# 5. Measures of risk and performance Flashcards

## Practice questions

- What are the two main differences between the formula for variance and the formula for semivariance?

• The semivariance uses a formula otherwise identical to the variance formula except that it only includes the negative deviations in the numerator and a smaller number of observations in the denominator.

- What is the main difference between the formula for semistandard deviation and target semistandard deviation?

• Target semivariance is similar to semivariance except that target semivariance substitutes the investor’s target rate of return in place of the asset’s mean return.

- Define tracking error and average tracking error

- 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.
- Average tracking error simply refers to the average difference between an investment’s return relative to its benchmark. In other words, it is the numerator of the information ratio.

- What is the difference between value at risk and conditional value-at-risk?

- Value at risk (VaR or 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.
- Conditional value-at-risk (CVaR), also known as expected tail loss, is the expected loss of the investor given that the VaR has been equaled or exceeded. CVaR will exceed VaR (if the overall maximum potential loss exceeds the VaR).

- Name the two primary approaches for estimating the volatility used in computing value-at-risk.

- Estimate the standard deviation (volatility) as being equal to the asset’s historical standard deviation of returns
- Estimate volatility based on the implied volatilities from option prices

- What are the steps involved in directly estimating VaR from historical data rather than through a parametric technique?

• Collect the percentage price changes

• Rank the gains/losses from the highest to the lowest

• Select the outcome (loss) reflecting the quantile specified by the VaR (e.g., for a VaR based on

95% confidence pick the observation with a loss larger than 95% of the other outcomes).

- When is Monte Carlo analysis most appropriate as an estimation technique?

• It is best used in difficult problems where it is not practical to find expected values and standard deviations using mathematical solutions.

- What is the difference between the formulas for the Sharpe and Treynor ratios?

• The Treynor ratio differs from the Sharpe ratio by the use of systematic risk rather than total risk in the denominator.

- Define Return on VaR.

• Return on VaR (RoVaR) is simply the expected or average return of an asset divided by a specified VaR (expressing VaR as a positive number):

- Describe the intuition of Jensen’s alpha.

• 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.

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.

Information ratio

has a numerator formed by the

difference between the average return of a portfolio (or other

asset) and its benchmark, and a denominator equal to its

tracking error: Information Ratio = [E(Rp) − RBenchmark]∕TE

where E(Rp) is the expected or mean return for portfolio p,

RBenchmark is the expected or mean return of the benchmark,

and TE is the tracking error of the portfolio relative to its

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.

Maximum drawdown

is defined as the largest decline over

any time interval within the entire observation period.

parametric VaR

A VaR computation assuming normality and using the

statistics of the normal distribution is known as this.