Question

You believe that 6 months from now, the 12-month treasury spot rate will be 7.00%. You believe that 1 year from now, the 6-month treasury spot rate will be 6.00%. You believe that 18 months from now, the 6-month treasury spot rate will be 5%. 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.
• Invest in a 24-month treasury but sell 6-month prior to maturity.
• You are indifferent between all 3 strategies.

Answer 1

Let us say that $10 is invested in each strategy now

Invest in an 18-month treasury.

Ending value of investment = $100 * (1 + 18 month spot rate)^18/12 =  $100 * (1 + 0.045)^18/12 = $106.83

Invest in a 12-month treasury, at maturity reinvest proceeds in a 6-month treasury

Ending value of investment = $100 * (1 + 12 month spot rate)^12/12 * (1 + 6-month treasury spot rate 1 year from now)^6/12

Ending value of investment = $100 * (1 + 0.042) * (1 + 0.06)^6/12 = $107.28

Invest in a 6 -month treasury, at maturity reinvest proceeds in a 12-month treasury

Ending value of investment = $100 * (1 + 6 month spot rate)^6/12 * (1 + 1-year treasury spot rate 6 months from now)^12/12

Ending value of investment = $100 * (1 + 0.04)^6/12 * (1 + 0.07)^12/12 = $109.12

Invest in a 24-month treasury but sell 6-month prior to maturity

Ending value of investment = ($100 * (1 + 24 month spot rate)^24/12) / (1 + 6-month treasury spot rate 18 months from now)^6/12

Ending value of investment = ($100 * (1 + 0.049)^24/12) / (1 + 0.05)^6/12 = $107.39

The highest return is generated by the strategy with the highest ending value of investment.

This is Invest in a 6 -month treasury, at maturity reinvest proceeds in a 12-month treasury, which generates an ending value of $109.12