estimation of the function 𝑔̂𝑘 = 𝛾𝑘 𝑓 + 𝛿𝑘 were obtained by kernel regression of 𝐹𝑙𝑜𝑤𝑖,𝑡+1 −
𝛼̂𝑋𝑖,𝑡 on 𝑟𝑖,𝑡 − 𝑟𝑚,𝑡 (𝑔̂0 obtained similar to 𝑔̂𝑘 when dummy variable is omitted).
Then 𝛾 and 𝛿 obtained by simple regression of 𝑔̂𝑘 on 𝑔̂0 .
On the last stage we obtain an estimate of 𝑓 by kernel2 regression of
𝐹𝑙𝑜𝑤𝑖,𝑡+1 − ∑𝑘 𝛿̂𝑘 𝐴𝑔𝑒𝑘𝑖,𝑡 − 𝛼̂𝑋
𝑦̂𝑡 ≡
1 + ∑𝑘 𝛾̂𝑘 𝐴𝑔𝑒𝑘𝑖,𝑡
on (𝑟𝑖,𝑡 − 𝑟𝑚,𝑡 ).
The second model used in this section simulates the relationship between risk and fund
flows in the future.
1
All nonparametric regressions computed with optimal bandwidth selection, described in Li and
Racine (2013)
2
Gaussian kernel was used in all nonparametric regressions.
𝐹𝑙𝑜𝑤𝑖,𝑡+1 = 𝛾∆𝑅𝑀𝑖,𝑡 + 𝛼1 𝑀𝐹𝑖 + 𝛼2 𝑀𝑆𝑖,𝑡+1 + 𝛿 , where
∆𝑅𝑀𝑖,𝑡 – fund 𝑖 relative risk measure change in period 𝑡,
𝑀𝐹𝑖 – fund 𝑖 management fee.
∆𝑅𝑀𝑖,𝑡 =
𝑅𝑀𝑖,𝑡 −𝑅𝑀𝑖,𝑡−1
𝑅𝑀𝑖,𝑡−1
(2)
, here
As risk measures (𝑅𝑀𝑖,𝑡 ) we consider empirical variance, semi-variance, value at risk
and expected shortfall. As the period for the assessment of risk, we chose a two-year interval
in order to obtain more robust estimates.
b) Data
The flow-return model is estimated on the set of 383 open-end mutual funds in the
period between 1999 and 2015. We use quarterly flow-return data. There are several “pro-s”
to use shorter time interval, than in (Chevalier, Ellison, 1997) 3. First, in Russia individual
investors, for the most part, oriented on the shorter investment horizon. Second, managers
respond to risk incentives more often than once a year.
Funds, oriented on institutional investor (fund with minimum initial purchase of
200 000 rubles), were excluded from the analytical set. Funds that merged with other funds
also were eliminated. Finally we obtain 4800 data points to estimate model (1).
The flow-risk model (2) was estimated on the same set of 383 open-end mutual funds.
As we need to estimate empirical risk measures (on 2 years intervals) in model 2, we consider
only funds of age 3 and greater. Therefore the amount of applicable data points is
substantially lower than for the first model (only 1 102 fund-years).
c) Results
Flow – return model is estimated separately for «young» (of age less 4 years) and
«old» (of age greater than 4 years) funds.
Figure 1 presents non-parametric regression results of function 𝑓 obtained from the
young funds and it’s 90% confidence bands.
It should be noted that flow-return relation on the 1st graph is normalized (it is cleared
from the effect of mutual fund industry growth, and other parameters under 𝛼 coefficients).
3
They use annual data.
Year t+1 net
flow
1
0.8
0.6
0.4
0.2
0
-0.4
-0.3
-0.2
-0.1 -0.2 0
-0.4
0.1
0.2
0.3
0.4
Year t excess return
-0.6
-0.8
-1
Figure 1 – Flow-performance relationship for funds of age<=2 𝑓̂ with 90% confidence
bands.
Graph on the figure 1 may be interpreted as presented the expected growth rate in year
𝑡 + 1 for young funds as a function of their excess return in year 𝑡. For example, such a fund
would be expected to grow by approximately 10 percent per quarter if it demonstrate no
exceed return. If it’s return exceed market by 10% expected growth rate is near 20%.
If we take a look on the left side of the 1st graph we will see that at extremely negative
returns fund contraction accelerated inversely large excess return lead to the acceleration of
fund inflows.
If in the last quarter excess return of the 2-year old fund was near 25% than manager
of the fund should slightly increase risk in the following quarter. In a good position fund will
receive extra inflow, in the bad situation the inflow rate will not change substantially.
Fund manager should reduce the risk of the fund if fund flows excessively sensitive to
small negative changes in excess return.
If we consider funds of age 6 and greater years (Figure 2), it is not
If we take a look on the flow-return relation of «old» funds (Figure 2) it is become
obvious that the «𝑓» - curve is much flatter for them than for young funds, especially in the
part of negative returns. It goes to show that individual investors have more trust in older
funds. Their clients believe that in spite of bad quarter the fund will stand and next quarter
will be batter.
Year t+1 net
flow
1
0.8
0.6
0.4
0.2
0
-0.4
-0.3
-0.2
-0.1
-0.2
0
0.1
-0.4
0.2
0.3
0.4
Year t excess return
-0.6
-0.8
Figure 2 - Flow-performance relationship for old funds (age>6) 𝑓̂ with 90%
confidence bands.
Model (1) estimated parameters presented in the table 1. To interpret table 1 correctly
we should remember that 𝛾 and 𝛿 coefficients had relative nature. They characterize the
relation between nonparametric parts of the model (1) for different age categories. For the
first and fourth age category 𝛾 = 1 and 𝛿 = 0 because we choose first age category as a
benchmark for the second and 4th as a benchmark for the 3rd. To obtain 𝑓̂ for the second age
category we should multiply 𝑓̂ for the first age category (figure 1) by (1-0.29) and then
subtract 0.04 from that product. Negative 𝛾2−4 in couple with positive 𝛾4−6 indicate that the
older fund flows are less sensitive to the past return performance.
Table1 – Coefficients from flow-return model
Independent
variables
𝛾2−4
𝛿2−4
Young funds (age <=4)
N = 1 343
-0.29
(0.33)*
-0.04
(0.15)
𝛾4−6
𝛿4−6
𝛼1
𝛼2
𝛼3
0.82
(0.29)
1.53
(0.20)
1.21
(0.10)
Old funds (age > 4)
N = 3 459
0.33
(0.59)
0.02
(0.35)
0.44
(0.11)
1.01
(0.35)
0.83
(0.06)
𝛼4
-0.18
(0.07)
-0.08
(0.04)
Note – estimated standard errors are in parentheses
If we take a look on the 𝛼1 and 𝛼2 coefficients we could see that excess return in 𝑡 + 1
and 𝑡 − 1 periods also have influence on fund flows in 𝑡 + 1 period.
In table 2 we had flow-risk regression results. As it seen from the table the most strong
Table 2 – Coefficients from flow-risk model.
Risk measure
Variance
(empirical)
Semi-variance
(empirical)
Value at Risk
(empirical, 𝛼 = 0,25)
Expected shortfall
(empirical, 𝛼 = 0,25)
𝛾
-0,9*
𝛿
0.23*
𝛼1
1.24*
𝛼2
0.21**
-1.44**
0.05*
1.15
0.34
-0.81
0.14
0.95
0.18
-1.19*
-0.02**
0.77
0.17
Note: * significant at the 0.1 level
** significant at the 0.15 level
It is seen from the table that all coefficients
3) Dose Russian fund managers actually manipulate risk in response to incentives?
In the previous section it was shown that the relationship between the yield of an openend mutual fund and fund flows is non-linear. This nonlinearity causes incentives to
manipulate risk for fund manager.
a) Risk incentives estimation
To estimate the risk incentives for fund managers we use the same approach as in
(Chevallier, Ellison, 1997). The only difference – is the shorter time interval (quarter instead
of the year).
According to (1):
𝐸[𝐹𝑙𝑜𝑤𝑖,𝑡 ] = 𝐸[(1 + 𝛾𝑘 )𝑓 (𝑟2𝑚 + 𝑢) + 𝛿𝑘 + 𝛼𝑋𝑖,𝑡 ], where
1+
𝑟2𝑚 - fund’s excess return in the first two months of the quarter;
𝑢 – random variable representing fund’s monthly return.
Assuming that 𝑢 distributed with mean zero and standard deviation 𝜎, and another
variable 𝑣, has mean zero and st. dev. 𝜎 + ∆𝜎 we can write risk incentives as follow:
𝑅𝐼𝑘 (𝑟𝑄(𝑡) ; 𝜎, ∆𝜎) = 𝐸[(1 + 𝛾𝑘 )[𝑓(𝑟𝑡 + 𝑣 ) − 𝑓(𝑟𝑡 + 𝑢)]]
(3)
Risk incentive graph for funds of th 1st age category is presented in the figure 3. The
function is interpreted as the expected increse in the 3rd month growth rate of a 1st age
category fund that results from increasing its risk in the 3rd month of the quarter from the
sample average to 50% above this average.
Risk Incentive
0.025
0.02
0.015
0.01
0.005
-0.4
-0.3
-0.2
0
-0.1
0
-0.005
0.1
0.2
0.3
0.4
2 month return
-0.01
-0.015
Figure 3 – Risk incentives for «young» mutual funds.
b) Model and data
To examine fund managers reaction to risk incentives the following model is used
∆𝛿𝑖,𝑡+1 = 𝛼𝑅𝐼𝑖,𝑡 + 𝛽𝐹𝑙𝑜𝑤𝑖,𝑡 + 𝛾𝑀𝑆𝑖 , where
(4)
𝑅𝐼𝑖,𝑡 - risk incentive at the end of the period 𝑡, measured from (3),
∆𝛿𝑖,𝑡+1 =
𝛿𝑖,𝑡+1 −𝛿𝑖,𝑡
𝛿𝑖,𝑡
– change in std. dev. in the period 𝑡 + 1.
To estimate this «risk-flow» model we use quarter data of fund flows and risk
parameters (4800 observations). Monthly risk indicators (funds 𝛽 and volatility) obtained
from InvestFunds (http://pif.investfunds.ru/analitics/coefficients/). Fund flows quarter data
obtained from nlu.ru (http://www.nlu.ru/export-excel.htm).
The results of the regression (4) presented in the table 4.
𝛼
fund age <=2
4>=fund age >2
1.21*
(0.64)
0.92**
𝛽
0.05
(0.10)
0.60
𝛾
0.12
(0.08)
0.02
6>=Fund age>4
Fund age>6
(0.53)
0.88**
(0.21)
0.21**
(0.19)
(0.48)
0.74
(0.32)
0.51
(0.47)
(0.04)
0.03
(0.00)
0.40
(0.34)
Note: * significant at the 0.1 level
** significant at the 0.15 level
Model (4) parameters estimates suggest that young funds managers pay more attention
to risk incentives than the older ones. These results are not surprising, young funds managers
often
4) Conclusion
From this study we could derivate several basic results.
First of all, the dependence between past performance of the fund and its net flow in
the next period obviously exists. This relation has non-linear character, as a result risk
incentives for fund managers appears.
Flow-performance relation as well as risk incentives are stronger for the young funds.
Young funds reaction to the risk incentives is much stronger than the reaction of the
older funds.
The flow-risk performance is most stronger for expected shortfall and semi variance
risk measures.
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