Question

In Mean-Variance Optimization, what happens to the required weight of an asset when you add a rule that forbids short-selling compared to a model without that rule?

Accepted Answer

In Mean-Variance Optimization, you are trying to find the perfect mix of investments that gives you the best return for the least amount of risk. Usually, the math might tell you to take a &#x27;short position&#x27; in an asset. This means you bet against an asset by borrowing it to sell it, hoping to buy it back cheaper later. When you add a rule that forbids short-selling, you are forcing your investment weights to be zero or higher, meaning you can only own assets, not bet against them. If the math originally wanted you to hold a negative amount of a specific asset, the new rule forces that weight up to zero. Because you can no longer use those negative weights to balance your portfolio, the model must shift those missing portions into other assets. This makes the weights of the remaining assets shift upward to make up for the loss of the negative bets. Think of it like a seesaw that is perfectly balanced; if you take away a weight that was pulling one side down, you have to add more weight to the other side to keep the board level.

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In Mean-Variance Optimization, what happens to the required weight of an asset when you add a rule that forbids short-selling compared to a model without that rule?

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