Correlation and corridor width

I will start by saying that I have seen historic posts that have asked the same question. I have read the replies and it still does not make intuitive sense that a high positive correlation would result in a wider corridor. As mentioned in other posts, if the assets will move together, the weights will remain mostly in tact, therefore making the corridor wider really doesn’t buy you anything.

I have committed this to memory since it doesn’t make intuitive sense to me, but would love to hear a valid explanation.

it does buy you a lot - in the sense that you do not have to adjust the weights - and therefore not incur costs for the rebalancing. If the change were small - it is now covered - so you do not incur the costs. However if the width were narrow - you would have had to rebalance and incur costs and increase tracking error.

bos_IT_guy , correlation is a statistical calculation. It is not meant to cover short term frames in the out of sample experience . So if you do have a short term fluctutaion in asset prices ( causing weights to shift ) , if correlations are higher , in the longer term , the risk of weights staying diverged are lower . In other words for higher correlation a natural reversion to the mean should take place as far as relative weights are concerned. There may be a lag in this happeing and the portfolio should be able to bear this temporary imbalance given the higher costs of rebalancing .

Think about the downside too. If correlations are high , when asset weight imbalance does occur , and the manager rushes to rebalance , she will face another weight imbalance when weights revert due to higher correlations .

This would be a round trip charge that will look unnecessary in hindsight ( after the temporary imbalance reverts )

I appreciate the explanations it definitely helps. I’m going to think of it in terms of the extreme - corridor width = 0%. If your corridor width was 0%, how much would you be alarmed if the weights went out of whack. In this case, there would be less to worry about because the chances of them getting too out of whack are low based on the positive correlation. That works for me. Thanks for your help!

Intuitive example:

Say you have a portfolio worth $ 100 with two asset classes A and B, having equal weights, i.e. 50%.

Assumptions: Corridor -> ±5%, Correlation: +1

So, if asset class A moves up by 10% (i.e. reaching 55) we expect that class B also reaches 55. Hence, we have now a portfolio worth $ 110 which, despite the 10% return, needs not rebalancing as stays invested 50% in classes A & B.

Were the correlation lower, it could be possible that weights would deviate from corridor.

It’s a quick and dirty example which I do not know whether is valid in practice but that’s how I have “pictured” this concept in my mind.

Perimel - your example conclusion is not exacly correct. if the corridor width were lower you would still not need to rebalance since the weighting is still 50/50.

say the corridor width in your example were lower (like 1%) then with 50% still in asset class A, and 50% in asset class B there would still not be a rebalancing event.

The reasoning is as Jani and bos_IT_guy stated is that proportions may get out of wack in the short term, but are expected to come back in line eventually.

Taking your example and instead of a perfect correlation, assume a correlation of a little less, say .95. In the short term asset A may increase to $55, while asset B only increased to $52. This puts the proportion at 51.40% for asset A and 48.60% for asset B. Using a 1% corridor width you would need to rebalnce at this point, however at the 5% corridor width you would not. Giving the portfolio a little more time without rebalancing, asset B may catch up to asset A and bring the portfolio back to a 50/50 weighting, or close.