# Tag Info

## Hot answers tagged diversification

12

### How do I find the most diversified portfolio, or least correlated subset, of stocks?

One simple method, based on the principles of mean-variance optimization, is to set the weights proportional to the product of the inverse of the covariance matrix and a vector of standard deviations. This implicitly assumes that the normalized expected return of each stock is equal. If you wish, you can take only the top 5 weights and set the others to ...

9

### Should the average investor hold commodities as part of a broadly diversified portfolio?

Yes Strategic Asset Allocation: Determining the Optimal Portfolio with Ten Asset Classes Strategic Asset Allocation and Commodities The Case for Commodities An Asset Class for All Seasons: The Benefits of a Strategic Allocation to Commodities No Should Investors Include Commodities in Their Portfolios After All? New Evidence My Take Although there ...

7

### How to simulate correlated assets for illustrating portfolio diversification?

Your formula looks like cointegration (between the price time series) rather than correlation (between the returns). To simulate "correlated random walks", i.e., random walks built from correlated innovations, you can just build the desired covariance matrix (for instance, put ones on the diagonal and $\rho$ everywhere else), take multivariate gaussian ...

7

### How do I find the most diversified portfolio, or least correlated subset, of stocks?

The problem of the selecting the best portfolio (according to some risk measure) with a limited number of assets can be formulated as a mixed integer linear or quadratic program and is reviewed in the recent paper "Portfolio selection problems in practice: a comparison between linear and quadratic optimization models". It can be solved for reasonable sizes ...

5

### How does one analyze diversification if stock prices follow a Cauchy distribution?

There is, in fact, a large literature on this subject, but you may have been searching for the wrong terms. This issue is broadly explored within the literature regarding a preference for higher moments. Cauchy distributions, themselves, are very hard to work with because they don't have any well-defined moments. One possible solution to this is to use ...

4

### How does one analyze diversification if stock prices follow a Cauchy distribution?

I think this is a very good and valid question. I will try to give a more general answer here. It is by now a well known fact that much of the classical stuff won't work in the manner it was thought and supposed to work. One of the points that are not clear when it comes to real financial time series is how they are distributed (they are obviously not ...

4

### age-sensitive correlation measurements in finances

You can use the Exponentially Weighted Average directly aswell, finding the covariances and then normalizing back to the correlations: $\sigma_{t+1,jk} = (1-\lambda) \sum_{n=0}^\infty \lambda^{n} r_{j,t-n} r_{k,t-n}$ (this assumes average returns 0 etc etc. More general versions can be derived)

3

### St Petersburg lottery pricing & short investing horizons

What a great question -- it touches on many issues at the core of quantitative finance. This answer might be a lot more than you bargained for, but it's too interesting to pass up. References Mostly, this subject falls somewhere at the intersection of these three highly-interrelated topics: risk-neutral valuation, rational pricing and the fundamental ...

3

### age-sensitive correlation measurements in finances

1) Calculate exponential averages (EMA) for time series A & B. 2) Calculate exponential standard deviations for A & B. My little hack for this is to calculate an EMA of squared returns, then subtract the squared EMA of simple returns, then take the square root of this. sqrt( ema(return^2) - ema(return)^2 ) 3) Apply the same concept to calculating ...

3

### Is this comment right about subadditivity?

You're right, I hope he meant exactly the opposite, and the formula you provided is indeed part of the definition of a coherent risk measure. In fact, I would say that the risk of the sum is less than or equal to the sum of the individuals as in some cases you would like your model to accept no diversification effect. As John mentioned in his comment, ...

3

### Should the average investor hold commodities as part of a broadly diversified portfolio?

Very informative and balanced is: The Strategic and Tactical Value of Commodity Futures by Claude B. Erb, CFA, and Campbell R. Harvey One well-known scientifically based passive investment fund in Germany (ARERO) draws a ratio of 15% for commodities (60% world stocks and 25% bonds, rebalanced on a yearly basis) as a conclusion out of this - see the live ...

2

### portfolio diversification tester

Maybe I don't get your question well, but what it appears that your goal is to buy securities in order to reduce the correlation between your portfolio constituents. So firstly you need a metric of diversification. Something simple you can use, is calculate the correlation matrix, and the weights of each position. A simple metric would be the sum of ...

1

### St Petersburg lottery pricing & short investing horizons

This may or may not be helpful, since I don't have anything to point you to that specifically addresses the high skewness of the distribution you mention. However, this sounds like it is probably an idiosyncratic risk, and that certainly has bearing on whether or not it would be priced. In the standard capital asset pricing model, the marginal investor ...

1

### age-sensitive correlation measurements in finances

Try this: Given some time horizon of K, which can be divided into subperiods of N, you will calculate a rolling correlation coefficient of length N, then you can use the EMA to weight the more recent correlation coefficient heavier (indirectly weighting the recent relationship more, vs the medium term part). Never came up with this problem in my work so ...

1

### Should the average investor hold commodities as part of a broadly diversified portfolio?

The controversy surrounding commodity futures flows from Gorton and Rouwenthorst (2004). The authors show an equal-weight portfolio of long positions in commodity futures provides a Sharpe ratio greater than the one earned by holding a cap-weighted portfolio of U.S. stocks (beginning in the 1950's through 2004 or so). In essence, why should holding a ...

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