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...

Jump Diffusion

The jump diffusion process recognizes the fact that not all stock movements follow a continuous smooth process. Natural disasters, revelation of new information, and other shock can cause a massive, instantaneous revaluation of stock prices. To account for these large shocks, the normal diffusion is augmented with a third term representing these jumps m-1k di sdz dq, 1.4.4 where l is the average number of jumps per unit of time, k is the average proportionate change of the jump the variance of...

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...

Patterns Of Downside Risk

In the preceding section, we argued that downside risk should receive a higher risk premium than upside risk. In this section we will look at the source and magnitude of this difference. The first thing to observe is how close the traditional measures of downside risk are to the standard deviation proxy among our recommended measures of downside risk. There will, of course, be some correlation because traditional measures of risk include the downside as well as the upside. The degree of...

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...