Chapter 4 CAIA

Question 1

Ex Post Returns

Answer 1

Ex post returns are realized outcomes rather than anticipated outcomes.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 71). Wiley. Edición de Kindle.

Question 2

Ex-Ante returns

Answer 2

Future possible returns and their probabilities are referred to as expectational or ex ante returns.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 71). Wiley. Edición de Kindle.

Question 3

Normal Distribution

Answer 3

The normal distribution is the familiar bell-shaped distribution, also known as the Gaussian distribution. The normal distribution is symmetric, meaning that the left and right sides are mirror images of each other. Also, the normal distribution clusters or peaks near the center, with decreasing probabilities of extreme events.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 72). Wiley. Edición de Kindle.

Question 4

Central Limit Theorem

Answer 4

The formal statistical explanation for the idea that a variable will tend toward a normal distribution as the number of independent influences becomes larger is known as the central limit theorem.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 72). Wiley. Edición de Kindle.

Question 5

Four Moments of Distribution

Answer 5

Generally, the first four moments are referred to as
 mean, 
variance, 
skewness, 
kurtosis.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 74). Wiley. Edición de Kindle.

Question 6

Mesokurtosis

Answer 6

If a return distribution has no excess kurtosis, meaning it has the same kurtosis as the normal distribution, it is said to be mesokurtic, mesokurtotic, or normal tailed, and to exhibit mesokurtosis.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 78). Wiley. Edición de Kindle.

Question 7

Platykurtosis

Answer 7

If a return distribution has negative excess kurtosis, meaning less kurtosis than the normal distribution, it is said to be platykurtic, platykurtotic, or thin tailed, and to exhibit platykurtosis.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 78). Wiley. Edición de Kindle.

Question 8

Leptokurtosis

Answer 8

If a return distribution has positive excess kurtosis, meaning it has more kurtosis than the normal distribution, it is said to be leptokurtic, leptokurtotic, or fat tailed, and to exhibit leptokurtosis.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 78). Wiley. Edición de Kindle.

Question 9

Covariance

Answer 9

The covariance of the return of two assets is a measure of the degree or tendency of two variables to move in relationship with each other.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 79). Wiley. Edición de Kindle.

Question 10

Correlation Coefficient

Answer 10

The correlation coefficient (also called the Pearson correlation coefficient) measures the degree of association between two variables, but unlike the covariance, the correlation coefficient can be easily interpreted. The correlation coefficient takes the covariance and scales its value to be between +1 and −1 by dividing by the product of the standard deviations of the two variables. A correlation coefficient of −1 indicates that the two assets move in the exact opposite direction and in the same proportion, a result known as perfect linear negative correlation. A correlation coefficient of +1 indicates that the two assets move in the exact same direction and in the same proportion, a result known as perfect linear positive correlation. A correlation coefficient of zero indicates that there is no linear association between the returns of the two assets. Values between the two extremes of −1 and +1 indicate different degrees of association.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 81). Wiley. Edición de Kindle.

Question 11

Spearman Rank Correlation

Answer 11

The Spearman rank correlation is a correlation designed to adjust for outliers by measuring the relationship between variable ranks rather than variable values. ​The Spearman rank correlation for returns is computed using the ranks of returns of two assets.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (pp. 81-82). Wiley. Edición de Kindle.

Question 12

Beta

Answer 12

The beta of an asset is defined as the covariance between the asset’s returns and a return such as the market index, divided by the variance of the index’s return, or, equivalently, as the correlation coefficient multiplied by the ratio of the asset volatility to market volatility:

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 84). Wiley. Edición de Kindle.

Question 13

Autocorrelation

Answer 13

The autocorrelation of a time series of returns from an investment refers to the possible correlation of the returns with one another through time.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 85). Wiley. Edición de Kindle.

Question 14

First Order Autocorrelation

Answer 14

First-order autocorrelation refers to the correlation between the return in time period t and the return in the immediately previous time period, t − 1.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 86). Wiley. Edición de Kindle.

Question 15

The three main reasons for non-normality in IM returns

Answer 15

There are three main reasons for the non-normality often observed in alternative investment returns: autocorrelation, illiquidity, and nonlinearity.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 95). Wiley. Edición de Kindle.

Question 16

Autocorrelation

Answer 16

1. AUTOCORRELATION: Price changes through time for many alternative investments will not be statistically independent, in terms of both their expected direction and their level of dispersion. Autocorrelation is a major source of that statistical dependence. Short-term returns, such as daily returns, are sometimes positively autocorrelated if the assets are not rapidly and competitively traded. Many alternative investments, such as private equity and private real estate, cannot be rapidly traded at low cost. Further, when reported returns can be influenced by an investment manager, it is possible that the manager smooths the returns to enhance performance measures. Thus, autocorrelation of observed returns can exist and is often found. Positive autocorrelation causes longer-term returns to have disproportionately extreme values relative to short-term returns. The idea is that one extreme short-term return tends to be more likely to be followed by another extreme return in the same direction, to the extent that the return series has positive autocorrelation. The autocorrelated short-term returns can generate highly dispersed longer-term returns, such as the returns that appear to be generated in speculative bubbles on the upside and panics on the downside.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 95). Wiley. Edición de Kindle.

Question 17

Illiquidity

Answer 17

2. ILLIQUIDITY: Illiquidity of alternative investments refers to the idea that many alternative investments are thinly traded. For example, a typical real estate property or private equity deal might be traded only once every few years. Further, the trades might be based on the decisions of a very limited number of market participants. Observed market prices might therefore be heavily influenced by the liquidity needs of the market participants rather than driven toward an efficient price by the actions of numerous well-informed buyers and sellers. With a small number of potentially large factors affecting each trade, there is less reason to believe that the outcomes will be normally distributed and more reason to believe that extreme outcomes will be relatively common. ​In illiquid markets, prices are often estimated by models and professional judgments rather than by competitive market prices. Evidence indicates that prices generated by models or professional judgments, such as those of appraisers, tend to be autocorrelated. The resulting returns are smoothed and tend to exhibit less volatility than would be indicated if true prices could be observed.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (pp. 95-96). Wiley. Edición de Kindle.

Question 18

Non-linearity

Answer 18

NONLINEARITY: A simple example of an asset with returns that are a nonlinear function of an underlying return factor is a short-term call option. As the underlying asset’s price changes, the call option experiences a change in its sensitivity to future price changes in the underlying asset. Therefore, the dispersion in the call option’s return distribution changes through time as the underlying asset’s price changes, even if the volatility of the underlying asset remains constant. This is why a call option offers asymmetric price changes: A call option has virtually unlimited upside price change potential but is limited in downside price change potential to the option premium. The result is a highly nonsymmetric return distribution over long time intervals. A similar phenomenon occurs for highly active trading strategies (such as many hedge funds or managed futures accounts), which cause returns to experience different risk exposures through time, such as when a strategy varies its use of leverage.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 96). Wiley. Edición de Kindle.

Question 19

Jarque-Bera Test

Answer 19

Numerous formal tests for normality have been developed. One of the most popular and straightforward tests for normality is the Jarque-Bera test.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 97). Wiley. Edición de Kindle.

Question 20

Four Steps in the Jarque-Berta test

Answer 20

Select a confidence interval (e.g., 90%, 95%, 97.5%, 99%, or 99.9%).

Locate the corresponding critical value (e.g., 5.99 for 95% confidence). ​

Compute the JB statistic (using formula 4.36 and the sample skewness and excess kurtosis).

Compare the JB statistic to the critical value.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (pp. 97-98). Wiley. Edición de Kindle.

Question 21

GARCH

Answer 21

GARCH (generalized autoregressive conditional heteroskedasticity) is an example of a time-series method that adjusts for varying volatility.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 98). Wiley. Edición de Kindle.

Question 22

Heteroskedasticity

Answer 22

Heteroskedasticity is when the variance of a variable changes with respect to a variable, such as itself or time.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 98). Wiley. Edición de Kindle.

Question 23

Homoskedasticity

Answer 23

Homoskedasticity is when the variance of a variable is constant.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 98). Wiley. Edición de Kindle.

Question 24

Autoregressive

Answer 24

Autoregressive refers to when subsequent values to a variable are explained by past values of the same variable. In this case, autoregressive means that the next level of return variation is being explained at least in part by modeling the past variation, in addition to being determined by randomness. Casual observation of equity markets and other financial markets appears to support the idea that one day’s variation, or volatility, can at least partially determine the next day’s variation.

Chambers, Donald R.. Alternative Investments: CAIA Level I (Wiley Finance) (p. 99). Wiley. Edición de Kindle.

Question 25

Three Important Features of Beta

Answer 25

There are several important features of beta. First, it can be easily interpreted. The beta of an asset may be viewed as the percentage return response that an asset will have on average to a one-percentage-point movement in the related risk factor, ​such as the overall market.

The second feature of beta is that it is the slope coefficient in a linear regression of the returns of an asset (as the Y, or dependent variable) against the returns of the related index or market portfolio (as the X, or independent variable).

Third, because beta is a linear measure, the beta of a portfolio is a weighted average of the betas of the constituent assets. This is true even though the total risk of a portfolio is not the weighted average of the total risk of the constituent assets. This is because beta reflects the correlation between an asset’s return and the return of the market (or a specified risk factor) and because the correlation to the market does not diversify away as assets are combined into a portfolio.

Chambers, Donald R.; Anson, Mark J. P.; Black, Keith H.; Kazemi, Hossein. Alternative Investments: CAIA Level I (Wiley Finance) (p. 85). Wiley. Edición de Kindle.

Question 26

What is the name of the risk that can be removed via diversification called?

Answer 26

The risk that can be removed through diversification is called diversifiable, nonsystematic, unique, or idiosyncratic risk.

Chambers, Donald R.; Anson, Mark J. P.; Black, Keith H.; Kazemi, Hossein. Alternative Investments: CAIA Level I (Wiley Finance) (p. 84). Wiley. Edición de Kindle.