ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

KIRAN KUMAR K V

Investors attempt
to optimize in a particular manner as proposed by Harry Markowitz’s Modern
portfolio theory
. And that manner is referred to by him as rationality.
According to the theory, rational behaviour is warranted as investors are led
to decide in uncertainty. Investors wanting to earn the maximum return is as
rational as sun rising in the east. Since the return on a risky asset depends
on values that various market and asset variables can take in future and the
future is unknown, it becomes imperative that rational behavior of investor
also considers risk of investing. A risky asset with higher expected volatility
is bound to be under-preferred by the rational investor versus a risky asset
with comparatively lesser expected volatility. The crux of efficient portfolio
theory as per Markowitz, thus, becomes the efficient frontier,
essentially a Pareto line optimizing in two dimensions – expected return and
the variance of such return (Markowitz
H. M., 1990). Also, it can
be noted that expected return is a desirable thing and variance of the return
is an undesirable thing. (Markowitz
H. , 1952)
Therefore, the
process of portfolio building is, evidently, aiming to earn maximum possible
return, while anchoring the risk parameter
. Maximizing the anticipated
return is a function of different variables estimated and used in the valuation
process. Whereas, curbing the risk in the portfolio requires defining the risk
in the first place. First, the asset class risk – that is hovering around the
class of the asset as a whole; second, the security-specific risk – that’s the
sensitivity of the security’s returns to changes in prices of the benchmark
portfolio. The asset class risk can be brought down by diversifying across
different classes of assets. Similarly, portfolio-specific risk can be reduced
by different portfolios with directional movements that are divergent from each
other.
The portfolio
theory of Markowitz has well established that the security-specific risk can be
brought down with ease by constructing a portfolio with an optimum proportion
of a set of securities between whom the co-linearity is minimum. A mutual fund
is supposed be a tool that can work in this direction, for an investor, who
wishes to rely on the professional to take up the risk management task. Every
mutual fund theoretically and practically is a diversified portfolio and
supposed to be bringing down the volatility factor for the investor, as
compared to a singular investment decision. And because, mutual funds take care
of the security-specific risk, to a large extent, the risk that investors may
have to focus would be the asset-class risk or the market risk.
It is well
established that a rational investor would choose a combination of risk-free
rate (defined as the rate in the absence of demand for any risk premium) and
risk premium, through the seminal contributions of William Sharpe. Sharpe
raised the question on the relationship between the risk and return of a
portfolio and developed an asset pricing model that focused entirely on
building a portfolio that minimized the difference between the marginal utility
of investing in any security in a given portfolio. This was achieved by
quantifying the assumed linear relationship between the expected returns on
securities and their covariance with the market portfolio, viz., beta. (Sharpe, 1990). The beta could be
obtained by,

       

……………Equation-1

Where,
βim

 is the beta of the security or portfolio i, Cim

 is the covariance between the security or
portfolio i and the market portfolio and Vm

 is the variance of the market portfolio. This
was proliferated with the risk premium demanded by the investor to satisfy his
utility function (which in turn depended on his risk appetite) and the
combination of beta adjusted risk premium and the risk free rate became the
expected return on a security or the portfolio.

By combining the
efficient frontier and the expected return arguments, it could be inferred that
market portfolio is supposed to be efficient and there exists a linear
relationship between expected return and beta. And this becomes the strong
argument in favour of mutual fund managers, theoretically speaking. Given that
mutual funds are able to manage the unsystematic risk – as measured by their
reduced variances of returns, are they also able to manage the systematic risk?
Note that, there is no way one can target to reduce the systematic risk, but,
the fund can deliver a return that is on par with the expected return of the
investor (again, as measured by the investor’s risk appetite).
Thus, this study
aims to test if mutual funds in the Indian context, have been able to
successfully generate a return that is in line with investor expectations. The
objective of this study is to investigate whether fund managers of Indian
mutual funds are efficient in managing the total risk and the unsystematic
risk.

Study Design

A sample of 35
Indian mutual funds were selected based on judgmental sampling. Judgmental as
the funds were selected to capture almost all the fund houses in India (listed
as per Value Research Online (Value Research Online, 2017). Also,
diversified equity funds, multi-cap funds, large cap funds and high one year
annualize return earned funds, in the pecking order were selected such that,
there is a representation of one fund at least from each fund house. Due to
availability of data and reliability study conducted, we could restrict our
sample size to 29 funds.
The data is
collected directly from the reported fund factsheets published by each fund
house in their websites’ downloads section. The fact sheets of the month of
December-2016 are sued for the computational purposes. The data pertains to REGULAR GROWTH option of each fund.
Standard deviation figures are annualized. Beta values are based on past three
years of historical Net Asset Values. 
The analysis is
carried out by following process:
Step-1: Computation of return on each of the sample mutual fund, assuming
mutual fund managers (who are essentially the investors in this case) behave
rationally, and thus, the fund returns fall on the efficient frontier. In other words, assuming mutual fund
portfolios and the market index portfolio are efficient portfolios, investing
in any of this portfolio would provide a maximum return for the investors,
while holding the risk at desirable level. This is computed using the Capital
Market Line Equation:

   

                                                                                      ………………Equation-2

Where,E(Rj)

is the expected return on efficient
portfolio j,

Rf 

is the risk-free rate,

 is the slope of the capital market line, and

 is the standard deviation of the portfolio j.

The slope of the
Capital Market Line is obtained using the equation given by:

         

                                                                                     ………………Equation-3

Where,ʎ

 
is the slope of the Capital Market Line,E(Rm)

 is the expected return on market portfolio, Rf

 is the risk-free rate and σM

 is the standard deviation of the market
portfolio returns.

Step-2: As the objective of the study is to see whether Indian mutual fund
managers are efficient in managing the non-diversifiable risk, which is
represented by the CML equation return as computed in table-2 above, it would
also be necessary to compare the returns of those portfolios, which do not
necessarily fall on the efficient frontier. The expected return and the
standard deviation of such portfolios should be falling below the CML, as these
are inefficient and not purposefully well-diversified. Such portfolios exhibit
linear relationship between their expected returns and covariance with the
market portfolio, but, need not give a conclusive pattern of such relation (Chandra, 2012). Such
relationship will result in an expected return as given by:

 

                                                                                  ………………Equation-4

Where,E(Ri)

is the expected return on
inefficient portfolio i, Rf

 is the risk-free rate,βi

 is the slope of the inefficient portfolio with
that of the market portfolio (which is supposed to be efficient with β = 1) also called the slope of the Security Market Line (SML), and σim 

 is the covariance of the returns of
inefficient portfolio and the efficient market portfolio. The βi 

 is computed by:

                                           ………………Equation-5
Where, βi 

 is the slope of the SML, E(Rm)

 is the expected return on market portfolio M, Rf

 is the risk-free rate,σ2M

 is the variance of the market portfolio M.

Presented below is
the table (Table-4) summarizing the expected returns (of both CML and SML
explanation) and the actual return of the funds:
If the CML and SML
were to determine fund manager behavior, there must exist a statistically
significant difference in the mean values of returns between the two series of
returns. We connote

µCML

  to represent the difference between fund’s
actual return and expected return based of firm’s total risk (i.e., standard
deviation) and

µSML

 to represent the difference between fund’s
actual return and expected return based of firm’s unsystematic risk (i.e.,
beta); Therefore, below hypothesis can be tested:

H0:

(Null Hypothesis: There is no
statistically significant difference between the mean excess returns of mutual
fund portfolios under CML and SML)

(Null Hypothesis:
There is a statistically significant difference between the mean excess returns
of mutual fund portfolios under CML and SML)
The t-test for
paired two sample for means is conducted and the results are presented below
(Table-5)
As the p-value of
the t-test for hypothesized mean difference in two variables is less than 0.05
(alpha value for 95% level of confidence), we reject the null hypothesis that
there is no statistically significant difference between the mean excess return
given by total risk management efficiency and unsystematic risk management
efficiency. Thus, we infer that there does exist a statistically significant
difference in the mean excess return given by two approaches. Combining the
hypothesis test result with that of the graphical presentation before, we can
induct that mutual fund managers are efficient in managing the unsystematic
risk, which in any case, the proof of Markowitz’s modern portfolio theory,
whereas the question, whether, fund managers can be more efficient than the
market itself, could not be answered, as no pattern could be established.

Conclusion

With the objective
of testing whether Indian mutual fund managers are efficient in managing their
respective portfolios such that benefits of diversification are delivered and
also an excess return is generated to compensate for the asset-class risk
assumed by the investor. The discussion on modern portfolio theory, asset
pricing models and market efficiency gave the direction to design the testing
process. The 29 Indian mutual funds those were selected have been used to
determine the excess returns generated by them, over and above the expected
returns. There were two such approaches used. One, total risk was taken as a
base to determine the expected return, with the assumption that investors,
expect mutual funds to compensate with higher return for  the total risk that they take. Capital Market
Line equation was used for the same. Two, non-diversifiable risk was taken as a
base to determine the expected return, with the assumption that investors are
rational enough to understand that markets are so efficient that no investor
could earn an excess return than the market. Hence, the expected return was
arrived at by adjusting for the unsystematic risk assumed by the investor.
Security Market Line equation served this purpose. We also tested the
hypothesis for difference in the mean excess returns under two approaches, and
concluded that there did exist a statistically significant difference between
the two.
Thus, we
conclude that Indian mutual fund managers are indeed managing the funds
efficiently in terms of bringing down the overall risk of investing in equity
securities for the retail investors to the extent of the unsystematic risk
.
This is a proof for the Markowitz’s theory of diversification (Markowitz H. , 1952). Does it mean
fund managers are doing great job? Not really. From this study we did find
that there is ample scope for the fund managers to design portfolios that can
bring down the systemic risk (Total risk minus unsystematic risk), which would
be possible with various other investing strategies ranging from value
investing to contra investing
.

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