Performance analysis and attribution Flashcards
The manager is not worth the money/fees if:
A levered index position would have achieved a similar risk-return profile.
Ex ante rules (e.g. buy growth stocks) could have achieved a similar return
•How the manager can create superior returns:
How the manager can create superior returns:
–Skill-based active strategies: market timing, factor timing, stock selection
–Advanced infrastructure: research capacity, better market access and economies of scale, trading environment, etc.
Performance measures
Risk-adjusted Information ratio Jensen’s alpha Treynor ratio Sharpe ratio
Dollar- and time-weighted returns
Jeden return (1+g)^n = (1+r)^n +....
Dollar-weighted returns
Internal rate of return considering the cash flow from or to the investment
Returns are weighted by the amount invested in each period:
Abinsung Copuons Casflows
Adjusting returns for risk
The simplest and most popular way to adjust returns for risk is to compare the portfolio’s return with the returns on a comparison universe.
The comparison universe is a benchmark composed of a group of funds or portfolios with similar risk characteristics, such as growth stock funds or high-yield bond funds.
Sharpe ratio
〖𝑆𝑅〗_𝑝= (𝑟(𝑝)−𝑟(𝑓)/𝜎(𝑝)
Rendeite Portfolio - risk free rate
Sharpe’s measure divides average portfolio excess return over the sample period by the standard deviation of returns for a given period.
It measures the reward to (total) volatility trade-off, as it is the slope of the Capital Allocation Line (CAPM)
Mutual funds can be compared amongst each other and to the benchmark based on the SR
Risk-adjusted performance measures
Sharpe ratio
Vola = standart abweichung
Volatility is only the relevant risk measure if the investor has invested her total capital in the mutual fund. Otherwise, the investor should only take the risk contribution of the mutual fund to her total risk, i.e., the systematic risk (beta), into account.
If the CAPM fails, funds can achieve higher SR than that of the market
Risk-adjusted performance measures
M^2
Developed by Modigliani and Modigliani
Create an adjusted portfolio (P*) that has the same standard deviation as the market index.
Because the market index and P* have the same standard deviation, their returns are comparable:
Portfolie Rendite - Markt Rendite = M^2
Treynor’s measure
(𝑇𝑅)(𝑝)=(𝑟(𝑝)−𝑟𝑓)/𝛽(𝑝)
Like the Sharpe ratio, Treynor’s measure gives excess return per unit of risk, but it uses systematic risk instead of total risk.
Unterscheid Treynor und Shape ratio
Treynor= systematic risk , market risk Shape = Total risk
Jensen’s measure or Jensen alpha
𝛼(𝑝)= 𝑟(𝑝)−[𝑟𝑓+𝛽(𝑝) (𝑟(𝑀)−𝑟𝑓)]
If a fund is merely part of a larger portfolio or you need to decide how much you are willing to pay to an asset manager, you need a measure that is informative about the value added by the fund compared to your current portfolio (or the benchmark).
Jensen’s alpha measures the expected excess return of a mutual fund in comparison to an investment in the market portfolio.
If the CAPM holds you should hold the market portfolio and if the APT holds you should simply hold the portfolio of the respective factors.
Jensen’s Alpha is well suited for portfolios that have such a high diversification that idiosyncratic risk is negligible.
Information ratio or Appraisal ratio
〖𝐼𝑅〗𝑝=𝛼(𝑝)/(𝜎(𝑒(𝑝))
unsystematic risk.
idiosyncratic
Morningstar Risk-adjusted Return (MRAR)
MRAR(γ)=[1/T ∑_(t=1)^T▒((1+r_t)/(1+r_ft ))^(−γ) ]^(12/γ)−1
