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"A full portfolio correlation matrix is a square matrix that displays the correlation coefficients between every pair of assets within a portfolio, with values ranging from -1 to +1. Each cell in the matrix represents the correlation between two assets, where a value of 1 indicates perfect positive correlation (assets move in the same direction), -1 indicates perfect negative correlation (assets move in opposite directions), and 0 indicates no correlation. The diagonal elements of the matrix are always 1, as each asset is perfectly correlated with itself. This matrix is derived from the covariance matrix by standardizing the covariances using the standard deviations of the respective assets. It is a key tool for assessing diversification benefits, as lower correlations between assets generally lead to reduced portfolio risk. The matrix can be used to calculate portfolio variance and standard deviation, which are essential for risk assessment in modern portfolio theory. For a portfolio with multiple assets, the full correlation matrix allows investors to understand the co-movement of all assets simultaneously, helping to identify potential diversification opportunities or risks".
Never heard of it before. Do play with correlations in setting up what is hoped to be a balanced portfolio. Following a wide range of assets over many years is a good way to get a sense of correlations. Doesn't always work. ISTM equities and bonds are thought to be negatively correlated. In '22 that wasn't the case. When an asset enters bubble territory (extreme overvaluation) trying to achieve balance by using correlations may be of little use. Suspect the opposite is also true of broken-bubble (steeply undervalued) assets. I've heard it said that gold is inversely correlated to most other assets. Dunno about that. ISTM it runs in immense cycles lasting 3-5 years on both the upside and downside. Can double or halve in value over a couple years time. Wouldn't suffice for my bomb shelter.
Can it be said cash is the ultimate non-correlated asset?
Portfolio Visualizer (PV) and Test Fol provide correlation matrix for holdings. It may be useful to glance at them and look for unusual values. One can also check if the portfolio is diversified - it isn't if all correlations are 0.95+.
For portfolio construction, other MPT stats such as SD, beta, Sharpe Ratios, may be more useful.
composite stats seem useful after using a correlation to test specific add\sell. time periods are critical input, as correlation1 in a real crisis. anyway, these are all crutches for risk via proxies like volatility. (thx for nothing howard marks!) imprecise but possibly longterm directional aids.
Quantifying how diversified is a universe of assets is an open problem in quantitative finance, partly because there is no definite formula for diversification1.
Let’s make the (reasonable) assumption that the way assets are moving together within a universe is important for its diversification.
This in turn makes asset correlations within a universe important in determining how diversified it is.
...Results The results obtained are remarkably consistent with those of Fleming and Kroeske(8):
The effective rank varies a lot through time(14), as illustrated on Figure 3 Evolution of the effective rank Figure 3. Evolution of the effective rank
The proportion of total variance explained is both very high and very stable through time(15), as illustrated on Figure 4. Figure 4. Proportion of the total variance explained
Another possible usage of the matrix effective rank, hinted in Fleming and Kroeske(8), is to use it as an indicator of systemic risk.
Indeed, it appears that the matrix effective rank bottoms around market crashes (financial crisis of 2007–2008, Corona crisis of 2020…).
Per AI: "Assets like real estate (REITs, farmland), natural resources (timber, water rights, minerals), precious metals (gold), private equity/credit, collectibles (art, wine), music royalties, and some insurance-based products (Whole Life) have historically shown low correlation with U.S. stocks while potentially offering positive real returns, acting as inflation hedges or diversifiers by deriving value from tangible assets or unique market dynamics rather than corporate earnings. "
Finding ways to invest in such assets is the tricky part. Private equity is opening up, but what kind of asset options are we really getting there?
(If there is a farmland option for the small investor, please do share.)
I think some here invest in wine, though the product disappears.
Comments
From Bing's AI:
"A full portfolio correlation matrix is a square matrix that displays the correlation coefficients between every pair of assets within a portfolio, with values ranging from -1 to +1. Each cell in the matrix represents the correlation between two assets, where a value of 1 indicates perfect positive correlation (assets move in the same direction), -1 indicates perfect negative correlation (assets move in opposite directions), and 0 indicates no correlation. The diagonal elements of the matrix are always 1, as each asset is perfectly correlated with itself. This matrix is derived from the covariance matrix by standardizing the covariances using the standard deviations of the respective assets. It is a key tool for assessing diversification benefits, as lower correlations between assets generally lead to reduced portfolio risk. The matrix can be used to calculate portfolio variance and standard deviation, which are essential for risk assessment in modern portfolio theory. For a portfolio with multiple assets, the full correlation matrix allows investors to understand the co-movement of all assets simultaneously, helping to identify potential diversification opportunities or risks".
Never heard of it before. Do play with correlations in setting up what is hoped to be a balanced portfolio. Following a wide range of assets over many years is a good way to get a sense of correlations. Doesn't always work. ISTM equities and bonds are thought to be negatively correlated. In '22 that wasn't the case. When an asset enters bubble territory (extreme overvaluation) trying to achieve balance by using correlations may be of little use. Suspect the opposite is also true of broken-bubble (steeply undervalued) assets. I've heard it said that gold is inversely correlated to most other assets. Dunno about that. ISTM it runs in immense cycles lasting 3-5 years on both the upside and downside. Can double or halve in value over a couple years time. Wouldn't suffice for my bomb shelter.
Can it be said cash is the ultimate non-correlated asset?
For portfolio construction, other MPT stats such as SD, beta, Sharpe Ratios, may be more useful.
composite stats seem useful after using a correlation to test specific add\sell.
time periods are critical input, as correlation
anyway, these are all crutches for risk via proxies like volatility. (thx for nothing howard marks!)
imprecise but possibly longterm directional aids.
The Matrix Effective Rank: Measuring the Dimensionality of a Universe of Assets
with U.S. stocks while providing positive long-term real returns?
Per AI: "Assets like real estate (REITs, farmland), natural resources (timber, water rights, minerals), precious metals (gold), private equity/credit, collectibles (art, wine), music royalties, and some insurance-based products (Whole Life) have historically shown low correlation with U.S. stocks while potentially offering positive real returns, acting as inflation hedges or diversifiers by deriving value from tangible assets or unique market dynamics rather than corporate earnings. "
Finding ways to invest in such assets is the tricky part. Private equity is opening up, but what kind of asset options are we really getting there?
(If there is a farmland option for the small investor, please do share.)
I think some here invest in wine, though the product disappears.