# Tag Info

9

If $Q$ is your covariance matrix, and $r$ is a vector of your expected returns, then the maximum Sharpe ratio is given by the following math program. $${\rm maximize} \frac{r^t x}{\sqrt{0.5 x^t Q x}}$$ subject to $$1^t x = m$$ $$x \in \{0,1\}^n$$ Where $x$ is a vector of indicators of which of the $n$ assets are part of the $m$ selected assets. While the ...

6

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 strategic decisions to make sense: each asset class should have at least one or two different "economic drivers" than the others you want tactical ...

6

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 textbooks, some people believe we could do better than that. One popular idea is that "market indexes overweight the most overvalued stocks", though this is ...

3

For such a problem ("selecting n out of m") you can use optimisation heuristics. These algorithms work well even for large n and m, and they are flexible: you may as well select a portfolio that minimises some other function, for instance, the portfolio's drawdown. The downside is that you may have to do some programming yourself. An example very similar ...

2

A quant technique that could be used to (partially) address this problem is the Mean Variance Spanning Test of Huberman and Kandel (1987). Abstract This is a statistical test of whether adding K new assets to an existing set of N assets improves the Efficient Frontier or not. Roughly speaking the test involves checking whether the new assets "add ...

2

As @piRSquared has pointed out, smart beta can be an ambiguous term which is fairly loosely defined. Cliff Asness wrote a paper defining smart beta as To be considered Smart Beta, we believe that these factors must also be simple and transparent. However, they don’t have to be the same for all managers or products. One can, and many do, argue that ...

2

The term "smart beta" is loaded and ambiguous. It means different things to different people. Some people manage products that they would argue are not smart beta while the rest of the industry vehemently disagrees. I've gone the route of defining what it means to me. Smart Beta Short Version Commoditized Factor Investing Longer Version Investment ...

2

I would say it could be short for annual turnover (precent/portfolio) Higher portfolio turnover often means higher transaction costs. The definition is usually the lesser of all buys and sells in a year divided by the average monthly NAV of the strategy. (Morningstar) Be aware that turnover numbers come in all colors and flavors and can in or exclude ...

2

I worked on volatility control funds for a few years a while back. Frequently, we would simply use the average as the threshold between high and low vol. That is because volatility is below average in normal times, but can quickly exceed the average during a correction. Mathematically, the fat right tail of an inverse-gamma distribution for an unknown ...

1

An approach which satisfies the requirements I listed above is the one laid out in Tracking Error and the Setting of Tactical Ranges, David E. Kuenzi, The Journal of Investing Spring 2004, 13 (1) 35-44.

1

Here's a thought. In 2-dim your score $(x, y) \in [-4,4]^2$ is best characterised as the minimal distance from the line $y=x$, along which your portfolio is balanced. I.e. wherever $y=x$ either at $(0,0), (-1,-1) (4,4)$ the weight is 50-50, since there is no minimal displacement vector. As a further example $(0,2)$ has minimal distance from the point $(1,1)... 1 This a Quadratically Constrained Quadratic Program (QCQP) (try searching for that) albeit the usual inequality constraint has been replaced by your equality constraint. maximise over$x_i\$ $$x_i'S_i - 0.01^2\lambda_i$$ s.t. $$x_i'Qx_i=0.01^2$$ You may have some success if you investigate techniques for solving the constraint in the first place and then ...

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