Chap 7 - Measures of Risk and Performance

Question 1

What is Variance and standard deviation ?

Answer 1

Definition
* Classic measure of total risk
* Not necessarily the best measure for alternative investments

Question 2

What is Variance ?

Answer 2

Variance, as a symmetrical calculation, is an expected value of the squared deviations, including both negative and positive deviations.

Question 3

What is semmi-variance ?

Answer 3

The semivariance uses a formula otherwise identical to the variance formula except that it considers only the negative deviations inside the summation. Semivariance provides a sense of how much variability exists among losses or, more precisely, among lower-than-expected
outcomes.

Question 4

How to calculate Semistandard deviation ?

Answer 4

Semistandard deviation, sometimes called semideviation, is the square root of semivariance.

Question 5

What is semivolatility ?

Answer 5

Semivolatility has been proposed as an improved measure of risk compared to semistandard deviation. Semivolatility is similar to semistandard deviation except that
it is unambiguously based on only the number of observations below the mean or
threshold (T*) and it subtracts 0.5, rather than 1.0, from that number.

where T∗ is the number of observations less than the mean (or threshold).

Question 6

What is Shortfall risk ?

Answer 6

Shortfall risk is simply the probability that the return will be less than the investor’s target rate of return.

Question 7

What is Target semivariance ?

Answer 7

Target semivariance is similar to semivariance except that target semivariance
substitutes the investor’s target rate of return in place of the mean return. Thus, target semivariance is the dispersion of all outcomes below some target level of return
rather than below the sample mean return.

Question 8

How to callculate Target semistandard deviation (TSSD) ?

Answer 8

Target semistandard deviation (TSSD) is
simply the square root of the target semivariance.

Question 9

When the target is the mean, target semivariance equals semivariance. A very high target return eliminates only the highest outcomes, whereas a very low target eliminates most of the outcomes. The target should typically be set equal to the investor’s target rate of return, such as the minimum return consistent with achieving
the investor’s goals.

Answer 9

True

Question 10

What is Tracking error ?

Answer 10

Tracking error indicates the dispersion of the returns of an investment relative to a benchmark return, where a benchmark return is the contemporaneous realized
return on an index or peer group of comparable risk. Although tracking error is sometimes used loosely simply to refer to the deviations between an asset’s return and the benchmark return, the term tracking error is usually defined as the standard
deviation of those deviations.

Question 11

Since tracking error is formed based on deviations from a benchmark
rather than deviations from its own mean, it is an especially useful measure of the dispersion of an asset’s return relative to its benchmark. Therefore, whereas standard
deviation of returns might be used for an asset with a goal of absolute return performance, tracking error might be used more often for an asset with a goal of relative return performance.

Answer 11

True

Question 12

What is a Drawdown ?

Answer 12

Drawdown is defined as the maximum loss in the value of an asset over a specified time interval and is usually expressed in percentage-return form rather than currency.

Question 13

What is a Maximum drawdown ?

Answer 13

Maximum drawdown is defined as the largest decline over any time interval within the entire observation
period.

For example, an asset might be
said to have experienced a maximum drawdown of 33% since 1995 (for example,
between 2000 and 2002), with individual drawdowns of 23% in 2000 and 14% in
2007.

Question 14

What is Value at riskk (VaR) ?

Answer 14

Value at risk (VaR) is the loss figure associated with a particular percentile of a cumulative loss function. In other words, VaR is the maximum loss over a specified time period within a specified probability.

Question 15

What are the two parameters for the Value at Risk ?

Answer 15

The specification of a VaR requires two parameters:
1. The length of time involved in measuring the potential loss
2. The probability used to specify the confidence that the given loss figure will not be exceeded

Question 16

Example of VaR ?

Answer 16

We might estimate the VaR for a 10-day period with 99% confidence as
being $100,000. In this case, the VaR is a prediction that over a 10-day period, there is a 99% chance that performance will be better than the scenario in which there is a $100,000 loss. Conversely, there is a 1% chance that there will be a loss in excess of $100,000, but VaR does not estimate the expected loss or maximum possible loss in extreme scenarios.

Question 17

what is a Conditional value-atrisk (CVaR) or tail expected loss ?

Answer 17

Conditional value-atrisk (CVaR), also known as expected tail loss, is the expected loss of the investor given that the VaR has been equaled or exceeded. Thus, if the VaR is $1 million, then the CVaR would be the expected value of all losses equal to or greater than $1 million. The CVaR provides the investor with information about the potential magnitude of losses beyond the VaR.

Question 18

The VaR provides a first glance at risk. It can be computed for a single risk exposure (such as a single security), for a portfolio, for an entire division, or for the entire firm. Numerous entities request or require the reporting of VaR, and they test through time whether a fund’s reported VaR is consistent with the actual risk that is experienced. The VaR is especially useful in situations in which a worst-case analysis makes no sense, such as in derivatives, where some positions have unlimited downside risk.

Answer 18

True

Question 19

What is a parametric VaR ?

Answer 19

A VaR computation assuming normality and using the statistics of the normal distribution is known as parametric VaR.

Question 20

Formula of parametric VaR ?

Answer 20

Parametric VaR = N × σ√Days × Value

N is the number of standard deviations, which depends on the confidence level
that is specified.
σ is the estimated daily standard deviation expressed as a proportion of price
or value (return standard deviation).
Value is the market value of the position for which the VaR is being computed.
For example, it might be the value of a portfolio.

Question 21

What is a Peer benchmarks ?

Answer 21

Peer benchmarks are based on the returns of a comparison or peer group. The peer group is typically a group of funds with similar objectives, strategies, or portfolio holdings. The group may include virtually all possible comparison funds, known as a
universe group, or a sampling.

Question 22

What is Performance attribution ?

Answer 22

Performance attribution, also known as return attribution, is the process of identifying the components of an asset’s return or performance. Performance attribution seeks to separate the total return of an investment into quantities that can be linked to various determinants such as market factors (e.g., the return of one or more indices) and managerial factors (e.g., market timing and superior asset selection).

Benchmarking is a simpler, popular, and practical form of attributing return.

Question 23

How does benchmarking work ?

Answer 23

In benchmarking, the return of an asset is simply divided into two components:
the benchmark return and the active return. The active return is the deviation of an asset’s return from its benchmark. The benchmark’s return is subtracted from the asset’s return for the same time period to form the active return. In effect, the benchmark return is attributed to the systematic performance of the asset, and the active return is attributed to the idiosyncratic performance of the asset.

Question 24

What is Jensen’s alpha ?

Answer 24

Jensen’s alpha is a direct measure of the absolute amount by which an asset is estimated to outperform, if positive, the return on efficiently priced assets of equal systematic risk in a single-factor market model.

Question 25

What is the information ratio ?

Answer 25

The information ratio is the amount of added return, if positive, that a portfolio generates relative to its benchmark for each percentage
by which the portfolio’s return typically deviates from its benchmark.

Question 26

What is the Treynor ratio ?

Answer 26

Treynor ratio is designed to compare
well-diversified investments and to compare investments that are to be added to a well-diversified portfolio. But the Treynor ratio should not be used to compare poorly diversified investments on a stand-alone basis.
The Treynor ratio offers the intuition of estimating the excess return of an investment relative to its systematic risk.

Question 27

What is the Sortino ratio ?

Answer 27

The Sortino ratio uses the concept of a target rate of return in expressing both the return in the numerator and the risk in the denominator. Sortino ratio is the use of downside risk rather than
the use of a target rate of return. To the extent that a return distribution is nonsymmetrical and the investor is focused on downside risk, the Sortino ratio can be useful as a performance indicator

Question 28

What is the M2 approach ?

Answer 28

The M2 approach, or M-squared approach, expresses the excess return of an investment after its risk has been normalized to equal the risk of the market portfolio.