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28 votes
Accepted

What are reasons not to do factor investing in equity markets?

This question goes to whether the historical returns to factors represent: Spurious results, overfitting, data mining... Mispricing Unexploitable effects Compensation for risk Case 1: Spurious ...
Matthew Gunn's user avatar
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14 votes
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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)...
Matthew Gunn's user avatar
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13 votes

Choosing the right statistical test for Mutual Fund Performance Evaluation

Define excess return $r^x_{it} = r_{it} - r^f_{t}$ as the return $i$ minus the risk free rate, and $f_{jt}$ similarly denotes the excess return of factor $j$ at time $t$. Let's say we have some factor ...
Matthew Gunn's user avatar
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13 votes
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cvxpy portfolio optimization with risk budgeting

The underlying problem: your ACTR constraints aren't convex The $i$th constraint on your risk contribution can be written: $$ w_i \sum_j \sigma_{ij} w_j \leq c_i s$$ And this isn't a convex ...
Matthew Gunn's user avatar
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11 votes
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What is the total correlation between assets in a portfolio?

This is indeed an interesting question. According to this website, a paper by Goldman Sachs [Tierens and Anadu (2004)] proposes three alternative methods for estimating average stock correlations: ...
vonjd's user avatar
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10 votes

Hedging Covid-19 and other low probability high loss risks

There's no easy answer to your question, as noob2 pointed out. You can look online for info from Universa. That fund does exactly what you are asking: https://www.universa.net/riskmitigation.html ...
RWP - Down by the Bay's user avatar
9 votes
Accepted

Portfolio Risk Decomposition - different methodologies

Different portfolio risk decompositions answer different questions. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using. Is the ...
Matthew Gunn's user avatar
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9 votes
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Suppose that we are wrong about the relevant class of distributions for financial economics and econometrics. Now what?

I will be glad to help, but let me first advise you away from working on this topic until you have an academic position. This topic has been poison for me, but I am slogging on anyways. Before you ...
Dave Harris's user avatar
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9 votes
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Why techniques for portfolio optimization do not take into account the non-fractionability of stock prices?

There are a few related reasons: The optimization becomes a lot harder when only discrete values are considered. Mean variance has a closed form solution for the continuous case but the case with ...
Bob Jansen's user avatar
  • 8,552
8 votes

Creating a Beta-Neutral Portfolio

There are more ways to approach this but the method I propose should work reasonably well in practice, especially if you increase the number of assets you hold. Calculate the beta of the stocks you'...
Bob Jansen's user avatar
  • 8,552
8 votes

What is the total correlation between assets in a portfolio?

I just want to add to vonjd's answer some info on the comparison of the 3 methods. This is too big for a comment so I'm posting as a separate answer but please upvote his answer, not mine. Do the ...
msitt's user avatar
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8 votes

non-subadditivity of VaR

Simple example where sub-additivity fails Let there be four possible outcomes $i=1,2,3,4$ that occur with equal probability $\frac{1}{4}$. Payoffs for $X$, $Y$, and $X + Y$ are given by: $$ X = \...
Matthew Gunn's user avatar
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8 votes
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Finding arbitrage opportunity

Generally speaking, let us consider a problem where you have a series of simple payoffs $f_{K_i}(S_T)$ of strike $K_i$, $i \in I$, that depend on the value of $S_T$ at time $T$, as well as a more ...
Daneel Olivaw's user avatar
8 votes
Accepted

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 ...
MGL's user avatar
  • 516
8 votes
Accepted

What are the quantitative requirements to distinguish between asset classes?

Defining asset classes from a quantitative perspective is an interesting question that is not really addressed "officially" as far as I know. Let's try to write some requirements you want ...
lehalle's user avatar
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7 votes
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How to check if a portfolio has momentum bias

It kind of depends what your objective is. First, momentum 'bias' isn't well-defined. Are you looking to eliminate momentum exposure for some reason? Momentum itself isn't even well-defined really: ...
Chris's user avatar
  • 1,643
7 votes

Most significant research articles for practical investors with research perspectives

A lot has happened since Markowitz and Sharpe. While their work is still considered foundational, the empirical/practical relevance of their models has been questioned by later work. Here are a few ...
Alex C's user avatar
  • 9,372
7 votes
Accepted

Hedging a trade for PCA component neutrality

Simple Directionality Spread Trade Hedge If the sum of the risks of the trade $t$ are zero (as in the case of the 2Y5Y10Y spread trade) that immediately gives a starting point from which to make a ...
Attack68's user avatar
  • 10.3k
6 votes
Accepted

Maximum Certainty Equivalent Portfolio with Transaction Costs

Seems like a small mistake in the last equation. It should read $\Delta^* = A^{-1} \left[\mu-\gamma \Sigma \omega_c - \frac{1}{\iota'A^{-1}\iota} \iota' A^{-1}(\mu-\gamma \Sigma \omega_c )\iota\...
krise's user avatar
  • 116
6 votes

What are reasons not to do factor investing in equity markets?

To add another perspective see this current and very relevant article with many unique and original insights (Kritzman is one of my favorite authors anyway): Cocoma, Paula and Czasonis, Megan and ...
vonjd's user avatar
  • 27.4k
6 votes
Accepted

non-subadditivity of VaR

VaR is not sub-additive in general. Relying on Mark Joshi comment, there are particular cases where it can be. Such cases occur for portfolios containing elliptically distributed risk factors. Of ...
JejeBelfort's user avatar
  • 1,219
6 votes
Accepted

How can I use a more efficient volatility estimator to improve the co-variance matrix?

Let $s$ be a $N\times1$ vector of standard deviations and $C$ be an $N\times N$ correlation matrix. The covariance matrix is equal to $$\Sigma=\text{diag}(s) \ C \ \text{diag}(s)$$ where $\text{diag}...
John's user avatar
  • 5,391
6 votes

Modeling Long-Term Mean Reversion in Asset Returns

You could use the two factor model of Schwartz-Smith. It's a very standard model in commodities, where you observe this kind of long term mean reversion (where "long-term" is here around a year). It'...
Juan Ignacio Gil's user avatar
6 votes

Logic behind sharpe ratio

Another intuitive interpretation of the Sharpe ratio is as a signal-to-noise ratio: $$\frac{\mu}{\sigma}$$ where you compare the strength of the signal (= return) to the level of noise (= risk). The ...
vonjd's user avatar
  • 27.4k
6 votes
Accepted

Rockafellar-Uryasev mean-CVaR optimiztion

$VaR_\alpha$ is a scalar choice variable in the minimization problem. In the Rockafeller-Uryasev paper, it is simply called $\alpha\in R$. (C.f., the program described in Theorem 2 of that paper, or ...
Drew's user avatar
  • 405
6 votes
Accepted

Construct a butterfly interest rate portfolio to eliminate PCA exposures

Let $S$ be your risk sarray, expressed in pv01, for each of your (implied) 10 instruments. You restrict the array to all zeroes except those corresponding to the 5Y, 7Y and 10Y risks, e.g. if 1Y:10Y ...
Attack68's user avatar
  • 10.3k
6 votes
Accepted

Efficient frontier doesn't look good

As i understand your question you are confused as to why the expected parabola-shape of the frontier is not depicted clearly. If you want to see the shape more clearly you can do one of two things: ...
jthg's user avatar
  • 445
6 votes

Regularizers to compute Minimum Variance Portfolio weights

The Minimum Variance Portfolio (without constraints, other than the weights sum to one) is usually found as $$w=\frac{\Sigma^{-1} \iota}{\iota^T\Sigma^{-1} \iota}$$ where $\Sigma$ is the Covariance ...
Alex C's user avatar
  • 9,372
6 votes
Accepted

How to calculate the net return of each "partner" at different times?

Generally, managers take subscriptions and redemptions periodically, the frequency of which is defined in their offering documents. At the end of each period (daily, monthly, quarterly, etc), a NAV ...
amdopt's user avatar
  • 4,338
6 votes
Accepted

Does mean variance optimization work in real life? If so, why are defined benefit pension funds so underfunded?

You are asking two questions: whether MVO works in real life and portfolio managers actually use it? whether defined benefit schemes use this tool? Concerning 1. the answer is generally no, although ...
Sebapi's user avatar
  • 461

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