ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?
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,

 is the beta
of the security or portfolio i,

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

 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,

is the expected return on efficient portfolio j,

 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,

  is the slope
of the Capital Market Line,

 is the
expected return on market portfolio,

 is the
risk-free rate and

 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,

is the expected return on inefficient portfolio i,

 is the risk-free
rate,

 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

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

 is computed
by:

………………Equation-5

Where,

 is the slope
of the SML,

 is the
expected return on market portfolio M,

 is the
risk-free rate,

 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

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

 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)
H1:

(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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