24 votes
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Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

Markowitz's concepts attracted a great deal of interest from theorists (and still do), but never had much application in practice. The results from practical application were always disappointing (...
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  • 9,597
15 votes
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Equivalent to Matlab's financial toolbox in python?

I took a quick look at Matlab's Financial Toolbox and attempted to map the features to corresponding Python packages – For asset allocation, portfolio optimization, and risk analytics: Standard ...
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11 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)...
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  • 6,354
10 votes
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What does the concept "standard Markowitz approach" include?

The Markowitz mean-variance model is the basis for many extensions and portfolio solutions that have been discovered over the years: The standard model (Markowitz, 1952, 1959) originally only ...
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9 votes

Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

There has been a split in the community ever since Mandelbrot published his paper "On the Variation of Certain Speculative Prices." See: Mandelbrot, B. (1963). The variation of certain speculative ...
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  • 4,105
9 votes

Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

It is more complicated than that: It is not the optimization per se that leads to inferior results but the data you use. Kritzman et al. makes a strong case in defense of optimization vs. 1/N in this ...
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7 votes

How to construct a Risk-Parity portfolio?

I am very happy with the following equivalent formulation for the risk budgeting problem (as presented in Bruder, Roncalli, 2012, Managing Risk Exposures using the Risk Budgeting Apporach): Let $b_i$,...
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7 votes
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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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  • 5,853
7 votes

What's the point of resampling?

The "estimation problem" in Portfolio Optimization is a serious one. The parameters (returns and covariances) are known very imprecisely. For example the covariance between stocks and bonds ...
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  • 9,597
6 votes

What is smart beta, alternative index, factor investing?

In recent years there has been much attention given to defining indexes other than market-cap based indices. While market-cap based indices approximate the theoretical Market Portfolio enshrined in ...
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6 votes
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Why would there be a positive risk-free rate?

Risk-free rate is that you get for letting someone else use your money in a riskless manner. Suppose we live in a world where there is no risk whatsoever. In particular, if you lend someone \$100 ...
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  • 471
6 votes
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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 ...
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5 votes
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Portfolio optimisation by asset allocation

There are very powerful software solutions out there, so you should not reinvent the wheel. One notable R package is PortfolioAnalytics. You can find a very good introduction here, where your ...
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5 votes

Stress Testing approaches at Pension Funds/Asset Management companies

Many long term investors use historical events and the market moves associated with such events to stress test their portfolios. For example, they use the dot-com bust, the latest "great recession", ...
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  • 5,325
5 votes

Asset Allocation with near zero rates

I'll add some comments, recognizing that 1) they are highly opinionated, and 2) they don't actually offer any real solutions. Hopefully more thoughtful and useful answers will emerge. First of all, ...
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4 votes

How to construct a Risk-Parity portfolio?

Another approach to construct a risk parity portfolio would be to use the formulation proposed by Spinu [1]: $$\begin{array}{ll} \underset{\mathbf{w}}{\textsf{minimize}} & \frac{1}{2}\mathbf{w}^{T}...
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4 votes

Portfolio choice problem of a CARA investor with n risky assets

This problem is from the exercise for Chapter 2 of Kerry Back's Asset Pricing Book. The setup of the problem is rather simple. You want to \begin{equation*} \begin{aligned} & \underset{\phi}{\...
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  • 650
4 votes

Is mathematical finance relevant in asset managament?

As a start: I am sure some asset managers don't know too much mathematical finance and do a good job. They exist. On the other hand as a mathematician I see mathematics (and classicial mathematical ...
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4 votes

Backtest Results needed to Model Validate my Modern Portfolio Theory model

There is a recent a paper recently using a population test of all CRSP data from 1925-2013 as a test of whether a mean and a variance exist versus they do not exist. It overwhelmingly excluded mean-...
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4 votes
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Risk Parity / Equal Risk Contribution with Tail Risk Measures

For question 1), lets add the topic of positive homogeneity to the discussion: Whenever a risk measure is positively homogeneous, we can calculate risk contributions. A risk measure is positively ...
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  • 2,894
4 votes
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Asset Allocation with near zero rates

Many pension funds use projected asset class returns (capital market assumptions or CMAs) and backward-looking estimates of volatilities and correlations to set the strategic asset allocation. A 10-...
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  • 3,365
4 votes
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Calculation of Market portfolio from efficient frontier

As @stans already said in the comments to your question, the existence of the market portfolio hinges on the existence of a risk free rate $r_f$, where risk free, in this context, means that its value ...
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4 votes

Find k of n assets that "minimize" the correlation matrix

(I take it that 5 out of 10 assets is just an example, because in this case all combinations could easily be checked.) Here would be an example how to do it in R ...
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4 votes
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What is the proper capital split/allocation between the long and short in a pairs trade?

There are many different approaches to creating a portfolio comprising long-short pairs trades. Many take the approach of market neutrality. They attempt to create a portfolio that is insensitive to ...
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3 votes
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Simulating returns from ARMA(1,0)-GARCH(1,1) model

This question has already been answered on Stack Overflow. As it is important to Quant Finance, so I have added R code here. Others users may add code of other programming software to simulate ARMA(...
3 votes

High values of skewness and kurtosis of realized protfolio returns

The skewness and kurtosis values you obtain appear to be of realistic magnitude. In general higher frequencies are more non-normal, i.e. have higher skewness and kurtosis. If non-normal returns are ...
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3 votes
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Asset Liability Management Test Topic Interpretation

Portfolios for some kind of investors effectively balance asset investments with liabilities incurred. Think about a pension account, where the future liability of the pension payment represents the ...
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  • 450
3 votes

Multi-asset class allocation

In this case it is important to differentiate between a liability-driven investment strategy (LDI) and a (the classical) benchmark-driven investment strategy. The first one is what you need in this ...
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3 votes

Why would there be a positive risk-free rate?

The risk free rate is important and the reason for the inclusion and consideration of the risk free rate is that investors do not get compensated for not taking on risk. Now, we can argue whether the ...
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3 votes

Monte Carlo based mean variance optimization

I believe the question to be too vague to be a good interview question. If you want to do Mean Variance Optimization (MVO) it's hard to see the point of Monte Carlo simulation. One of the good thing ...
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