So I’m a little confused on this and was hoping someone can maybe help me out…
I watched Mark Meldrum’s videos, and from those I gathered that it’s generally best to immunize with a bond/portfolio that has the greatest convexity(with the tradeoff of lower yield). However, after missing a few practice questions related to this topic, many had the optimal immunization choice as the bond/portfolio with the lowest convexity. I know that lower convexity makes it more like a zero-coupon bond, but is there an easy way to remember when you should try to aim for the higher/lower convexity, based upon what you’re trying to immunize?
If you expect stable rates (upward sloping), you should sell convexity (reduce it) as those trade with lower yields and bonds benefit from convexity when rates are volatile.
If you expect volatile interest rates, relative to your liabilities, increasing the convexity will help so that your assets gain more due to a rate decrease and lose less due to a rate increase.
So let’s say hypothetically you’re given three choices for immunization and there are no rate volatility or yield curve expectations listed in the question. Choose the one with maximum convexity(assuming duration, etc. etc.are all the same)?
You want convexity to be higher than convexity of the liabilities to protect it during parallel shifts.
Convexity and dispersion of cash flows, however, creates structural risk. So you want the convexity of your portfolio to be higher than the liability, but minimally higher to limit structural risk from twists and shifts in the yield curve.
Portfolio A has convexity of 8.5, portfolio b has convexity of 10.5, and portfolio c has convexity of 11.5. All else equal you would select portfolio b
Seems right. How about single liabilities vs multiple liabilities? In the case of multiple liabilities would you want convexity to be the highest possible?
You want BPVA = BPVL, that’s most important. Then you can pick a portfolio that has a slightly higher convexity. Doesn’t matter whether its single or multiple liabilities. If you expect high interest rate volatility, then you can pick a portfolio with a much higher convexity.
be careful selecting a portfolio with “much higher convexity” when you are immunizing. The goal of immunizing is meeting the FV of the liability. Selecting a much higher convexity portfolio than liability increases your structural risk to shifts and twists in the yield curve and could leave you exposed.