FINANCE

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​Investment- Alpha 
Skill vs. Luck
If each person in a roomful of people randomly buys 10 stocks and holds them for five years, some of those persons may see the value of their investments rise. Does this suggest that they are skilful investors? At the same time, other people in the room may watch the value of their investments plummet. Does that suggest that they are terrible investors?

The answer to both queries is no. The stocks were chosen randomly, thus the result is entirely attributable to luck. But even when stocks are not chosen randomly, luck can play a large factor in investment outcomes, so investors need a mechanism to discern between skill and luck.  

The calculation and analysis of reward-to-risk ratios allow investors to understand the level of risk that has historically been taken to earn the total return generated by the fund. All things being equal, a manager who delivers a consistently high reward-to-risk ratio could be said to be more competent than one who consistently produces a lower ratio. Investors who invest in a fund that is managed on an active rather than a passive basis are effectively paying for the manager’s investment ability and expertise. 

Manager skill is commonly referred to as alpha. Perhaps the best approach to describe the concept of alpha is to evaluate the sources of a fund’s return, which is formed of three elements: 
Market return
Luck Skill 

Market Return Managers of passive funds attempt to provide returns for investors just as active managers intend to produce returns. But passive managers are not attempting to generate value by picking stocks that they feel will outperform other securities. Instead, they typically acquire and hold in the appropriate amounts only those securities that are contained in their benchmark. Although this procedure involves some expertise, it is not so much investment skill as effective management. When the value of the benchmark rises, the value of the passive fund monitoring it should also rise; conversely, when the value of the benchmark declines, the value of the passive fund should also fall. Therefore, over time, the fund should deliver a return (before the deduction of costs) equivalent to that of the set benchmark

Given that most actively managed funds are benchmarked against market indexes, such as the S&P 500, and fund managers will own many of the same securities that are in the index, some of the return generated by an actively managed fund will come from market movements due to the benchmark. Arguably then, investors in actively managed funds should not pay higher fees for fund returns that are generated by the market rather than by the investment acumen of their fund manager because investors can get market returns more cheaply by participating in passively managed funds.

Luck
Some of the return earned by a fund is the consequence of luck rather than discretion. The prices of financial assets held in funds are altered by events that cannot be expected by a fund management, such as natural disasters or geopolitical events.  

Skilful fund managers may be unlucky on sometimes while unskilled fund managers could experience some good luck. Because luck tends to equal out over the long term, it is crucial that investors are able to separate luck from expertise. But it is not always easy to do so. 

Skill A skillful fund manager is able to contribute value to a fund over and above changes to the fund’s value that are driven by market movements and that might have been achieved by a passive fund manager.  

Because luck may even out over time, a skilful manager is one who contributes this value consistently over time. Outperformance over the returns from a relevant market benchmark that are the result of manager talent and not luck is often referred to as alpha. 

Distinguishing Between Sources of Return 
Investors strive to discern between these three sources of fund returns. To do so, reward-to-risk ratios, such as the Sharpe ratio and the information ratio, are evaluated together with other indicators, such as a fund’s alpha, beta, standard deviation, and tracking error. A careful review of these variables over multiple time periods can assist investors decide whether outperformance has lasted over time and whether there is evidence of manager talent.  
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