View Full Version : Minimizing Correlation

greggye

August 9th 2005, 09:51 AM

I'm a summer intern and I was asked to try and take a portfolio that contains various securties and make it so the correlation between US Large Cap Stocks and the Portfolio (which contains US Large Cap Stocks) is zero. I've been looking up how to do it for quite a while and I'm stumped. I would greatly appreciated any help or input anyone has that could help push me in the right direction.

Ken

August 9th 2005, 09:08 PM

Is this a problem where you use the beta values of the stocks?

greggye

August 10th 2005, 07:00 AM

yes I believe so. Each asset in the portfolio is given a specific weight, an expected return, and a estimated risk given as the standard deviation. They want to make it so that the portfolio is not correlated with the US stock market.

AVB

August 16th 2005, 12:50 PM

Beta =P x (sd_stock * sd_market) / (sd_mrkt*sd_mrkt)

where sd = standard deviation,

P = correlation coeff of market and stock.

Since sd's are fixed (for a given length of time) we can say that if we minimise beta we also minimise P.

It sounds to me then that you need to calculate beta for each stock, then minimise the average beta over the portfolio subject to whatever diversification conditions, etc that have to be adhered to.

There are a number of ways to calculate beta.

A quick method that can be used to estimate beta over the short term is:

'If the stock is observed to move x% of the market move on average, it is said to have a beta of x%.'

Another method is regression analysis. This assumes you have some past data, and know what the risk-free rate of interest is (approximately). The metho is:

'Perform a regression of the share price movements against movements in the market index.

The regression fits the best value of beta in the formua

Return_on_stock = risk_free_rate + beta * (market_return - risk_free_return).

There are other methods that I haven't mentioned.

However, if your company already has access to beta measurments, then simply, solve as a minimisation problem (average weighted beta) subject to whatever conditions your potfolio has to meet. (Excel solver may be useful).

Remember that level of leverage can affect the beta value. But that should only concern you if you are using industry betas' (don't think you are) as opposed to individual betas'.

I don't actually work in this field, but spent yesterday studying for a UK exam that includes a discussion of beta. However, much of my reasoning is just that 'my reasoning' so beware of my unqualified advice!

Good luck.

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