# Why is the correlation low when returns are high and vice versa?

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Why is the correlation low when returns are high and vice versa?

Thank you!

Think about the financial crisis in 2008. Everything was going down at the same time (i.e. +1 correlation) thus returns were negative and correlations were high.

The classic phrase is “diversification fails when it is needed most”.

this is why conditional correlations can be used when stress testing the portfolio and during scenario analysis.

With all due respect, you’re conflating correlation of prices (which will be positive and could be close to +1 when the prices of both securities are falling) with correlation of returns (which could be anything when the prices of both securities are falling: positive, zero, or negative).

Lots of people in finance do this. It’s (part of) the reason that I insist on my candidates and students specifying _correlation of asset A’s and asset B’s returns _, instead of the incredibly sloppy correlation of assets A and B.

Yet I specifically said " thus returns were negative"…

In my example returns were all negative which I stated. Yes correlation can be +1 with returns all being positive or 0.

Which is, of course, irrelevant.

You can have two sets of returns, all of which are negative, which have a correlation of −1. Or zero. Or +1. Or anything else.

The fact that they’re all negative means nothing in this context.

Let’s say we have assets A and B which are identical in every way in terms of return and magnitude of return as well. Lets say for both assets A and B in year 1 and 2 returns were -50% and -25%. Correlation would be +1

In what you said it is possible in the above example for them to be 0 or -1. How?

indeed what the text is getting at and in the original post is that when returns across all assets are negative then correlations increase - i.e. In a crisis.

Can you give more context?

That isn’t remotely what I said.

You added a condition: “identical in every way in terms of return and magnitude of return as well.

Of course if their returns are identical in every way their correlation of returns will be +1. Duh.

So what?

What I said is that if you have two assets whose prices are both going down − negative returns every period − while their correlation of prices will be strongly positive, their correlation of _ returns _ can be strongly positive, moderately positive, zero, moderately negative, or strongly negative.

I’m not disputing that. What I’m disputing is this:

It is simply not true that when all assets have negative returns that their correlations of _ prices _ are +1. They will likely be strongly positive, but not necessarily +1.

More to the point, it is patently false that when all assets have negative returns that their correlations of _ returns _ are +1. In fact, they needn’t be positive at all. In fact, they can be −1.

And I’m disputing this:

You’re saying that two assets having negative returns requires (“thus”) that correlations be high. If you mean correlation of prices, you’re correct. If you mean correlation of returns, you’re completely wrong. Unfortunately, you, like most people in finance, didn’t specify which characteristic (prices or returns) you meant when you were discussing correlations. Such sloppy language leads to sloppy thinking, and many people in finance make stupid statements about correlation because of it.

Note, by the way, that it’s low correlations of returns (not prices) that we’re taught is the cornerstone of diversification.

Idk about anyone else but I’m getting a headache on this thread. Feel like we are getting too in the weeds. S2000magician is undoubtedly probably right. I always thought prices drive returns so I’m not following this. If prices are down, returns ar e down. And during contagion they both become more correlated. But now that’s false?

I don’t want to get side tracked too much but, unless you’re saying that at times returns are positive with declining prices (short positions)? Which is why correlation of returns are more important than the correlation of prices.

Once again, that’s not what I said. In fact, I said just the opposite:

Follow closely what I _ am _ saying:

Just because prices on two securities are constantly falling – the returns of each is negative every period – doesn’t necessarily mean that their correlation of returns is positive. It’s possible to have a correlation of prices above +0.90 and have any of the following:

• Correlation of returns = +1.0
• Correlation of returns = +0.5
• Correlation of returns = 0.0
• Correlation of returns = −0.5
• Correlation of returns = −1.0

In fact, it’s relatively easy to create any of these situations. You should give it a try, if only to convince yourself that it’s true.

Ok yes technically/mathematically. Yes. I was using the extremes of correlation being +1 and -1 as an oversimplification to try to illustrate the point that we are getting at (which you agreed with) and to answer the original posters question. This whole thing added 0 value to the original poster and now they are confused.

If you would prefer, I will start adding qualifiers to each and every answer and example I post on here just like I did with my basis risk example which I figured you were going to beat me up over like this so I just added 10 qualifiers to cover my ass.

When I post on here it is to help fellow candidates understand a concept by making a simple illustration because, at least for me, that’s how I begin to understand things.

Just wanted to ask how on this. Let’s go back to assets A and assets B. Could you provide me with a series of 5 returns for each asset where the returns in every time period are negative for each asset and the correlation is -1 or even negative at all? I tried doing that and my excel must be broken…

I think you put words in my mouth here and assumed that I didn’t know something. Personally, when talking with my clients I usually use the phrase, “just to clarify” because it is always dangerous when talking with clients and colleagues to make assumptions on what they maybe meant or what they may/may not know.

In my oversimplification if we took a snapshot of returns for S&P 500 and EAFE during 2008 both returns would be negative and quite large in magnitude and thus correlation would be high (and by “high” I mean correlation was higher than historical). Let me know if that’s not the case. Again trying to illustrate the point here rather than saying “during 2008 the correlation between the S&P 500 and EAFE was .965147561687748444547894818981987358791136 but in other times the correlation here was only .3588654651384651318616513115168416103158981654753”

But Ill start being more exact if you wish. Don’t know how much value that adds to other candidates though.

Okay I am officially confused and not sure what value this is adding for us. I need an example of how prices can all be falling and have a high positive correlations yet have negative returns correlations.

Sorry googs. I would give you one but Bill would beat me over the head if its not exact enough and up to his standards.

Yes…an example is exactly what is needed for me to understand why this is such a point of contention. Am I at least right in thinking that, in practice, if prices are falling and have a high positive correlation the correlation of returns will also be high and positive? Theoretically it won’t always be the case I understand, but what is an applied example?

I would be careful Mickey, Bill is going to tear that example up even though that’s the case

It’s not a matter of being exact. Talk about putting words in someone’s mouth.

The examples are simple. Trivial, even.

Stock A has these monthly returns for one year, in the order named:

−1%, −2%, −1%, −2%, −1%, −2%, −1%, −2%, −1%, −2%, −1%, −2%

Stock B has these monthly returns for one year, in the order named:

−2%, −1%, −2%, −1%, −2%, −1%, −2%, −1%, −2%, −1%, −2%, −1%

Over to you: what’s the correlation of prices for the year, and what’s the correlation of returns for the year? (To make the first question easier, assume that they’re both priced at \$100 on the first day of the year.)

Sorry about the delay! Was off study for a couple of days.

This is from Topics test Asset Allocation - Kohler.

Schumacher says: “I have the following three concerns with respect to investing internationally:

Concern 1: In times of market stress, diversification benefits can be drastically reduced.

Concern 2: Capital in some countries does not flow freely across borders, which can result in increased market segmentation.

Concern 3: Traditional mean-variance analysis may not apply.”

Schumacher’s concern about international investments that Roth might find advantageous most likely pertains to:

market integration.

the efficient frontier.

conditional correlation.

Incorrect.

The lack of market integration (or the absence of free cross-border capital flows) can be an advantage if it increases market segmentation and helps prevent correlations with other markets from rising. Increased integration of markets can decrease diversification benefits, whereas returns in segmented markets will be influenced mostly by a specific country’s own macroeconomy and will be less subject to changes in correlations when volatility increases. Global correlations tend to increase in times of increased volatility and even appear to be conditional on global volatility. The efficient frontier and traditional mean–variance analysis using unconditional correlations would not apply because correlations remain low when returns are high but become high when returns are negative.

Once again, you’re saying that because they’re both always negative, the correlation must be (“thus”) high.

That’s absolutely wrong.

Now you’re just acting petty and stupid. You know very well that I said nothing about using 20 decimal places of precision.

You’re completely missing the point: if you don’t realize that the correlation of prices can be +0.9 while the correlation of returns is −0.9, then you have a fundamental lack of understanding of how prices, returns, and correlations work. Not some exaggerated, stupid, 20-decimal-place misunderstanding. Fundamental. Basic.

Put the example I gave above into Excel. I’ll patiently await your apology.

If you simply don’t make statements that stem from a lack of understanding, you’ll add a lot of value.