Risk Management And Investment Management Flashcards
Risk premium of the market
- E(rm) - rf is the market risk premium
- γ is the risk aversion of the “average” investor
Security Market Line (SML)
Beta
Tracking Error
Information Ratio
Is the ratio of alpha to tracking error
Sharpe Ratio
Grinold’s “fundamental law” of active management
Marginal VaR
- VaR is the portfolio VaR
- W is the portfolio value
- The change in portfolio VaR resulting from taking an additional dollar of exposure to a given component. It is also the partial (or linear) derivative with respect to the component position
Undiversified VaR
The sum of individual VaRs, or the portfolio VaR when there is no short position and all correlations are unity
Incremental VaR
- Evaluates the total impact of a proposed trade on portfolio p
- The change in VaR owing to a new position. It differs from the marginal VaR in that the amount added or subtracted can be large, in which case VaR changes in a nonlinear fashion
Individual VaR
The VaR of one component taken in isolation
Component VaR
- VaRi = wi * σi * α(95%)
- CVaRi = ρi,p * VaRi
- A partition of the portfolio VaR that indicates how much the portfolio VaR would change approximately if the given component was deleted. By construction, component VaRs sum to the portfolio VaR
Vector Beta
Relationship between the marginal VaR and Beta
Component VaR relation to total VaR and correlation of asset i
Percent contribution to VaR of component
The ratio of individual returns to Betas of the optimal portofolio are equal
- Ei = expected return of asset i
The individual Betas of the global minimum portofolio are equal
Active return decompositon
- wi is the weight on fund i with return Ri
- Rib represents the return on the benchmark for fund i, and wib
Maximizing the portfolio information ratio subject to a fixed TEV (Tracking Error Volatility)
- wi = tracking error volatility of manager i
- xi = the fraction of the portfolio invested with manager i
Liquidity duration for security i
Modified Dietz method
Risk-adjusted performance measures
M2 measure purpose
- To compute M2, an active portfolio is mixed with a position in T-bills so that the resulting “adjusted” portfolio matches the volatility of a passive market index
- Because the market index and portfolio have the same standard deviation, we may compare their performance simply by comparing returns
Treynor ratio purpose
- When employing a number of managers, nonsystematic risk will be largely diversified away, so systematic risk becomes the relevant measure of risk.
- The appropriate performance metric when evaluating potential components of the full risky portfolio is now the Treynor measure: this reward-to-risk ratio divides expected excess return by systematic risk (i.e., by beta).
When a portfolio is optimally combined with a baseline indexed portfolio, the improvement in the Sharpe measure will be determined by its information ratio
- H = hedge fund
Application of the Sharpe, Treynor and Information ratio
Relationship between alpha and the Sharpe, Treynor and Information ratio
Systematic Variance
Correlation coefficient between a portfolio and the market index using systematic risk
- σe = non-systematic risk
t-statistic of the alpha estimate
- SCL = security characteristic line
MV(Perfect timer per $ of assets)
MV(Imperfect timer per $ of assets)
- P1 the proportion of the correct forecasts of bull markets and P2 the proportion for bear markets
Quadratic programming portfolio construction
Quadratic programming requires many more inputs than other portfolio construction techniques because it entails estimating volatilities and pairwise correlations between all assets in a portfolio. Quadratic programming is a powerful process but given the large number of inputs and the less than perfect nature of most data, it introduces the potential for noise and poor calibration.
Linear programming portfolio construction
Linear programming does not necessarily select the portfolio with the lowest level of active risk. Rather, it attempts to improve on stratification by introducing many more dimensions of risk control and ensuring that the portfolio approximates the benchmark for all these dimensions.
Screening portfolio construction
The screening technique strives for risk control by including a sufficient number of stocks that meet the screening parameters and by weighting them to avoid concentrations in any particular stock. However, screening does not necessarily select stocks evenly across sectors and can ignore entire sectors or classes of stocks if they do not pass the screen. Therefore, risk control in a screening process is fragmentary at best.
Stratification portfolio construction
Stratification separates stocks into categories (for example, economic sectors) and implements risk control by ensuring that the weighting in each sector matches the benchmark weighting. Therefore, it does not allow for overweighting or underweighting specific categories.
Combined VaR of 2 positions
Surplus confidence interval
- = Expected surplus - (α * volatility of the suplus)
- α = z-score of the confidence level
- A two-tailed confidence interval is used when looking for the lower-bound of the entire confidence interval
How to correct the low correlation of illiquid assets using monthly data
Artificially low asset class correlations leading to the appearance of low systematic risk is a bias faced by hedge funds with illiquid holdings that use monthly valuation data. One way to correct for this is to use enlarged regressions with additional lags of the market factors and to sum the coefficients across lags
M2 formula
MVaR in terms of σpBi,p and σiρi,p
