Maurice Chia
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Maurice Chia

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## Your All-ETF Portfolio: Too Correlated? [View article]

## Your All-ETF Portfolio: Too Correlated? [View article]

## Power Optimization: Only When The Time Is Right [View article]

## Power Optimization: Only When The Time Is Right [View article]

## Power Optimization: Only When The Time Is Right [View article]

## The Art Of Non-Normal Rebalancing [View article]

## Refining Our Optimized Portfolio With Western Refining Inc. [View article]

## Power Optimization: There's Something About Wal-Mart [View article]

## The Art Of Non-Normal Rebalancing [View article]

## In Search Of The Ultimate Efficient Portfolio [View article]

## In Search Of The Ultimate Efficient Portfolio Part 2 [View article]

Suppose you had 2 stocks in your portfolio. You would calculate the weighted return of these 2 stocks to arrive at the portfolio expected return. Let the weight for stock1 and stock2 be w1 and w2 respectively.

The portfolio volatility where volatility is defined as standard deviation would be the square root of this whole formula: (w1 x volatility1)^2 + (w2 x volatility2)^2 + 2w1w2 x volatility1 x volatility2 x correlation between stock1 and stock2.

My purpose of showing you this formula is so that you appreciate the fact that the weights are calculated not just on the basis of correlation but the aggregate result of individual volatilities and the correlation that exists between each and every pair of stocks, at the level of expected return of the portfolio.

So in the article above, why wasn't more weight put on the other 15 stocks? It is a combination of reasons. If any weight was put at all on any of these 15 stocks it would be because by doing so, it helped reduce portfolio volatility,while maintaining the expected portfolio return which is the weighted average of all the stocks that are included in the portfolio.

If any of the 15 stocks did reduce portfolio volatility, it was because it was negatively correlated (or more precisely, less than perfectly positively correlated) to either one or both of the 2 stocks to the extent that the reduction in portfolio volatility due to the effects of correlation was greater than any increase in portfolio volatility due to the introduction of the new stock.

To elaborate on the process, let's say you started with the 2 stocks that you refer to above. You then try to include stock3 but it does not pass the criteria for inclusion into the portfolio. Do you then discard stock3? The answer is not just yet.

This is because you will not know if stock3 combines with stock4, or stock5, etc to form an even lower volatility portfolio at the given return. In other words, you have to analyze all possible combinations before deciding which will be the efficient portfolio (i.e. lowest portfolio volatility for the given return) that sits on the frontier. Do this process for each and every possible portfolio return and you will then be able to construct the entire efficient frontier.

Generating this by hand will obviously take forever. And there is no closed-end formula that will give you the answer. Optimizers use an iterative process which is an algorithm that loops until a certain tolerance is met.

I hope this gives you a clearer picture of what is involved.

To answer your second question, the optimization process will reduce the stocks automatically according to the process I just described. This usually turns out to be a manageable number.

But if you want all 187 in the final analysis, you have to use a constrained frontier which artificially forces a minimum and/or maximum allocation for each and every stock. In a sentence, it is possible to impose any kind of constraint, as long as, it makes sense to do so.

## In Search Of The Ultimate Efficient Portfolio Part 2 [View article]

In a universe that consists of only one asset class, the correlations among the different stocks would necessarily be highly positive, resulting in many stocks being disqualified.

Note however that you will see concentrations in varying numbers and degree, depending on where you are along the frontier but this in turn is dependent on the exact interplay between the returns, volatilities and correlations of the stocks in the universe under study.

Having said that, practitioners sometimes constrain the frontier to "force" a minimum or maximum allocation to each stock so no stock is left out or not too much weight is allocated to one stock.

This is mostly done when each stock in the universe has been pre-selected based on other criteria (e.g. value investing) and the practitioner does not want the optimizer to discriminate against, say, a stock that has almost equal diversification advantage but slightly lower return.

Your comment gives me an idea for my next article which I hope you will also read.

## The Art Of Non-Normal Rebalancing [View article]

## The Art Of Non-Normal Rebalancing [View article]

## Rebalancing The PowerShares QQQ Trust ETF [View article]

2009 : -32.7%

2010: 61.4%

2011: 23.6%

2012: 11.3%