## ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

## ARE INDIAN MUTUAL FUNDS SUCCESSFULLY ANCHORING THE RISK?

####
*KIRAN KUMAR K V*

*KIRAN KUMAR K V*

to optimize in a particular manner as proposed by Harry Markowitz’s

*Modern*

portfolio theory. And that manner is referred to by him as

portfolio theory

**.**

*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)

process of portfolio building is, evidently,

**aiming to earn maximum possible**

return, while anchoring the risk parameter. Maximizing the anticipated

return, while anchoring the risk parameter

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.

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.

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.,

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

*beta*obtained by,

** **…

……………Equation-1

βim

is the beta of the security or portfolio *i*, C*im*

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.

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).

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

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**.

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.

carried out by following process:

**Computation of return on each of the sample mutual fund, assuming**

*Step-1:*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

is the expected return on efficient

portfolio *j*,

**f**

is the risk-free rate,

is the slope of the capital market line, and

is the standard deviation of the portfolio *j*.

Capital Market Line is obtained using the equation given by:

** **

………………Equation-3

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.

**As the objective of the study is to see whether Indian mutual fund**

*Step-2:*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*, 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:

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.*

the table (Table-4) summarizing the expected returns (of both CML and SML

explanation) and the actual return of the funds:

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)

** **

There is a statistically significant difference between the mean excess returns

of mutual fund portfolios under CML and SML)

paired two sample for means is conducted and the results are presented below

(Table-5)

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

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.

**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.

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.

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