In this series of posts we will cover the 101 most important concepts from the Level I CFA Program curriculum. These blogs are designed to break down complex topics into smaller, easily manageable bite-sized segments and are ideal for revision. The concepts were specially handpicked to ensure that you are well prepared for the exam. All the Best! Click below for details
Present value is the current value of a future cash flow. Longer the time period till the future amount is received, lower the present value. Higher the discount rate, lower the present value. Future value is the value to which an investment will grow after one or more compounding periods. Longer the time period till which the investment is allowed to grow, higher the future value. Higher the interest rate, the higher the future value. The future value and the present value of a single sum of money can be calculated by using the formulae given below or by using the TVM… Read More
The NPV of an investment is the present value of its cash inflows minus the present value of its cash outflows. The NPV of a project is calculated as: Consider a project which requires an initial investment of $10,000. It is expected to generate $5,000 in the first year, $6,000 in the second year and $7,000 in the third year. The cost of capital for this project is 10%. Calculate the NPV of this project. Solution: Using the financial calculator: CF0 = -10,000; CF1 = 5,000; CF2 = 6,000; CF3 = 7,000; I = 10. CPT NPV =… Read More
Money-weighted rate of return The money-weighted rate of return is simply the IRR of a portfolio taking into account all cash inflows and outflows. If a manager controls the cash inflows and outflows of a portfolio, then use money-weighted return to measure performance. An investor buys a stock for $10 at time t=0. At the end of Year 1, he receives a dividend of $1 and purchases another stock for $12. At the end of Year 2, he receives a dividend of $0.5 per share and sells both shares for $13. Calculate the money-weighted return. Solution: Year Outflow Inflow Net… Read More
Consider a T-Bill with a face value of $100 and 60 days to maturity. It is selling at a discount of $2 i.e. at a price of $98. Calculate BDY, HPY, EAY and MMY. Solution:
Arithmetic mean is the sum of all the observations divided by the total number of observations. A population average is called population mean (µ). A sample average is called sample mean (). The sample mean is used as the ‘best guess’ approximation of the population mean. A stock had the following returns in the past three years: 10%, -5%, and 20%. Calculate the arithmetic mean. Solution: Arithmetic mean = (10 – 5 + 20)/3 = 8.33% Median is the midpoint of a data set that has been sorted from largest to smallest. If we have an even number of observations,… Read More
A quantile is a value at or below which a stated fraction of the data lies. Some examples of quantiles include: Quartiles: distribution is divided into quarters Quintiles: distribution is divided into fifths. Deciles: distribution is divided into tenths. Percentile: distribution is divided into hundredths. The formula for the position of a percentile in a data set with n observations sorted in ascending order is: Ly = (n+1) y /100 Calculate the first quartile of a distribution that consists of the following portfolio returns: 3%, 4%, 6%, 9%, 11%, 12%, 14% Solution: The first quartile = (7+1) 25/100 = 2nd item in the data set (4%)…. Read More
Range is the difference between the maximum and minimum values in a data set. Range = maximum value – minimum value The annual returns of a portfolio manager for the past 4 years are 4%, 2%, 6%, 8%. Calculate the range. Solution: Range = 8% – 2% = 6% Mean absolute deviation (MAD) is the average of the absolute values of deviations from the mean. The annual returns of a portfolio manager for the past 4 years are 4%, 2%, 6%, 8%. Calculate MAD. Solution: X = (4 + 2 + 6 + 8)/4 = 5 Variance is defined… Read More
A distribution is said to be symmetrical when the distribution on either side of the mean is a mirror image of the other. In a symmetrical distribution, mean = median = mode. If a distribution is non-symmetrical, it is said to be skewed. Skewness can be negative or positive. A positively skewed distribution has a long tail on the right side, which means that there will be frequent small losses and few large gains. Here the mean > median >mode. The extreme values affect the mean the most which is pulled to the right. They affect the mode the least. A negatively skewed distribution has a… Read More
Covariance is a measure of how two variables move together. A positive covariance indicates that the variables tend to move together in the same direction. Whereas, a negative covariance indicates that the variables tend to move in opposite directions. If two variables X and Y have expected values of E(X) and E(Y), then the covariance can be calculated as: Cov (X,Y) = E[X – E(X)] [Y – E(Y)] Calculate the covariance of two stocks A and B given two possible states of the economy. Refer to the table below. Scenario P(Scenario) Expected Returns of A Expected Returns of B Recession 0.2 1% 3% Expansion 0.8… Read More
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