Understanding Alternative Investments – A look at Standard Normal
Alternatives or alternative investments are the one of the categories of asset classes, these types of investments include hedge funds, private equity, or venture capital or include the use of leverage or derivatives as part of the investment style. Example long-short style of investing in equities used by hedge funds or derivatives. Historical returns are not good for analysing the future compared to traditional investments. For example in options pricing, implied volatility means what the market is implying the future volatility of a stock based on changes in options pricing. This example is enunciated to discern the difference between historical volatility and implied volatility. The return distribution of these assets don’t have a normal distribution, are less transparent, and have different measures to understand risk. These asset classes are good for diversifying risk from a portfolio as they are less correlated with traditional assets, but have shown a higher correlation with traditional assets during the financial crisis. Investments have concepts like hurdle rate, clawback, and waterfall structure that have to be looked at separately from that of traditional investments. Alternatives have a higher tail risk compared to traditional investments, many not linked to market prices. Some important differences between traditional and alternative investments are articulated here. Normal distribution follows a bell curve distribution, with skewness of zero, have symmetry about the mean, kurtosis of 3, and Mean= Median = Mode. The area of a normal distribution is always 1. Kurtosis measures the heaviness of tails or outliers. An excess of kurtosis i.e. if the measure is higher than 3 highlights a non-normal return with more data points away from the mean. Alternative investments have more observations or data points on either side of the mean. A better way to understand this concept is through a standard normal. Alternative investments have more observations or data points on abnormal distance on either side of the mean. A better way to understand this concept is through a standard normal. Usually observations above 3 standard deviation are outliers for normal distributions.
Above: Standard Normal | The middle Road
Standard Normal has a mean of zero and a standard deviation of 1. This type of distribution standardizes variation of the observations from the mean through the 3-sigma rule – 68-95-99.7. 68 percent of the data points lie within 1 standard deviation of the mean, 95 percent within 2 standard deviations, and 99.7 percent within 3 standard deviations of the mean. Probabilities of expected returns falling within 1, 2, and 3 standard deviations (S.D) of the mean in a normal distribution. 
The Z-score of an observation is defined as the number of standard deviations it falls above or below the mean. Z-score for an observation X that has a distribution mean µ and standard deviation σ is below. Statistics online course will take a detailed look at standard normal. The Z-score of an observation is defined as the number of standard deviations it falls above or below the mean. Z-score for an observation X that has a distribution mean µ and standard deviation σ is on the left side. These concepts along with t distribution will be covered in the free online course on Statistics. Measures of risk adjusted return are Sharpe and Treynor Ratio. Sharpe ratio captures excess return over risk free security like T-bills in the US that have a zero-variance divided by standard deviation, Treynor divides excess return over risk free security by beta. These measures are good for asset returns that have normal distribution but not for nonnormal. Ratios like Sortino ratio, VaR (Value at Risk) and Expected Shortfall (ES) are used to understand downside risk.
The following is a brief from the Introduction to Valuation course on The middle Road.
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