4. Cash as an Investment Portfolio. In this question, we'll compare two investment portfolios Portfolio A contains only cash, and Portfolio B contains only U.S. Treasury bonds. (Here, we're talking about standard bonds, not inflation-protected bonds.) Both portfolios start with S100. Portfolio B is maintained in the following way. All of the initial funds are invested in one-month Treasury bonds, and once those bonds mature, the entire payout is used to buy a new set of one-month Treasury bonds. This is repeated every month. (a) Denote by it the interest rate on the bonds that mature in month t. That is, for every dollar in Portfolio B in month t - 1, we get 1 it dollars in month t. How do you calculate the value of portfolio B after n months? (b) Treasury bonds are typically considered virtually risk-free and totally liquid, so the price should coincide with the present value. Suppose that, in month t-1, you buy a bond with face value F that matures in month t. Given it, how would you compute the price of this bond? (c) Go to FRED, and download data on the yield on 1-month Treasury bonds (code: DGSIMO) and the CPI (code: CPIAUCSL). When you select the yield data, use the drop-down menu to change the frequency to monthly. (Next to the drop-down for frequency, there's a drop-down called "Aggregation method," which should be set to "average.") Also, the yields from FRED are annualized, and we want them to be monthly. Consequently, all of the yields should be divided by 12 before you use them in any calculations below i. Plot the yield series over the entire span of time for which data is available. ii. Over the same time span, plot the price of a one-month treasury bond that has a face value of $1 ii. Suppose that Portfolios A and B are started in August, 2001. Plot the value of both portfolios, in dollars, over time on the same set of axes. iv. To convert the value of an asset from dollars to goods, it's necessary to divide by the dollar value by the price of goods. Plot the value of both portfolios, in goods, over time on the same set of axes, starting in August 2001 v. The above should show that Portfolio A performs poorly, relative to Portfolio B, over the span of time considered. Now, suppose that Portfolios A and B are started in January 2009 Repeat parts iii and iv. Now, compared to what you saw in parts iii. and iv., Portfolio A doesn't appear do as badly relative to Portfolio B. Why