Elijah Ongeri Matini BBM2735/14
BBM 413 Assignment
A measure of performance on a risk-adjusted basis. Alpha takes the volatility (price risk) of a mutual fund and compares its risk-adjusted performance to a benchmark index. The excess return of the fund relative to the return of the benchmark index is a fund's alpha.
Alpha is one of five technical risk ratios; A positive alpha of 1.0 means the fund has outperformed its benchmark index by 1%. Correspondingly, a similar negative alpha would indicate an underperformance of 1%.
The Jensen index, or alpha, bears some relation to the capital asset pricing model, or CAPM. The CAPM equation is used to identify the required return ...view middle of the document...
This calculation method contrasts with both the Treynor and Sharpe measures in that both examine the average returns for the total period for all variables, which include the portfolio, market and risk-free assets.
Alpha is a good measure of performance that compares the realized return with the return that should have been earned for the amount of risk borne by the investor. Technically speaking, it is a factor that represents the performance that diverges from a portfolio's beta, representing a measure of the manager's performance. For example, it's insufficient for an investor to consider the success or failure of a mutual fund merely by looking at its returns. The more relevant question is this: was the manager's performance sufficient to justify the risk taken to get said return?
Applying the Results
A positive alpha indicates the portfolio manager performed better than was expected based on the risk the manager took with the fund as measured by the fund's beta. A negative alpha means that the manager actually did worse than he or she should have given the required return of the portfolio. The regression results usually cover a period between 36 and 60 months.
b) Standard deviation
Standard deviation is a measure of how "spread out" a set of data is. If it is large, you have a large range of numbers. If it is small, most of your data points are close to the average.
To find it, you need to subtract the "mean" (average) of the data from each data point, square your answers, add them all together, divide your answer by the number of data points minus 1, and take the square root.
So it's advantage is, it gives you a better picture of your data than just the mean alone. Disadvantages would be that it doesn't tell you the full range of the data, and it can be effected by "outliers" (rare numbers much smaller or larger than everything else in the data set) to give a skewed picture.
It is one of the most commonly used method to measure absolute risk. It is a statistical measure of dispersion around a central tendency. For example, during a 15-year period from August 1, 1992, to July 31, 2007, the average annualized total return of the S&P 500 Stock Index was 10.7%. This number tells you what happened for the whole period, but it doesn't say what happened along the way.
The average standard deviation of the S&P 500 for that same period was 13.5%. Statistical theory tells us that in normal distributions (the familiar bell-shaped curve) any given outcome should fall within one standard deviation of the mean about 67% of the time and within two standard deviations about 95% of the time. Thus, an S&P 500 investor could expect the return at any given point during this time to be 10.7% +/- 13.5% just under 70% of the time and +/- 27.0% 95% of the time.
c). R SQUARED.
Symbolized as r2, the coefficient of determination is the square of the correlation coefficient.
R squared, is a number that indicates how well data fit a statistical model –...