I’m a bit confused as to when you want portfolio convexity to exceed that of the liabilities and when you don’t. I originally thought that you always want it to exceed liability convexity but there are some readings when it talks about minimizing convexity. If anyone can help simplify this for me that would be great. Are there exceptions to the rule and what are they?
Rule for single liability = minimize asset convexity.
Rule for multiple liabilities = have asset convexity be somewhat higher than liability convexity.
Higher convexity means more structural risk, so you want to minimize convexity when immunizing liabilities all else equal.
However, in order to immunize multiple liabilities the convexity of the asset portfolio has to be greater that the convexity of the liability portfolio. This is because you need a greater dispersion of asset cash flows relative to liability cash flows to immunize the liabilities.
Convexity has intrinsic value related to volatility, like an option. Hence, there is going to be a trade off between yield and convexity. So, if a manager anticipates a period of lower than expected volatility, it might make sense to sell (reduce) convexity as a tactical move even if it drops below liabilities.
BTW, which readings exactly are you referencing?
They were referring to immunizing multiple liabilities so your statement is incorrect.
In order to immunize liabilities 3 conditions must hold.
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Market value of assets must be greater than the market value of liabilities
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Basis point value of assets must equal basis point value of liabilities
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Convexity of assets must be greater than the convexity of liabilities