# Tag Info

Accepted

### Philosophical Question about Factor Models

This is actually a rather involved question, and different interpretations exist. A narrow, linear algebra based interpretation is that the stochastic discount factor lies in the linear span of the ...
• 6,954
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### Calculating alpha and its meaning

Alphas from a time-series regression are error terms in the cross-sectional, linear relationship between expected returns and factor betas. If a factor model were correct those error terms (the alphas)...
• 6,954
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### Is market price of risk always negative?

Summary Yes, the market price derived from the moments of the SDF is negative. Assets pay high returns (are risky) if they negatively correlate with the SDF (and thus positively correlate with ...
• 16k
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### Fama-French factor model: why mimicking portfolios?

The innovation of Fama and French's Three Factor Model wasn't in finding book to market ratios forecast returns but in reconciling that empirical regularity with the standard framework of macro-...
• 6,954
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### Excess, Residual and Active Return

Active return: $R-R_m$ i.e. your security (or portfolio) compared to the market portfolio. Used to judge performance before the CAPM was invented Excess return: $R-R_f$ the security compared to the ...
• 11.4k

### Definitions of Beta

I slightly disagree with Alex’s comment. The CAPM does not read as \begin{align*} r_{i,t} = r_{f,t}+ \beta_{i} (r_{m,t}-r_{f,t}) + \varepsilon_{i,t}. \end{align*} There is an important difference ...
• 16k
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### Difference between CAPM and single index model

As you know the equation that describes them is the same. The single index model is an empirical description of stock returns. You do some regressions using data and you come up with Alphas, Betas ...
• 11.4k
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### How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?

To be consistent with the average daily returns that you specified, your first strategy would need to have a daily standard deviation of 31,749 USD and the second a standard deviation of 7,937 USD. ...
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### How high can Beta be in CAPM?

Infinity is rather non-sensical. A better question perhaps is whether you can put some theoretical bounds on an asset's market beta. An asset's volatility bounds its market beta Let $R_i$ be the ...
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### Is CAPM a cross sectional or time series model?

To answer your question directly: CAPM is a cross-sectional model, and is NOT a time series model. CAPM aims at explaining variance of single asset's return by overall market return of the same ...
• 712
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### CAPM model as a regression

If you really believed the CAPM's prediction that $\alpha=0$, then imposing $\alpha=0$ in your estimation would indeed lead to your 2nd formula. The problems? The CAPM doesn't work so imposing a ...
• 6,954
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### How are modern portfolio theory (MPT) and CAPM related?

CAPM states that the expected return of any given asset should equal $ER_i=R_f+β_i (R_m-R_f)$, with α being the error term of the previous equation. Now, as α has an expected value of zero, then only ...
• 516
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### Inverse Covariance Matrix Transformation from CAPM

This is the result of the Sherman-Morrison inversion for the sum of an invertible matrix and an outer product. You will find this (and many other helpful methods) in the Matrix Cookbook. Specifically, ...
• 6,663
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### Mathematical Derivation of Residual Risk

Note that $\beta$ is the coefficient of the portfolio regressed on the benchmark. That is \begin{align*} r_P = \alpha+\beta r_B + \varepsilon, \end{align*} where $\varepsilon$ is the residual. The ...
• 21.1k

### What mechanisms does the market use to brining an asset back to the market line, as defined by CAPM?

Supply and Demand That's a great question and your question has a simple answer. @Daneel showed you the maths'' behind it. It boils down to: if an asset has too high returns than the CAPM predicts, ...
• 16k
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### utility function and CAPM in portfolio theory

Please have a look at this image, which I have copied from here: Here, the point M is the tangency portfolio of the capital market line. As you can see, the investor A (left hand side) can attain ...
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### How to use factor models for prediction?

You kinda mentioned in your questions, but the predictive model is essentially a lagged version of the "factor model". Part of the problem comes from the subscripts, the model itself doesn't really ...
• 712
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### CAPM - Expected vs. actual returns

Based on your comments on other answers, i would like to provide you a summary on the difference of the CAPM-Alpha and Jensen's-Alpha. CAPM The CAPM is an economic model for asset pricing. It states ...
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### CAPM yields very poor fit (low R-squared). Is that normal?

Question 1 There may be at least two reasons for this (aside from possible programming errors or poor data): The model is actually a very poor approximation of reality, as Matthew Gunn indicates in ...
• 3,156
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### how can we know the residual return will be uncorrelated with the market return

Let us ignore the riskless rate for simplicity of the presentation. If you have (historical or simulated) return series $r_i$ for the portfolio and $r_i^M$ for the market, then the beta is the OLS ...
• 13.7k
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### What are the assumptions in the first-stage of Fama-MacBeth (1973)?

The CAPM is an economic theory that expected returns in excess of the risk free rate should be linear in the regression beta on the market.  \operatorname{E}[R_i - R^f] = \beta_i \operatorname{E}[R^...
• 6,954
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### Finding a minimum variance portfolio when using a regulariser?

You're not going to get an analytic formula except in special cases of function $\rho(x)$. And you're probably going to want $\rho$ convex. If $\rho$ is convex, the problem is a convex optimization ...
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