While this information may be useful, it does not fully address an investor's concerns about risk. The field of behavioral finance has contributed to an important component of the risk equation, demonstrating the asymmetry between how people perceive gains and losses. In the language of probability theory, the field of behavioral finance introduced by Amos Tversky and Daniel Kahneman in 1979, investors are showing a loss aversion. Both Tversky and Kahneman document that investors have placed nearly twice the weight on pain associated with loss compared to the feeling of goodness associated with gain.
Often times, what investors really want to know is not just how deviating an asset is from its expected outcome, but how the bad things look in the lower left side of the distribution curve. Value at Risk (VAR) attempts to provide an answer to this question. The idea behind the VAR technique is to quantify the loss in an investment with a certain level of confidence over a specified period. For example, the following statement might be an example of VAR: "With a confidence level of about 95%, the maximum you can lose on this investment of $ 1,000 over two years is $ 200." The level of confidence is a statement of likelihood that depends on the statistical properties of the investment and the shape of its distribution curve.
Of course, even a procedure like VAR doesn't guarantee that 5% of the time it will be much worse. Spectacular disasters like the one that struck the hedge fund Long-Term Capital Management in 1998 remind us that so-called "emerging events" may happen. In the case of LTCM, the anomaly was the Russian government's default on its outstanding sovereign debt obligations, an event that threatened to bankrupt the hedge fund, which had highly leveraged positions of more than $ 1 trillion; Had it collapsed, it would have led to the collapse of the global financial system. The US government created a $ 3.65 billion loan fund to cover LTCM losses, enabling the company to survive market fluctuations and liquidation in an orderly manner in the early 2000s.
Manage experimental and passive risks
Another risk measure directed towards behavioral trends is regression, which indicates any period in which an asset's return is negative in relation to a previous high mark. In measuring regression, we try to address three things:
The amount of each negative period (how bad it is)
Duration of each (how long)
Frequency (how many times)
For example, in addition to wanting to know if a mutual fund beat the S&P 500, we also want to know how relatively dangerous it is. One measure of this is beta (known as "market risk"), based on the statistical property of covariance. Beta larger than 1 indicates greater market risk and vice versa.
Beta helps us understand the concepts of negative and positive risk. The chart below shows a time series of returns (each data point named "+") for a given portfolio R (p) versus the market return R (m). Returns are adjusted in cash, so the point at which the x and y axes intersect is the equivalent cash return. Plotting a line of best fit through the data points allows us to identify passive (beta) and active (alpha) risks.
Regression line is its beta. For example, the color gamut of 1.0 indicates that for every unit of increase in market return, portfolio return also increases by one unit. A money manager who uses a passive management strategy can try to increase the return of a portfolio by taking on more market risk (i.e. beta greater than 1) or reduce portfolio risk (and return) instead by reducing portfolio beta to less than 1.
Alpha and Active Risk Management
If market level or systemic risk is the only influencing factor, then portfolio return will always be equal to the beta adjusted market return. Of course, this is not the case: returns vary due to a number of factors unrelated to market risk. Investment managers who follow an active strategy bear other risks of generating returns in excess of market performance. Active strategies include tactics that enhance stock selection, sector or country, fundamental analysis, position sizing, and technical analysis.
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