4. Cash as an Investment Portfolio. In this question, we\'ll compare two investm

Question

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 $100. 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 i the interest rate on the bonds that mature in month t. That is, for every dollar in Portfolio B in month -1, we get 1+i 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?

Explanation / Answer

Answer )

a ) As we are getting a return of 'i' at end of a month , it means

here, P =principle invested in start , i = monthly interest rate ,n = number of month.

Answer b)

Pv = Future cash flow / ( 1+ discounting rate ) ^ n

if cash flow(generated from coupon rate) = discount rate ,

PV = future value

I.e in the current case ,

Value of bond = i / (1+i) + F/(1+i) ....for unit time period ,

Month Investment(principle) Amount (portfolio) 1 P P+P*I 2 P(1+i) P(1+i) + P(1+i) *i =>P(1+i)^2 3 P(1+i)^2 P(1+i)^2+P(1+i)^2*i =>P(1+i)^3 4 . . n P(1+i)^n

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