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Index models - The single index model

12 important questions on Index models - The single index model

What is the intercept of the regression equation denoted by Alpha?

This is the security's expected excess return when the market excess return is zero.

What is the security beta?

It is the slope coefficient, the security's sensitivity to the index: it is the amount by which the security return tends to increase or decrease for every 1% increase or decrease in the return on the index.

What is the systematic risk premium?

We call this the systematic risk premium because it derives from the risk premium that characterizes the entire market, which proxies for the condition of the full economy or economic system.

What is the nonmarket premium?

The remainder of the risk premium is given by the first term in the equation, Alpha, which is a nonmarket premium.

When is an alpha non zero?

Alpha may be large if you think a security is underpriced and therefore offers an attractive expected return. If managers believe that they can do a superior job of security analysis, then they will be confident in their ability to find stocks with nonzero values of alpha.

What does Alpha i mean?

The stock’s expected return if the market is neutral, that is, if the market’s excess return, rM - rf, is zero

What does ßi(rm - rf) mean?

The component of return due to movements in the overall market; ßi is the security’s responsiveness to market movements

What does ß^2i stdev^2m mean? (Schrijf het uit)

The variance attributable to the uncertainty of the common macroeconomic factor

What are the two advantages of the single index model to the Markovitz model?

First, for large universes of securities, the number of estimates required for the Markowitz procedure using the index model is only a small fraction of what otherwise would be needed. Second, the index model abstraction is crucial for specialization of effort in security analysis. If a covariance term had to be calculated directly for each security pair, then security analysts could not specialize by industry.

What is the cost of using the single-index model?

The “cost” of the model lies in the restrictions it places on the structure of asset return uncertainty. The classification of uncertainty into a simple dichotomy—macro versus micro risk—oversimplifies sources of real-world uncertainty and misses some important sources of dependence in stock returns. For example, this dichotomy rules out industry events, events that may affect many firms within an industry without substantially affect- ing the broad macroeconomy.

When can the optimal portfolio derived from the single index model be significantly inferior to the Markovitz model?

When stocks with cor- related residuals have large alpha values and account for a large fraction of the portfolio.

Why is the idiosyncratic risk component diversifiable?

The ei s are independent, and all have zero expected value, the law of averages can be applied to conclude that as more and more stocks are added to the portfolio, the firm-specific components tend to cancel out, resulting in ever-smaller nonmarket risk. Such risk is thus termed diversifiable.

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Index models - The single index model

12 important questions on Index models - The single index model

What is the intercept of the regression equation denoted by Alpha?

What is the security beta?

What is the systematic risk premium?

What is the nonmarket premium?

When is an alpha non zero?

What does Alpha i mean?

What does ßi(rm - rf) mean?

What does ß^2i stdev^2m mean? (Schrijf het uit)

What are the two advantages of the single index model to the Markovitz model?

What is the cost of using the single-index model?

When can the optimal portfolio derived from the single index model be significantly inferior to the Markovitz model?

Why is the idiosyncratic risk component diversifiable?

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