 # Category: 101 Concepts for Level I

#### Concept 10: Safety First Ratio

Shortfall risk is the risk that portfolio’s return will fall below a specified minimum level of return over a given period of time. Safety first ratio is used to measure shortfall risk. It is calculated as:     A portfolio with higher safety first ratio is preferred over a portfolio with a lower safety first ratio. An investor is considering two portfolios A and B. Portfolio A has an expected return of 10% and a standard deviation of 2%. Portfolio B has an expected return of 15% and a standard deviation of 10%. The minimum acceptable return for the investor is 8%…. Read More

#### Concept 11: Central Limit Theorem

According to the central limit theorem, if we draw a sample from a population with a mean µ and a variance σ2, then the sampling distribution of the sample mean: will be normally distributed (irrespective of the type of distribution of the original population). will have a mean of µ. will have a variance of σ2/n. Suppose the average return of the universe of 10,000 stocks is 12% and its standard deviation is 10%. Through central limit theorem, we can conclude that if we keep drawing samples of 100 stocks and plot their average returns, we will get a sampling… Read More

#### Concept 12: Calculating Confidence Intervals

To calculate a confidence interval for a population mean, follow these steps: Refer to the table below and select t statistic or z statistic as per the scenario. Sampling from Small sample size Large sample size Normal distribution Variance known z z Variance unknown t t (or z) Non–normal distribution Variance known NA z Variance unknown NA t (or z) Use the following formulae to calculate the confidence interval:     For a Z distribution, 90% confidence à critical value = 1.65 95% confidence à critical value = 1.96 99% confidence à critical value = 2.58 You take a random… Read More

#### Concept 13: Selection of Sample Size & Sampling Biases

Increasing the sample size reduces the standard error and gives us narrower confidence intervals. However, while increasing sample size we must consider two things: Cost involved: Compare the cost of getting more data to the potential benefits of increasing precision. Risk of sampling from a different population: In the process of increasing sample size if we get data from a different population, then the accuracy will not improve. Biases observed in sampling methods are: Data-mining bias: Analyzing the same data repeatedly, till a pattern is identified. To avoid this bias test the pattern on out of sample data. Sample selection bias: Excluding… Read More

#### Concept 14: Steps of Hypothesis Testing

Hypothesis is a statement about the value of a population parameter developed for the purpose of testing a theory. Hypothesis testing is the process of assessing the accuracy of a statement about a population on the basis of analysis conducted on a sample. In order to test a hypothesis, we follow the following steps: State the hypothesis. Identify the appropriate test statistic. Specify the level of significance. State a decision rule to accept or reject the hypothesis. Collect sample data and calculate the test statistic. Decide if the hypothesis can be accepted/rejected. Make an economic or investment decision. Null hypothesis (H0) is the… Read More

#### Concept 15: Hypothesis Tests Concerning a Single Mean

We use the following table to decide which test statistic and which corresponding probability distribution to use for hypothesis testing. Sampling from Small sample size Large sample size Normal distribution Variance known z z Variance unknown t t (or z) Non–normal distribution Variance known NA z Variance unknown NA t (or z)   You believe that the average returns of all stocks in the S&P 500 is greater than 10%. You draw a sample of 49 stocks. The average return of these 49 stocks is 12%. The standard deviation of returns of all stocks in the S&P 500 is 4%…. Read More

#### Concept 16: Common Chart Patterns

Reversal Patterns signal the end of a trend. The four kinds of reversal patterns are: Head and shoulders pattern: Consists of the left shoulder, the head, and the right shoulder. Indicates the end of an uptrend. You can profit by going short on the security, the price target is: Price target = neckline – (head – neckline) Inverse head and shoulders pattern: Is a mirror image of the head and shoulders pattern. Indicates the end of a downtrend. You can profit by going long on the security, the price target is: Price target = neckline + (head – neckline) Double tops… Read More

#### Concept 17: Price, Income and Cross-Price Elasticities of Demand

Elasticity of demand is measured as a ratio of percentage change in quantity demanded to a percentage change in other variables. Own-price elasticity Own-price elasticity of demand is usually always negative. If |own price elasticity| > 1, then demand is elastic. If |own price elasticity| < 1, then demand is inelastic. If own price elasticity = -1, then demand is unit, or unitary, elastic. Income elasticity If income elasticity > 0, then the good is a normal good. If income elasticity < 0, then the good is an inferior good. Cross price elasticity If cross price elasticity > 0, then… Read More

#### Concept 18: Substitution and Income Effects

Substitution effect When a good’s price falls, due to substitution effect consumers buy more of this good as compared to other goods for which the prices have remained the same. Substitution effect is always positive. Income effect When a good’s price falls, real income rises. If the good is a normal good, the income effect will be positive and more of this good will be purchased. If the good is an inferior good, the income effect will be negative and less of this good will be purchased. Giffen goods Giffen goods are highly inferior for which the negative income effect… Read More

#### Concept 19: Economies and Diseconomies of Scale

Economies of scale: As output increases, the long-run cost per unit decreases. Factors contributing to economies of scale include: Increase in output larger than increase in input Specialization More expensive but more efficient equipment Lower waste and lower costs Better use of market information Volume discounts from suppliers Diseconomies of scale: As output increases, the long-run cost per unit increases. Factors contributing to diseconomies of scale include: Increases in output are less than increases in input Company size becomes too large to manage efficiently Duplication Higher labor costs Higher resource costs