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Behavioral portfolio theory

CFAI Vol 2 pg 38 says “The greater the concavity of the utility curve, the earlier the satiation of a specific security. Thus, the greater the concavity of the utility curve, the greater the number of securities included in the layer”.

Can someone explain why this is the case? I don’t seem to understand the relationship between the concavity of the utility curve and the number of assets in the layer.

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My take is the the greater the concavity, the less risk seeking, so the portfolio has more assets and more diversified

I thought this part was pretty clear and did not think too much of when I read through it. A concave utility means diminishing marginal utility , i.e. as utility increases its rate of increase slows more and more . You are more satisfied with 1 cola but less with second and even less with third.

Instead of second cola , utility will be more with bagel.

Instead of 3rd cola or 2nd bagel a burger may be more satisfying . So very soon with diminishing marginal utility you will be diversified in diet or investments.

If you do not have diminishing marginal utility , for example you have incrreasing slope of utility for increasing utility  also known as convex utility , then you demand more and more of the same thing , such as second or third cola, second bagel etc. Your diet or investments are not diversified simply because you are still deriving utility without substitution. You get concentrated instead of diversified.

Thats great thought