Luestion 4 (TIPS). This question is designed to illustrate the mechanics of 1 avestors may protect themselves against inflation risk by investing in TIPS (Tre ury Inflation-Protected Securities) rather than regular Treasuries. For simplicity, in this question, we will only consider bonds with one-year maturit and pays a single coupon at maturity with a coupon rate of 2%. Further, assume that you can invest any fractional number of dollars (e.g. \$3,847.294910237593) into bonds. Before proceeding further, let me explain how TIPS payments adjust with inflation. Suppose you invest $100,000 into one-year-maturity TIPS with a 2% interest rate. Suppose inflation in the subsequent year turns out to be x=5%. Then, the bond principal will be adjusted to $100,000(1+5%)=$105,000, and your coupon payment will become $105,0002%=$2,100. Your total payment one year later is going to be $105,000+$2,100=$107,100. In contrast, payments from regular Treasuries do not adjust with inflation. For all questions below, your goal as an investor is to ensure that you receive no less than $10,000 one year from now in real terms. That is, if subsequent national inflation were x%, you want to receive no less than $10,000(1+x%) payment next year, 3 Suppose that the inflation rato next year will bo x=10% with 50% probability or a0% with 50% probability. You don't have a crystal ball so you don't know which scenario will happen, (a) (0.6 point) Lot's work out how much you have to invest to achiove your goal. - Suppose you can only invest in regular Treasuries (ono-ycar-maturity, 2% coupon rate). How much moncy do you have to invest today to ensure that you achiove your goal? - Supposo you can invest in TIPS. How mudi do you have to invest to ensure you nochiove your goal? (b) (0.5 point) Do you seo tho boncit of TIPS rolntivo to rogular Treasurfes in tirms of prototing investons from infilation rihk? Pleaso applain