## ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

particular manner as proposed by Harry Markowitz’s

*Modern portfolio theory*.

And that manner is referred to by him as

**. According**

*rationality*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)

building is, evidently,

**aiming to earn maximum possible return, while**

anchoring the risk parameter. Maximizing the anticipated return is a

anchoring the risk parameter

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.

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.,

**. (Sharpe, 1990). The beta could be**

*beta*obtained by,

** **………………Equation-1

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.

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).

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

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 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.

following process:

**Computation of**

*Step-1:*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

frontier.

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

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*.

Line is obtained using the equation given by:

** **………………Equation-3

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.

**As the objective**

*Step-2:*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

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

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:**

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)

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

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.

**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

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

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.

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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