Question 2 (TIPS inflation protection).

This question is designed to guide you to think through the mechanics, as well as the limitations, of protection against inflation risk using TIPS (Treasury Inflation Protected Securities). For simplicity, in this question, we will only consider TIPS that is one-year maturity and pays a single annual coupon with a coupon rate of 2%. Further assume that you can invest any fraction number of money into TIPS (e.g. $3,847.294910237593). How does TIPS adjust with inflation? Suppose you invest $100,000 into a one-year TIPS with 2% interest rate. Suppose national inflation in the subsequent year is x = 5%. Then, the bond principal will be adjusted to $100, 000(1+5%) = $105, 000, and your coupon payment will become $105, 000 2% = $2, 100. Your total payment one year later is going to be $105, 000 + $2, 100 = $107, 100.

(a) Your goal is to receive $10,000 one year from now in real terms. To be clear, this refers to all the cash you receive from TIPS - coupon and principal combined. You don't know what inflation will be next year. To achieve this goal, how much do you need to invest into TIPS today?

(b) As discussed in lecture 7, different goods have different inflation rates. Suppose you are saving for college tuition, which costs $10,000 today but its price will change at rate y%. y% can differ from the national inflation rate x% by at most 5%. x% can be anywhere between -10% to +10%. Recall that TIPS adjust with the national inflation rate x%. How much do you need to invest in TIPS today to guarantee that you are able to pay tuition next year using cash payoff (again, coupon and principal combined) from your TIPS investment?

Hint: figure out the worst case scenario. That is, within the possible ranges of x and y (10% x% 10%, and x%5% y% x+5%), which combination of x and y values require the highest amount of investment today?

(c) One of the stated purposes of TIPS is to help investors protect themselves from the uncertainty of inflation risk. Given your answer to question (b), how does the dispersion in inflation rates across goods impact the ability of TIPS to achieve this stated goal?