# Corridor Width - Asset Correlation

Can somebody explain to me why asset correlation means we should have larger corridors? Intuitively, it seems the opposite would be true.

Say you have 60% allocated to large-cap, and 40% to mid-cap stocks, their correlation would be very high, so even as the market is volatile the weights should remain fairly in line. Therefore, for large moves in the market you would expect the deviations to be very small. Therefore based on my logic, the corridor should be fairly narrow (i.e you don’t need a large corridor).

Why is it the inverse? Why allow a large corridor for assets whose correlation should take care of keeping the allocation % in line with each other.

I guess because you are not diversifying your risk away if you trade in and out of these assets. Narrow corridors would force you to rebalance often but it’s of no benefit if your risk is not lowered much - the assets are highly correlated.

Correlation of what, exactly? Returns? Or prices?

If you think like that, you should get opposite results in terms of every factor (correlation, volatility…).

If two assets move in lockstep, then despite returns inc/dec, the overall allocation should roughly hold since everything is moving together.

When you say, “If two assets move in lockstep”, are you referring to their prices, or their returns?

Returns

So if you have two assets – A and B – and the correlation of their returns is +1.0, and the average returns are +5% for asset A and -5% for asset B, you think that their proportion in your portfolio will remain close to constant?

Don’t understand you example. If A has a +5% return while B had -5% return, wouldn’t that imply that the assets are uncorrelated?

i didn’t get mired in the details with this one. I just assumed what they were saying was, that if asset returns tend to move together (ie correlated) then despite the movement, the overall allocations will stay relatively stable.

Remember that correlation means how two variables move _ relative to their own means _. This goes back to Level I.

If A’s returns are 6%, 4%, 6%, 4%, 6%, 4%, . . . and B’s returns are -4%, -6%, -4%, -6%, -4%, -6% . . . then A’s mean return is 5%, B’s mean return is -5%, and whenever A’s return is above its mean, B’s return is abive its mean (and vice-versa). The correlation of returns is +1.0 , but A’s value is going up while B’s value is going down.

The point is that saying “two assets are correlated” is a meaningless phrase (though common amongst financial types). You have to specify what characteristic of those assets has a high correlation. And high (positive) correlation of returns does not imply high (positive) correlation of prices.

You are indeed correct. Moreover, even if it is the correlation of market value, a high correlation alone does not tell us that the weights of the two assets will not change much. It is the slope that matters. A very steep one would mean the value of one asset will deviate significantly given a small change in the other.

However, this is the the question cleverCFA is asking here. He is trying to figure out why the sync movement of two assets will lead to a wider corridor.

chance of the assets moving out of their bands is higher when asset correlations are higher. so a wider corridor is necessary to prevent the move from triggering a rebalance.

if assets a and b are highly correlated to each other - when asset A moves higher - either Asset A may break its corridor or B might. (which overall means a higher probability of a rebalance). To prevent this move from triggering a rebalance - the widths of the two bands must be higher.

Thanks cpk123 for your answer. I don’t understand or agree with this though.

If you have a portfolio with 2 assets and they are perfectly correlated (i.e. cor = 1). If the weights are \$30 to A and \$70 to B. If A doubles to \$60, B should double to \$140. The weights have remained in line with the original allocation (30%/70%) due to the high positive correlation. So why do we need a wide corridor since the risk of them getting out of line, by my logic at least, is smaller than if they were uncorrelated?

I’m obviously missing something here. What is it I’m not getting?

The general principle here is the easier deviation is, the narrower the corridor should be.

For example, large volatilty, very easy to deviate, so corridor should be narrower; High correlation, not so easy to trigger alarm (though the deduction here is problematic due to reasons above), corridor should be wider.

Short but sweet explanation. I’ll take it. Thanks andyxu.