Question

You believe that 6 months from now, the 12-month treasury spot rate will be 7%. You believe that 1 year from now, the 6-month treasury spot rate will be 6.00%. Given the treasury spot rates below, which of the following strategies would generate the highest return?

Term	Spot Rate
6-month	4.00%
12-month	4.20%
18-month	4.50%
24-month	4.90%
30-month	5.40%
36-month	5.70%
42-month	6.00%
48-month	6.40%

• Invest in an 18-month treasury.
• Invest in a 12-month treasury, at maturity reinvest proceeds in a 6-month treasury.
• Invest in a 6 month treasury, at maturity reinvest proceeds in a 12-month treasury.
• You are indifferent between all 3 strategies.

Answer 1

In order to compare the return from investing in different strategies, we will assume that an Investor has $ 1000 to Invest. Keep in mind that the spot rate is an annual yield.

1) Investing in an 18-month treasury:

The return from this strategy can be computed as follows:

$ 1000 * (1+0.045)^(18/12) = 1068.2537.

Thus the return can now be calculated as [ (1068.2537 / 1000) - 1 ] * 100 = 6.82537%

Note: The power term is 18/12 as 4.5% is an annual rate but we are investing for 18 months.

2) Investing in a 12-month treasury and at maturity reinvesting the proceeds in a 6-month treasury:

First, we will calculate the money that we will have at the end of 12 months. This can be calculated as follows:

$ 1000 * (1.042) = $ 1042.

At the end of 12 months we will have $ 1042. Now, since we believe that the 6-month spot rate 1 year from now will be 6%, we will assume that the proceeds will be reinvested at this rate.

$1042 * (1.06)^(6/12) = $ 1072.804661

The return can now be calculated as follows:

[ (1072.903661 / 1000 ) - 1 ] * 100 = 7.28046 %

3) Investing in a 6 month treasury and reinvesting the proceeds at maturity in a 12-month treasury:

Initially we are going to invest 1000 at the 6 month rate. The money that we will have at the end of 6 months can be calculated as follows:

$ 1000 * (1.04)^(6/12) = 1019.8039

Now, we will invest it at the 12 month spot rate, which according to our belief, will be 7 % after 6 month.

1019.8039 * (1.07) = 1091.19017.

The return from this strategy can be calculated as follows:

[(1091.19017 / 1000) - 1] * 100 = 9.119 %

According to the above calculations, it would be ideal to invest in the 3rd strategy as it has the highest return over an 18 month period.