what is the purpose of performance measurement?
- identify superior managers
- compensate managers
- understand sources of return
what is the formula for the sharpe ratio?
= ( RP - Rf )/stdv of portfolio
what does the sharpe ratio tell us?
- optimising investment (highest abnormal returns for lowest SD, compare to benchmark)
- the higher the better
what is the formula for the treynor ratio?
( RP - R of BM)/Beta
what does the treynor ratio tell us?
- best performing fund (differences due to level
of diversification and systematic risk) - the higher the better
Used primarily in identifying portfolios with similar levels of systematic risk- exposure to a particular market/ market risk
what is the formula for Jensen’s alpha?
α = RP- [Rf + beta (RM–Rf)]
what does Jensen’s alpha tell us?
-tells us the level of abnormal returns
-higher is better
Used primarily in identifying portfolios with similar levels of systematic risk.
what is the formula for Tracking error?
TE= difference in standard deviation x sqrt (payment periods in a year)
what does Tracking error tell us?
- active risk, extra risk taken to generate abnormal returns
- higher is not always better, (could be negative returns)
what is the formula for the information ratio?
=(RP - Rf)/Tracking Error
= Active Return/Active Risk
= α / σε
what does the information ratio tell us?
- exposure to abnormal returns, if same TE but higher info ratio, this means they have higher abnormal returns
- The higher the better
- A ratio of 0.5 is considered good performance.
- Presumes that Tracking Error is the key risk
which performance measurement requires a two tailed test to test significance?
Jensen’s alpha
how is the t-stat calculated?
significant at 5% value?
= α - Ho/SE(α)
= -1.96 or 1.96 or both
What is the allocation affect? which skills does this reflect?
understanding the correct weights to use for a particular market segment
- market timing skills
What is the selection effect? which skills does this reflect?
understanding if the correct choice of assets was made within each market segment
- Security selection skills
How is allocation effect calculated?
Sum of all (asset delta weights (Portfolio-BM)) x (R of BM for asset)
How is selection effect calculated?
Sum of all ((R Portfolio- R BM) x W of portfolio)
whats another way ( RP - Rf) may be shown?
mean (mu)
