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market timing involves

portfolio managers shitfing funds between a market-index portfolio and a safe asset depending if the market index is expeted to outperform the safe asset

- trying to predict future market movements 


style analysis involves:

Regressing fund returns on multiple indexes representing a range of asset classes;

  Using the regression coefficient for each index to make inferences regarding the allocation to that style; and,


Timing ability is indicated by

the curvature of the plotted line.

  • Lines that become steeper show good timing ability.
  • The steeper slope shows that the manager maintained higher portfolio sensitivity to market swings (i.e., a higher beta) in periods when the market performed well. This ability to choose more market-sensitive securities in anticipation of market upturns is the essence of good timing.
  • In contrast, a declining slope as you move to the right means that the portfolio was more sensitive to the market when the market did poorly and less sensitive when the market did well. This indicates poor timing.


With respect to historical investment performance

and future 


Geometric is better

Arithmetic is better


geometric is always less than arithmetic


when is sharpe ratio appropriate?

when it is the only risky asset held by the investor i.e. invest in T-Bill and the risky portfolio

it represents their entire risky investment fund


when is treynor appropriate

when this is one of the many stocks that the investor is analysing to form an acively managed stock portfolio

one of the many portfolios combined in the a large investment portfolio


If the stock is mixed with the index fund,

investment is an active portfolio to be mixed optimally with a passive market-index portfolio

the contribution to the overall Sharpe measure is determined by the information ratio;


graph of M^2


process of performance evaluation is complicated by several factors 

statistical inferences.

Specifically, many observations are needed in order to conclude that results are significant and not the result of noise;


process of performance evaluation is complicated by several factors 

distribution of portfolio returns has the potential to change.

It is reasonably safe to assume that the mean and variance of returns stemming from passive management strategies are constant over short return intervals; but,

Making this assumption is dangerous for active strategies, where managers deliberately change the composition of their portfolios based on ongoing financial analysis. Indeed, assuming constant mean and variance of returns for active portfolios can lead to incorrect conclusions


process of performance evaluation is complicated by several factors

 Survivorship bias

underperforming funds will tend to be closed down, leaving only more successful ones to be evaluated / serve as performance benchmarks.


if the investor:

Was able to correctly time the market and shift funds into the asset with the stronger expected performance,

the portfolio would have a higher beta and excess return in a bull market than it would in a bear market, meaning the SCL would be curved, and would have an increasing slope.



a manager who does no timing,

but simply maintains a high beta, will do better in up markets and worse in down markets