Kernel Density Estimation

The empirical cdf with pj increasing in steps of (1 T) from 0 to 1 is too jagged in appearance to directly compare to theoretical, smooth distribution. Statisticians have tried to remove the jump discontinuities among them by smoothing and averaging the nearby values, Silverman (1986). If we choose parametric densities such as N(m, o2) or the logistic (4.3.2), we place observed data into a straightjacket of a particular form of the chosen density. The finan- Theoretical quantiles Figure 4.3.3...

Empirical cdf and Quantile Quantile QQ Plots

Rather than disregard the normal distribution in all applications, we will give it the benefit of the doubt and let the numbers tell us if an approximation is good. A test of the goodness of fit is usually made for discrete pdf's like the binomial and Poisson by preparing a table of observed Obs and fitted Fit values with say j 1,2, , k rows. The Pearson goodness of fit statistic is simply where we have inserted an additional subscript j for the jth row. We reject the null hypothesis of a good...

Overoptimistic Consensus Forecasts by Analysts

Any company's data on past performance involve many factual series including gross earnings, EBITDA earnings before interest, taxes, depreciation, and amortization , net profits, and its price-to-earnings ratio PIE ratio . Stock market research services, such as Value Line, publish reports on individual companies available at most public libraries. Yahoo finance and other places also provide such information on line. The S amp P 500 stock index is often regarded as a leading indicator of market...

Using CAPM for Capital Investment Decisions

Since CAPM beta is widely reported and commonly known by investors in the stock market, the management of a corporation knows the value of their firm's own beta. It also determines the equity cost of capital to the firm. Hence it is recommended that the management decisions regarding the choice among investment projects should check whether the project yields a rate of return that exceeds the cost of capital. If the cost of debt financing is assumed to be equal to that of equity financing, a...

Pearson Type IV Distribution for Our Mutual Fund Data

We can see from the estimates in Table 2.1.2 that the normal distribution is not appropriate. Kurtosis is high, and the returns are negatively skewed. If we plot the observed point in a diagram with Pearson's skewness p1 on the horizontal and p2 on the vertical axis, as in Figure 2.1.1, we note that AAAYX mutual fund falls in the region of Pearson's type IV curve. This is not good news. Type IV is the hardest to work with since it involves imaginary roots of the quadratic in 2.1.6 , so we...