Suppose that you manage a retirement fund that must pay a level stream of guaran

Question

Suppose that you manage a retirement fund that must pay a level stream of guaranteed annual benefit payments over the next thirty years. Your goal is meet these obligations with minimum risk, at minimum cost today. Explain the benefits and disadvantages of the following investment strategies.

a.) Invest in a portfolio of 30-year Treasury bonds with a coupon equal to the par yield, i.e., Treasury bonds selling for their par value.

b.) Invest in equal face value amounts of Treasury zero’s maturing in years one through thirty.

c.) Invest in equal portfolio weights (present value) of Treasury zero’s maturing in years one through thirty.

d.) Invest in a duration-matched portfolio of Treasury bonds of various coupons and maturities.

e.) Invest in a duration- and convexity-matched portfolio of Treasury bonds of various coupons and maturities.

f.) Invest in a 50%/50% mixture of Treasury bonds and corporate bonds which have higher yields, while matching the overall duration to the duration of your liabilities.

Explanation / Answer

a.) Invest in a portfolio of 30-year Treasury bonds with a coupon equal to the par yield, i.e., Treasury bonds selling for their par value.

This is a conservative strategy that focuses on capital preservation. The disadvantage is that infaltion will eat in to the corpus and reduce the consumption potential of the beneficiaries over time.

b.) Invest in equal face value amounts of Treasury zero’s maturing in years one through thirty.

This is also by and large conservative, but incurs reinvestment risks. The losses in bond protfolios will be less than more risky investments, but the movement of the yield curve and the interest rate changes will expose the portfolio to more capital losses than maturity matching strategies, such as in option (a)

c.) Invest in equal portfolio weights (present value) of Treasury zero’s maturing in years one through thirty.

The reinvestment risks are spread out evenly across the duration of the fund management. Hence the reinvestment risks and the interest rate risks can be said to cancel each other out to some extent. Given that the corpus will be depleted by the end of the 30 year period, this closley matches the payout pattern and seems the most suitable to the purpose.

d.) Invest in a duration-matched portfolio of Treasury bonds of various coupons and maturities.

This strategy provides coupon payments in addition to capital gains and hence is a less conservative strategy. It is also more complicated to construct and the response of the portfolio to the yield curve shifts and the interest changes become more non-linear and unpredictable and may not be suitable to provide a steady income stream, being more suitable to a more aggressive return oriented portfolio strategy.

e.) Invest in a duration- and convexity-matched portfolio of Treasury bonds of various coupons and maturities.

Matching convexity in addition to duration seeks to immunize the portfolio against second order changes in the yield curve and interest rate changes. Multi-duration, coupon yielding bonds may be more suitable to more aggressive return oriented portfolio strategies.

f.) Invest in a 50%/50% mixture of Treasury bonds and corporate bonds which have higher yields, while matching the overall duration to the duration of your liabilities.

This is a more aggressive strategy with some protection against inflation being provided by the use of higher yield bonds. The possibility of default on higher yielding bonds will also be more and hence may make it unsuitable for inclusion in a portfolio targeted at providing a steady revenue stream.

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