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

**. 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**

*rationality***, essentially a Pareto line optimizing in two dimensions – expected return and the variance of such return**

*efficient frontier***(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)**

**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.

**.**

*beta***………………Equation-1**

*i*,

*i*and the market portfolio and

## Study Design

*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 s

elected 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**.

*REGULAR GROWTH*option of each fund. Standard deviation figures are annualized. Beta values are based on past three years of historical Net Asset Values.

**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**

*Step-1:**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**

*j*,

*j*.

**………………Equation-3**

**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**

*Step-2:***(Chandra, 2012)**. Such relationship will result in an expected return as given by:

**………………Equation-4**

*i*,

**………………Equation-5**

*M*,

*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

**H**

_{0}:

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

**H**

_{1}:

The t-test for paired two sample for means is conducted and the results are presented below (Table-5)

## Conclusion

**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*.