47. Analysis of Active Portfolio Management Flashcards
3 Necessary Benchmark Qualities
- The benchmark is representative of the assets from which the investor will select.
- Positions in the benchmark portfolio can actually be replicated at low cost.
- Benchmark weights are verifiable ex ante, and return data are timely ex post.
Value added aka active return
RA=RP-RB
Value added from asset allocation
Value added from security selection
The risk– return trade-off of a portfolio can be represented in either ______ or _______ terms.
absolute or relative
Sharpe Ratio
The Sharpe ratio is used to compare the absolute portfolio return in excess of a riskless rate with the volatility of the portfolio return. The ratio provides a measure of how much the investor is receiving in excess of a riskless rate for assuming the risk of the portfolio.
Leverage created by borrowing risk-free cash and investing in risky assets also does not affect the portfolio’s Sharpe ratio.
An important property is that the Sharpe ratio is unaffected by the addition of cash or leverage in a portfolio.
Excess return/excess risk
Two-fund separation
The proposition that, independent of preferences, investors should form portfolios using two funds— one of which is the risk-free asset and the other the risky asset portfolio with the highest Sharpe ratio.
Information Ratio
The information ratio tells the investor how much active return has been earned, or is expected to be earned, for incurring the level of active risk. Active return, RA, is the difference between the managed portfolio return, RP, and the benchmark portfolio return, RB.
Unlike the Sharpe ratio, the information ratio is affected by the addition of cash or the use of leverage.
Active return/active risk
Relationship bw Sharpe & Information Ratios
The squared Sharpe ratio of an actively managed portfolio is equal to the squared Sharpe ratio of the benchmark plus the information ratio squared: The equation implies that the active portfolio with the highest (squared) information ratio will also have the highest (squared) Sharpe ratio.
For any given asset class, an investor should choose the manager with the highest expected skill as measured by the information ratio, because investing with the highest information-ratio manager will produce the highest Sharpe ratio for the investor’s portfolio..
Level of active risk that leads to the optimal result
Total risk of active portfolio
Correlation Triangle
Information Coefficient
Signal quality is measured by the correlation between the forecasted active returns, μi, at the top of the triangle, and the realized active returns, RAi, at the right corner, commonly called the information coefficient (IC).
Transfer Coefficient
The correlation between any set of active weights, Δwi, in the left corner, and forecasted active returns, μi, at the top of the triangle, measures the degree to which the investor’s forecasts are translated into active weights, called the transfer coefficient (TC).
Grinold Rule
μi = ICσiSi
where IC is the expected information coefficient and Si represents a set of standardized forecasts of expected returns across securities, sometime called “scores.”
Mean– variance-optimal active security weights for uncorrelated active returns, subject to a limit on active portfolio risk, are given by:
Using the Grinold rule, mean– variance optimal active weights are:
Information Coefficient eq
IC is the ex ante risk-weighted correlation
Expected active portfolio return
Information ratio of unconstrained optimal portfolio
