Concept explain : ( From Investopedia )

A measure of performance on a risk-adjusted basis.

Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index used as a benchmark, since they are often considered to represent the market's movement as a whole. The excess returns of a fund relative to the return of a benchmark index is the fund's alpha.

Alpha is most often used for mutual funds and other similar investment types. It is often represented as a single number (like 3 or -5), but this refers to a percentage measuring how the portfolio or fund performed compared to the benchmark index (i.e. 3% better or 5% worse).

Alpha is often used with beta, which measures volatility or risk, and is also often referred to as "excess return" or "abnormal rate of return."

Using alpha in measuring performance assumes that the portfolio is sufficiently diversified so as to eliminate unsystematic risk.Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund's return. In other words, alpha is the return on an investment that is not a result of general movement in the greater market. As such, an alpha of 0 would indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any value.

The concept of alpha was born with the advent of weighted index funds like the S&P 500 for the stock market and the Wilshire 5000 for the securities market, which attempt to emulate the performance of a portfolio that encompasses the entire market and that gives each area of investment proportional weight. With this development, investors could hold their portfolio managers to a higher standard of just producing returns: producing returns greater than the investor would have made with a blanket market-wide portfolio.

Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which calculates the expected return of an asset based on its beta and expected market returns. Beta is also known as the beta coefficient.

Beta is calculating using regression analysis. Beta represents the tendency of a security's returns to respond to swings in the market. A security's beta is calculated by dividing the covariance the security's returns and the benchmark's returns by the variance of the benchmark's returns over a specified period.

A beta of 1 indicates that the security's price moves with the market. A beta of less than 1 means that the security is theoretically less volatile than the market. A beta of greater than 1 indicates that the security's price is theoretically more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market. Conversely, if an ETF's beta is 0.65, it is theoretically 35% less volatile than the market. Therefore, the fund's excess return is expected to underperform the benchmark by 35% in up markets and outperform by 35% during down markets.

The research shows that on a gross-return basis, active fund managers are able to generate alpha, exploiting the bad behavior of individual investors, on the other hand, majority of the active fund's return are much lower than market on average.

In their book " The Incredible Shrinking Alpha " , Larry Swedroe and Andrew Berkin   explaining why actively managed funds are slowly being replaced by indexed funds.

 According to them , Alpha is the holy grail of investing. It is the mathematical term for the amount of return an investment earns above an appropriate risk-adjusted benchmark. In plain English, it's a measure of skill. When I think of "alpha," I picture a group of identical runners, each of the same height and weight, and each having the same size ball chained to their right ankle. The one that completes a sprint the fastest, given the same "risk factors," has shown the most inherent skill, or "alpha."

Alas, in the investment world, alpha is increasingly harder to come by. This is important because it is the quest for alpha-the hope of earning excess returns per unit of risk assumed-that enables active managers to charge the fees they do.

Of course, not all active fund are underperforming the market , we have encountered many super investors like Warren Buffett , Peter Lynn, Walter Schloss , John Templeton , Carl Icahn etc. who have beating the market in the long run. 

But one need to also remember that " Buffett's Alpha " is one in multi-millions ! and how many Warren Buffett we have in this world ?

Well, if the Beta is better in the long run, then most of the investors should try to invest in Index ETF rather than investing in mutual fund or by our own.

Human being always like to do something exciting and thrilling, we want to take control of our decision making in all aspect of life. 

Even in "passive investing " like Index ETF , we try to create something different , like "factor investing " or so call " smart beta".

According to Investopedia , Smart beta is a set of investment strategies that emphasize the use of alternative index construction rules to traditional market capitalization based indices. Smart beta emphasizes capturing investment factors or market inefficiencies in a rules-based and transparent way. 

The increased popularity of smart beta is linked to a desire for portfolio risk management and diversification along factor dimensions as well as seeking to enhance risk-adjusted returns above cap-weighted indices.

There is no single approach to developing a smart beta investment strategy, as the goals for investors can be different based on their needs, though some managers are prescriptive in identifying smart beta ideas that are value creating and economically intuitive. Equity smart beta seeks to address inefficiencies created by market-capitalization-weighted benchmarks

Managers may also choose to create or follow an index that weights investments according to fundamentals, such as earnings or book value, rather than market capitalization.

"Beta" measures the volatility of an individual security/portfolio, as compared to the broader, whole securities market. The stock market, which often uses the STI Index as its proxy, has a beta of one. Individual stocks are then ranked according to how much they deviate from that beta.

A stock with a beta of two has a return that, generally, changes by twice the magnitude of the overall market's returns - whether returns are positive or negative. "Smart" refers to the use of an alternative methodology rather than following an index's size-based (market-cap) allocations.

Traditional market-cap weighted indexes, weight their constituents based solely on market caps, giving larger companies a bigger slice of the index even if a company is considered overvalued.

On the other hand , smaller cap companies are given smaller allocations, even if other characteristics indicate they are poised for growth.Smart beta solves this "size" bias through the use of its objective rules-based screens rather than a cap-weighted methodology.

Below link from CFA Institute provide us a very good read on "factor investing " or smart beta in general :

Link : https://www.cfainstitute.org/learning/products/publications/irpn/Pages/irpn.v2014.n1.6.aspx