Week 6 Flashcards
What is the M^2 measure?
A variation of the Sharpe ratio, it measures the difference in the average return between the managed portfolio and the market benchmark portfolio, assuming they have equal portfolio volatility.
M^2 = return of hypothetical portfolio - return of market portfolio.
How do we make the managed and market benchmark portfolio have the same volatility for the M^2 measure?
Create a hypothetical portfolio made from t-bills and the managed portfolio such that the standard deviation of the hypothetical portfolio is equal to the managed portfolio weight * the managed portfolio standard deviation.
This weight will end up being the standard deviation of the market divided by the standard deviation of the managed portfolio.
What is a good value for M^2? How does our capital allocation line compare to the capital market line?
If M^2 is negative then our managed portfolio is underperforming the benchmark with the same standard deviation. Positive means overperformance. Our capital allocation line for the hypothetical/managed portfolio will have a smaller slope than the capital market line if it is underperforming, or higher if it is overperforming.
The intercept will be the same (risk-free rate)
What is the information ratio?
How can we work out an optimized sharpe ratio from this?
The information ratio is given by alpha of the portfolio divided by the standard deviation of the diversifiable risk.
The Sharpe ratio of the the optimized portfolio can be determined when we have an active and a passive portfolio. It is given by the sqrt(Sharpe ratio of market)^2 + (information ratio)^2).
What risk adjusted measurement of stock performance should we use?
Typically the Sharpe ratio is one of the best. If the evaluated portfolio is the total investment ratio then the Sharpe ratio or M^2 is most appropriate. If it is only part of the total investment portfolio then Jensen’s alpha or the Treynor ratio is more appropriate. If the evaluated portfolio is mixed (containing both active and passive portfolios), then the information ratio is most appropriate.
What does performance attribution do?
Decomposes portfolio returns into different components, asset allocation contribution, and security selection contribution.
How is performance attribution done?
- Set up a benchmark (“bogey”) portfolio investing in different asset markets and/or industries with a: target weight structure, a market index for each market and/or a market index for each industry.
- Calculate the return on the benchmark portfolio and managed portfolio (sum weights * category return).
- Explain difference in return between managed portfolio and benchmark.
- Summarize the differeneces in performance into appropriate categories.
How do we determine the performance attribution from asset allocation?
Sum of (excess managed weights of asset relative to benchmark * benchmark return).
How do we determine the performance attribution from security selection?
Sum of (excess return of category relative to benchmark * weight in managed portfolio).
