Define Alpha and the TE with the return excess of a Benchmark

Alpha: Average Return Excess

TE: Standard Deviation of the Return Excess

How do active portfolio managers react on market booms and downturns?

The adjust the active beta

Boom -> Beta > 0

Downturn -> Beta < 0

What is “Jensens alpha” and what does it include?

It is the excess return adjusted by the systematic risk. It includes fraction of return which does not correlate with the benchmark return and idicates the selction and allocation strategies.

What is the difference between absolute and relative optimization?

Absolute

Based on total return and total risk

Relative

Same as absolute but with a strict benchmark perspective

Benchmark reflects market expectations and is defined independend from the managers expectation

Define the TAA

TTA is a short-midterm decision the deviate from the strategy portfolio to outpeform the benchmark

How should the active management return be in terms for the market equilibrium?

The aggregate return of the active management cannot be positive. After correcting the transaction costs, the average return should be below the benchmark.

What does a high TE in terms or risk mean?

The higher the TE, the higher the idiosyncratic risk.

State the formula for the market portfolio benchmark

How can we decompose the beta in the market portfolio benchmark?

The Benchmark Beta is always 1.

What is the formula for the information ratio?

What happens with the information ratio, if the benchmark is the risk free rate?

It coincides with the sharpe ratio

What is the relationship between the information ratio and the invesment options of a manager?

The Investment Options of a Manager a restricted by the residual frontier. This is the slope of the IR.

How do we interpret an increasing IR Ratio?

His forecasting skills are increasing

What is the formula of the “fundamental law of active management”?

Define the formula

IC -> Info Coefficient represents the manager skills

BR -> Breadth is the numbe rof independent investments decisions per year

In the “fundamental law of active management”, which strategy dominates in terms of

market timing vs a-priori selection?

The Selection dominates, because a low forecasting skill can be compesate with with a large number of forecasts. Therefore, a good forecasting skill cannot compesate a relative low number of forecasts.

How do we calculate the “mean squared forecast error”?

How do we measure our “out of sample” RSquared? How do we interpert the outcome?

If our outcome is negative, our prediction has a higher MSFE than the historical average. Therfore our predicitons are not good

What happens with the premium, if everyone is trying to time the market?

The premiums will disappear

How does the TAA outperform a Benchmark?

Selection

Under or overweighting of a single assets

Allocation

Under or overweighting of asset classes

Market-timing

What is the trade off function? Define each component

a -> Excess Return

TE -> Standard Deviation

Y -> Riskaversion of the residual risk

What is the relationship of VA(P) and IR?

The VA is limited by the IR. If The IR Increases -> Forecasting Skills of a Manager increases. Therefore we could generate a higher trade off for our VA function

Why is it not possible to use the selection strategy in the “fundamental law of market Management ” infintley?

transactions costs

IC is constant, marginal researches are decreasing.

State the formula for managerial skills

Market-Timing + Jensen alpha

Is Equity Risk Premium predictable?

Yes, but only a small predictability. Even in a efficient Market. Equity Risk Premium are predictable due to the ecomoic state. If Prices drop -> we Excpect that Returns in the futue will be high

But a large predictability in the stock market could be signal for market ineffecieny

How should a Portfolio Manager behave if he dont have forecasting skills?

In this case, the Manger should hold the benchmark portfolio

Define the alpha in terms of the benchmark excess returns

State the Market Timing Formula

State the Formula for the expected excess retrun from Grinold and Kahn (2000). Please describe the components

What is the difference between the IR Formula and the Law of active management?

The Law of active management ist only an approximation of the IR.

What is the predictive regression model to forecast stock returns?

X is the variable to predict equity risk premium

Rt is the return in excess of the risk free rate

Why is the stock market like an insruce market?

If Investors buy high and sell low due to their risk aversion, they paid a premium. Therefore the buyer will get the premium because he expect high returns.

“If predictability is real, it is likely to persist”. Please describe this statement

If High Returns are results from high risk, Investor will recognize these chances but are afraid of it. Investor will not change their portfolio and the high returns will remain

“If it is truly irrational, or a market inefficiency, it is least likely to persist.”

If Highe Returns do not have higher risks and are decisions are easy, many investors will change their portfolio and invest in the opportunity

News react Quickly and Investors react quickly and the investment opportunity will vanish

How does the residual risk change in terms of the VA Formula?

It increases with managers capabilty and decreases with investors risk aversion

How much should be predictable in terms of R Squared

< 1% Monthly

What is teh Null-Hypothesis of 𝑀𝑆𝐹𝐸-adjusted statistics, based by Clark and West

The historical MSFE is less or equal than the predictive MSFE.

If we assume a random walk, how should our Beta and RSquared be in a predictive regression model?

In the random walk, returns are not predictable. Therefore our beta and RSquared should be zero

How can we improve our MSFE?

Campbell and Thompson (2008)

We can improve if we restrict the coefficients, for example the Equity Premium cannot be negative

Rhapach and Zhou

Diffusion indices

Macro and technical predictors can improve our predictability

What did Rapach, Wohar, and Rangvid (2005) shows in terms of MSFE?

Interes Rate are the most reliable predictors for stock market

What did Rapach, Strauss, and Zhou (2013) show in theri study in terms of MSFE? Please state also their arguements

Lagged US Returns delivers gains for non US-Countries. Reasons for that are

US is a large trading partner

US Stock ist the largest and most liquid stock market

What are the pefromance component of the return decomposition?

Selectivity

Timing

Strategy

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