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We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said:

It should be noted, however, that dedicated portfolios cost typically from 3% to 7% more in dollars terms than do “immunized” portfolios that are constructed based on matching present value, duration, and convexity of the assets and liabilities. "

When would dedicated portfolios be better than 'immunized' portfolios, where you would have to manage accordingly? Immunized portfolios are dependent on duration, convexity, and present value of cash flows. The book says,

"Portfolios that are constructed by matching these three factors are immunized against parallel shifts in the yield curve, but there may still be a great deal of exposure and vulnerability to other types of shifts, and they need to be actively managed, which can be costly. By contrast, dedicated portfolios do not need to be managed after they are constructed."

What are these other variables? Also, you might have access to more instruments (possibly)? But other than that, I'm not sure when to use dedicated portfolios or just calculate how to immunize the portfolio. Anyone have insight on this?

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With a dedicated portfolio all interest rate risk has been eliminated, since you hold ZCB's that deliver exactly the cash you need when you need it. So it is a perfect hedge against i.r. risk.

With an immunized portfolio you have reduced i.r. risk (by matching duration and convexity) but you still have a probability distribution of outcomes. Yields at different maturities do not always increase by the same amount [i.e. non parallel shifts], so you are exposed to changes in the shape of the yield curve. This cuts both ways, you could end up with more $ than you need or less.

So it is a question of how safe do you want to be. If you can't tolerate any slippage between the cash flows you will get and your projected needs, then go with dedication, which will force you to have a pretty specific portfolio including some zero coupon bonds that may well be illiquid and thus cost you more. If you can handle some variation, the immunization may be enough, and you have more choices of what bonds to buy.

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Take a step back and consider the purpose of immunization: your firm is planning future expenditures, and these are firm commitments. You need to make sure to have cash on hand when these expenditures occur. So you buy bonds, which you plan to sell right before your bills are due. Now you're exposed to interest rate risk.

You have two basic options:

You immunize/fully immunize. Now you don't have to worry about small/any interest rate changes.

You don't immunize. Now you have to estimate the probability distribution of interest rate changes, and figure out how much to allocate (and in which bonds) to have a portfolio that will meet its goals with some specified probability. The higher the probability you want, the more you will have to allocate today.

So, the other variables are the fund's goals and the probability distribution of interest rate changes.

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