Correlation and Portfolio Additions

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jumpstart
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Correlation and Portfolio Additions

Post by jumpstart » Thu Jul 11, 2019 7:12 pm

Hi.

First, thanks in advance for helping me to understand more fully what is probably understood innately by most on this forum.

When adding a new asset class to a portfolio, how should I account for the influence of correlation? For instance, suppose I have a 3-asset portfolio with a return/SD of 8/14, and I'm considering adding an asset with a return and SD of 7/13 and/or another asset with a return/SD of 5/6. Also assume I can generate a matrix of correlations between the new assets and each asset in my current portfolio. I understand the qualitative nature of adding non-correlated assets to a portfolio, but I'm fuzzy on the quantitative part.

1) I think the return of the new portfolio is the weighted average of the expected returns of each component, independent of their correlations. True?

2) Is there a straightforward way to compare each addition and the resulting expected portfolio SD? Or is this a more complicated calculation? I'm not reluctant to use something more complicated, but I'm also interested to know if there's a quick and dirty way to assess. Something along the lines of using Sharpe ratios and correlations.

Thanks.


Random Walker
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Re: Correlation and Portfolio Additions

Post by Random Walker » Thu Jul 11, 2019 9:42 pm

I think with correlations changing over time all you can do is pretty much make qualitative decisions. I agree the expected return of a portfolio is the weighted average of the portfolio component expected returns. The SD of the portfolio will be less than the weighted average of the individual SDs of the portfolio components because of correlations less than one.
Although the above is way more qualitative than quantitative, given all the unknowns of investing, I think it is quite sufficient to make a decision regarding a single potential portfolio addition. What a potential new addition to a portfolio contributes depends on expected returns, volatility, correlations to other portfolio components, when and how those correlations tend to change, and cost. Small allocations like 4-5% to some investments can make marginal improvements to a portfolio. Although the improvements may be small and incremental, they can be improvements nonetheless.

Dave

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jumpstart
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Re: Correlation and Portfolio Additions

Post by jumpstart » Fri Jul 12, 2019 7:52 am

Moto and Random: thanks.

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vineviz
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Re: Correlation and Portfolio Additions

Post by vineviz » Fri Jul 12, 2019 8:05 am

jumpstart wrote:
Thu Jul 11, 2019 7:12 pm
1) I think the return of the new portfolio is the weighted average of the expected returns of each component, independent of their correlations. True?
jumpstart wrote:
Thu Jul 11, 2019 7:12 pm
2) Is there a straightforward way to compare each addition and the resulting expected portfolio SD? Or is this a more complicated calculation? I'm not reluctant to use something more complicated, but I'm also interested to know if there's a quick and dirty way to assess. Something along the lines of using Sharpe ratios and correlations.
You can, using the formula for portfolio variance in the link MotoTrojan provided earlier. The math gets tedious for portfolios with more than two assets, but you can simplify the problem you pose by treating your existing portfolio as a single asset: calculate its variance, the variance of the proposed new asset, and the correlation of the new asset with the existing portfolio.

Easier, IMHO, is just to use a tool like PortfolioVisualizer to do all the work. It computes the summary statistics painlessly and quickly.

Here I tested three different bond funds combined with a hypothetical existing mix of stock funds.

Image
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

asif408
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Re: Correlation and Portfolio Additions

Post by asif408 » Fri Jul 12, 2019 8:55 am

I think you are making it way too complicated, and my advice will be more simplistic. As Dave said correlations change over time. Since correlations are dynamic, any quantitative approach is likely to fail, so I'll offer qualitative advice, which will likely be more useful.

Correlations tend to be lower or fall when an asset class is new and hard to invest in (e.g., think CCFs in the late 90s/early 2000s), or is old but has fallen out of favor (e.g., like gold mining stocks, and to a lesser extent, international developed and emerging markets stocks today). About the best you can do is to starting adding to these assets to your portfolio when they are new and hard to invest in (hard) or old but fallen out of favor (easier, but requires patience), and building bigger positions over time, then waiting for any potential benefit you may get.

Also remember that correlation is not a panacea. An asset needs to have an expected return in the ballpark of the asset class you are adding it to. For example, the VIX has an almost inverse correlation with the S&P, but in almost any real life situation, will gut your portfolio returns if you add it.

Random Walker
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Re: Correlation and Portfolio Additions

Post by Random Walker » Fri Jul 12, 2019 9:50 am

As I believe Asif was alluding to, it’s important to think about what one is trying to accomplish when adding a new investment to a portfolio. That necessarily requires one to consider what investment he is partially or completely removing to create the position. That involves comparing expected returns, looking at correlations, and thinking about the effect on overall expected return and expected volatility of the portfolio as a whole. For example, in the recent past I created an allocation to expensive and tax inefficient alternatives in taxable space. They have equity like expected returns pre tax and virtually uncorrelated to both stocks and bonds. Initially this might seem silly, but the position was created from municipal bonds. So the overall effect on the portfolio was to increase expected return after tax compared to munis, increase volatility to a lesser extent, increase overall portfolio efficiency.

Dave

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jumpstart
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Re: Correlation and Portfolio Additions

Post by jumpstart » Fri Jul 12, 2019 12:09 pm

Again, thanks. All good food for thought.

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vineviz
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Re: Correlation and Portfolio Additions

Post by vineviz » Fri Jul 12, 2019 12:21 pm

Random Walker wrote:
Fri Jul 12, 2019 9:50 am
As I believe Asif was alluding to, it’s important to think about what one is trying to accomplish when adding a new investment to a portfolio. That necessarily requires one to consider what investment he is partially or completely removing to create the position. That involves comparing expected returns, looking at correlations, and thinking about the effect on overall expected return and expected volatility of the portfolio as a whole. For example, in the recent past I created an allocation to expensive and tax inefficient alternatives in taxable space. They have equity like expected returns pre tax and virtually uncorrelated to both stocks and bonds. Initially this might seem silly, but the position was created from municipal bonds. So the overall effect on the portfolio was to increase expected return after tax compared to munis, increase volatility to a lesser extent, increase overall portfolio efficiency.
This is a crucial point: setting aside all the details and assumption behind modern portfolio theory, the fundament innovation was that it presents a framework for managing the portfolio as one entire unit instead of managing each component on its own terms.

Diversification is one piece of that framework, but it's obviously not the only piece. I don't have an allocation to alternative risk premia the way that Random Walker does, but I add recently add an allotment to local currency emerging market bonds using the same sort of process he outlines here: based on the expected returns and expected variance of iShares J.P. Morgan EM Local Currency Bond ETF (LEMB), I consider treat it as part of my international equity allocation instead of my fixed income portfolio. My portfolio has similar expected returns to the previous iteration but lower expected volatility (because LEMB improves the diversification), and thus overall better portfolio efficiency.

Correlation and variance are the tools you need to make that diversification decision, but expected return is needed to decide whether the better diversification will help or hurt your chances of meeting your investment goals.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

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patrick013
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Re: Correlation and Portfolio Additions

Post by patrick013 » Fri Jul 12, 2019 3:29 pm

jumpstart wrote:
Thu Jul 11, 2019 7:12 pm
Is there a straightforward way to compare each addition and the resulting expected portfolio SD? Or is this a more complicated calculation? I'm not reluctant to use something more complicated, but I'm also interested to know if there's a quick and dirty way to assess. Something along the lines of using Sharpe ratios and correlations.
Usually I try to reduce beta weighted by AA. This model does almost the same thing by reducing SD.
The efficient frontier tab has some correlation info so some small correlations may show up otherwise a better SD will be calc'd for some target return. This is easier than an Excel spreadsheet.

Most important is getting an adequate bond AA. Could be more important than all these stats.

https://www.portfoliovisualizer.com/opt ... total1=100
age in bonds, buy-and-hold, 10 year business cycle

Topic Author
jumpstart
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Re: Correlation and Portfolio Additions

Post by jumpstart » Fri Jul 12, 2019 3:36 pm

Correlation and variance are the tools you need to make that diversification decision, but expected return is needed to decide whether the better diversification will help or hurt your chances of meeting your investment goals.
Yes, and given this, maybe a shortcut using Sharpe might be helpful, at least at a 30,000 ft level. I've done some subsequent poking around and stumbled on an observation something along the lines that a new asset deserves a closer look if the Sharpe of the proposed addition is greater than the product of the current portfolio Sharpe and the correlation of the new asset. Seems intuitively attractive at first blush, but I have to give the arithmetic some thought.

Topic Author
jumpstart
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Re: Correlation and Portfolio Additions

Post by jumpstart » Fri Jul 12, 2019 3:40 pm

Thanks, patrick. I've never looked at pv closely enough to ever have appreciated this feature.

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vineviz
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Re: Correlation and Portfolio Additions

Post by vineviz » Fri Jul 12, 2019 3:58 pm

jumpstart wrote:
Fri Jul 12, 2019 3:36 pm
Correlation and variance are the tools you need to make that diversification decision, but expected return is needed to decide whether the better diversification will help or hurt your chances of meeting your investment goals.
Yes, and given this, maybe a shortcut using Sharpe might be helpful, at least at a 30,000 ft level. I've done some subsequent poking around and stumbled on an observation something along the lines that a new asset deserves a closer look if the Sharpe of the proposed addition is greater than the product of the current portfolio Sharpe and the correlation of the new asset. Seems intuitively attractive at first blush, but I have to give the arithmetic some thought.
Sharpe ratios are great at loading up portfolios on assets that have recently performed unusually well. It’s not an investment approach that I favor but . . .
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

Topic Author
jumpstart
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Re: Correlation and Portfolio Additions

Post by jumpstart » Fri Jul 12, 2019 8:25 pm

Roger that, vine. Thanks.

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