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 ...
- 6,864
13
votes
Accepted
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)...
- 6,864
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 ...
- 6,864
13
votes
Accepted
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 ...
- 6,864
12
votes
Accepted
Which algorithms do robo-advisors use?
After having done a lot of research on the topic I found the following excellent research piece on ETF.com:
Wealthfront modifies historic asset-class returns with current market
implied expected ...
- 27.3k
11
votes
Accepted
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:
...
- 27.3k
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 ...
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 ...
- 6,864
9
votes
Accepted
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 ...
- 8,436
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'...
- 8,436
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 ...
- 741
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 = \...
- 6,864
8
votes
Accepted
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 ...
- 7,855
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 ...
- 516
8
votes
Accepted
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 ...
- 4,289
7
votes
Accepted
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: ...
- 1,608
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 ...
- 9,272
7
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 ...
- 4,690
7
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 ...
- 11.4k
6
votes
Accepted
Mean Variance Portfolio theory and real-world problem?
Mean-variance (MV) is a framework rather than a prescription. This framework allows one to make, discuss, and defend his investment decision.
In practice, there are many ways to make adjustments to ...
- 741
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\...
- 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 ...
- 27.3k
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 ...
- 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)$$
where $\text{diag}...
- 5,371
6
votes
Modeling Long-Term Mean Reversion in Asset Returns
You could use the two factor model of Schwartz-Smith. It's a very standard model in commodities, where you observe this kind of long term mean reversion (where "long-term" is here around a year).
It'...
- 560
6
votes
Logic behind sharpe ratio
Another intuitive interpretation of the Sharpe ratio is as a signal-to-noise ratio: $$\frac{\mu}{\sigma}$$ where you compare the strength of the signal (= return) to the level of noise (= risk).
The ...
- 27.3k
6
votes
Accepted
Rockafellar-Uryasev mean-CVaR optimiztion
$VaR_\alpha$ is a scalar choice variable in the minimization problem. In the Rockafeller-Uryasev paper, it is simply called $\alpha\in R$. (C.f., the program described in Theorem 2 of that paper, or ...
- 405
6
votes
Accepted
Efficient frontier doesn't look good
As i understand your question you are confused as to why the expected parabola-shape of the frontier is not depicted clearly.
If you want to see the shape more clearly you can do one of two things:
...
- 435
6
votes
Regularizers to compute Minimum Variance Portfolio weights
The Minimum Variance Portfolio (without constraints, other than the weights sum to one) is usually found as
$$w=\frac{\Sigma^{-1} \iota}{\iota^T\Sigma^{-1} \iota}$$
where $\Sigma$ is the Covariance ...
- 9,272
6
votes
Accepted
Shrinkage of the Sample Covariance matrix, theory
Yes. It comes from a core theorem of statics, Stein's Lemma. It shook the foundations of the field of statistics when it came out. It blew up an entire way of viewing mathematical statistics. ...
- 4,289
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