More stumbling around correlations

Continuing with correlation, I noted in my last post that the correlation over a historical 1-year rolling period seems far too volatile to look like a stable relationship for two assets (stocks and bonds) to look weakly correlated.

From 2002 to mid-2012, the trailing 365 day correlation between equity and bonds looked like this:

 Which begs the question, are these two assets really good diversifiers if their correlation varies so much? I observed in the previous post (and independently concluded by turckerreport), over shorter-time frames, correlation is essentially useless for trading, since the relationship swings from one extreme to another.

And I know over 10 years, correlations tend to stay low. So I tried running the data over longer timreframes: 2-year and 3-year periods.

Looking at 2 and 3 year correlations suggests that correlations are more stable over 2 to 3 years, swinging less from one end to another. So it seems for now at least, I needn’t rehaul my portfolio of unit trusts, as long as I’m looking at a 3yr holding period.

The question then becomes, what causes correlations to rise and fall?

The literature I skimmed through by MSCI Barra and one Li Lingfeng suggest inflation expectation and interest rates have something to do with it. 

Although the exact nature of the relationship between these two forces is beyond my limited grasp of economics. Plus, some of the terms in there are as complex as the names that attributed to them. For example:

“Scruggs and Glabadanidis (2001) strongly reject models which impose a constant correlation restriction on the covariance matrix between stock and bond returns. Fleming, Kirby and Ostdiek (1998) find a strong volatility linkage across stock-bond-bill markets, and attribute it to the information flow in these markets. However, they associate the information flow with volatility and do not identify the exact information that causes the comovement. David and Veronesi (2001) show that the uncertainty about inflation and firm earnings explains some of the changes in the variances and covariance of stock and bond returns.”

I mean, I know it’s English, but it might as well be in Latin because that I have very little clue as what are the implications of the conclusions stated in the paragraph. 

Yes, I took a few economics courses as a freshman, but freshman economics and investing are two different things altogether. And as much as I enjoyed microeconomics 101, macroeconomics (it was a Keynesian view of economics I believe) was not as accessible to me, and I had a tough time even grasping at straws. 

Stumbling around correlations

Correlations are misleading.

I make that statement from personal experience, since I never had to grapple with such concepts while I was studying the methods of systemic functional linguistics and feminist discourse. And while it’s given me a firm background in writing for readability, it’s not particularly useful for any grounding in numbers.

So everything henceforth is the spewage of an untrained mind. You have been warned.

Typically, this is what a correlation matrix looks like:

Correlation Matrix, end-2001 to end-2011	MXWD Index	JP Morgan Global Aggregate Bond Index	S&P Gbl Property TR Index (US)
MXWD Index
JP Morgan Global Aggregate Bond Index	-0.06
S&P Gbl Property TR Index (US)	0.97	-0.10
ThompsonReuters/Jefferies Commodity CRB Index	0.72	0.03	0.72

Correlation goes to two extremes of 1 or -1, and 0. And over 10-year data, the relationships do hold quite well. That was until I came across this post on intermarket analysis at Tuckerreport, which in a nutshell says there is no stable correlation between the movements of various markets on a daily basis. This is all good, because from the point of view of trading, you’re talking about short-term bets that are unlikely to hold for more than a week, so even if you had a strong correlation between two markets, on its own, it does little to determine which direction of a trade to take, or generating buy/sell signals.

From a long-term investor’s point of view though, does correlation add any value to building a diversified portfolio? I’m defining a diversified portfolio as a portfolio consisting of two or more weakly-correlated assets.

Tracking That Tucker

A picture tells a thousand words, so using the CORREL function in excel, I pulled rolling 1-year correlation between equities and bonds.

Correlation runs from +1 to -1. Put crudely, it’s the how two random variables move together. If the correlation of two numbers approaches 1, they move together, for instance, as age increases, so does height. If the correlation approaches -1, they move apart, for instance, the amount of air that escapes a balloon increases as the size of the balloon decreases. A low correlation of around 0 implies there is no strong relationship between two variables, i.e. independent relationship, like your age and how many bowls of laksa you eat a week. For diversification purposes, I’m looking for assets that hold low correlation.

Chart1: Equity versus bonds

The traditional equity-bond mix actually has seen periods of high-correlation, somewhat contrary to conventional wisdom. Does this mean the weak correlation between equity and bonds is a myth? 

Puzzling Valuations: Varying Timeframes

I’m a bit of an attention butterfly, I tend to slit from one idea to another, and quickly lose interest when too much time is spent on the same topic. So this will probably be the last post where I look at valuations for a while at least.

Just to recap: looking at the Straits Times Index, I plotted forward 12-mth returns versus PE ratios and PB ratios. Both support the idea of ‘buy low sell high’ albeit to varying degrees and the relationship looked clearer in the case of PB ratios.

The question now is what happens if I plot varying time frames? Say short term (3 months) and long terms (24 months), bearing in mind, the data set starts at end-2008 and ends in May-2012, so I can’t do much longer than 2-years of rolling returns.

If I look at 3 month forward returns, here’s how it varies with PE ratios…

 And 24 month ratios…

The general observation seems to be that you’re got far better chances of making money buying low selling high if you hold for 24 months than if you held for 3 months. Referring back to an earlier post, 24 months might be better holding period than 12 months, since observations of positive returns are 1) more numerous and 2) higher in 24 months than in 12 months.

Then again this all based on historical data, which is never a guarantee of future returns. Still…it’s as far as I can tell the only thing I have to base any future projections on. So reader beware, we plunge further onward into historical data.

Now for PB ratios, starting with 3-month forward returns…

And 24mth forward returns…

Again, the historical data seems to support the notion that holding for 24-mths (and even 12mths) is more likely to make more money than a 3-mth timeframe if you enter at low valuations. At high or in-between levels, returns seem far more modest.

So what does this all mean?

Firstly, “buy and hold” works with “buy-low-sell-high”.  This is based on historical data, and the general common sense that if you get in when valuations are low, you’re far more likely to make money in the long-term (24mths), than in the short-term (3mths).

Secondly, long-term isn’t the same as forever. Often, 12mths is all you need to see your investment turn in a decent return if you enter at low valuations. Although some would prefer you buy and hold like Warren Buffett, (i.e. forever) the reality is that for the STI at least, 12months seems a reasonable holding period to see positive returns.

The pity is data isn’t easy to come by, so most individual investors are at a disadvantage unless they happen to have access data.

Um, that’s a different sort of Data.