Your cart is currently empty!
Month: June 2013
-
Credits and Debits
It is certainly possible to learn everything you need to know about financial reporting and analysis (for both Level I and Level II) without understanding fully credits and debits, but it is unquestionably more difficult than if you do understand them. The good news is that they’re not difficult to understand. Income statements gave rise…
-
Margin Call Price
The price at which you will receive a margin call on a long position in a stock is given by: \[margin\ call\ price\ =\ P_0\left(\frac{1\ –\ initial\ margin}{1\ –\ maintenance\ margin}\right)\] where: \(P_0\): initial price of the stock The price at which you will receive a margin call on a short position in a stock…
-
Degree of Total Leverage (DTL)
The degree of total leverage (DTL) is defined as: \[DTL\ =\ \frac{\%\ change\ in\ Net\ Income}{\%\ change\ in\ Sales}\ =\ \frac{\dfrac{\Delta Net\ Income}{Net\ Income}}{\dfrac{\Delta Sales}{Sales}}\] Suppose that a company has only variable expenses – 70% of sales – and no interest expense; taxes are 40% of EBT. If Sales are $100,000 and ΔSales is $1,000, then,…
-
Degree of Financial Leverage (DFL)
The degree of financial leverage (DFL) is defined as: \[DFL\ =\ \frac{\%\ change\ in\ Net\ Income}{\%\ change\ in\ EBIT}\ =\ \frac{\dfrac{\Delta Net\ Income}{Net\ Income}}{\dfrac{\Delta EBIT}{EBIT}}\] Suppose that a company has no interest expense, and that taxes are 40% of EBIT. If EBIT is $20,000 and ΔEBIT is $300, then, taxes will be $8,000 (= $20,000…
-
Degree of Operating Leverage (DOL)
The degree of operating leverage (DOL) is defined as: \[DOL = \frac{\%\ change\ in\ EBIT}{\%\ change\ in\ Sales}\ =\ \frac{\dfrac{\Delta EBIT}{EBIT}}{\dfrac{\Delta Sales}{Sales}}\] Suppose that a company has only variable expenses, and those are 70% of sales. If Sales are $100,000 and ΔSales is $1,000, then, expenses will be $70,000 (= $100,000 × 70%) Δexpenses will…
-
Herfindahl-Hirschman Index (HHI)
The Herfindahl-Hirschman Index (HHI) is a measure of the degree of concentration in an industry; it is defined as: \[HHI\ =\ \sum_{i=1}^n MS_i^2\] where: \(n\): number of firms in the industry \(MS_i\): market share of firm i (Technically, if there are more than 50 firms in the industry, the HHI sums over only the largest…
-
Macaulay Duration, Modified Duration, and Effective Duration
In this article I’ll cover three quantities that go by the name of “duration”: Macaulay duration Modified duration Effective duration I’ll explain how each type of duration is calculated, the characteristics of each type of duration, the similarities and differences amongst the types of duration, and how they are used in practice. Types of Duration…
-
Sample Standard Deviation
In comparing the formulae for the standard deviation of a population: \[\sigma\ =\ \sqrt{\frac{\sum_{i=1}^N \left(X_i\ –\ \mu_X\right)^2}{N}}\] and the standard deviation of a sample: \[s\ =\ \sqrt{\frac{\sum_{i=1}^n \left(X_i\ –\ \bar X\right)^2}{n\ –\ 1}}\] the obvious difference that strikes one immediately is the for the population standard deviation the denominator is the population size – \(N\)…
-
Kurtosis
Kurtosis is generally viewed as a measure of peakedness of a probability distribution (how tall the center of the distribution is compared to, say, a normal distribution); the taller (and thinner) the center peak, the higher the kurtosis. Another way of describing kurtosis is as a measure of how fat the tails (extreme ends, positive…
-
Skewness
Skewness of a probability distribution is a measure of its asymmetry; the higher the (absolute value of the) skewness, the more asymmetric the distribution. Symmetric distributions have skewness of zero. The formula for the skewness of a sample is: \[skewness\ =\ \frac{n}{\left(n\ -\ 1\right)\left(n\ -\ 2\right)}\frac{\sum_{i=1}^n \left(X_i\ –\ \bar X\right)^3}{s^3}\ ≈\ \frac1n\frac{\sum_{i=1}^n \left(X_i\ –\ \bar…