Price of a Zero-Coupon Bond Maturing - Finance Assignment Help

Assignment Task :

You observe that the current three-year discount factor for default-risk free cash flows is 0.68. Remember, the t-year discount factor is the present value of $1 paid at time t, i.e. cl, = (1 + rt)-t, where 71 is the t-year spot interest rate (annual compounding). Assume all bonds have a face value of $100 and that all securities are default-risk free. All cash flows occur at the end of the year to which they relate. 
a) What is the price of a zero-coupon bond maturing in exactly 3 years?  
b) Your friend makes the following observation about the above bond: "Since there is no risk of default and there are no coupons to re-invest, buying the 3-year zero coupon bond today is a risk-free investment; that is, you are guaranteed to earn an annual return of 13.72% (i.e. 3-year spot rate)". Explain why your friend is not entirely correct and how you would modify the statement to make it correct. 
c) In addition to the bond in (a), you observe the following: a 2-year coupon bond paying 10% annual coupons with a market price of $97, and two annuities that are trading at the same market price as each other. The first annuity matures in 3 years and pays annual cash flows of $20, while the second annuity pays annual cash flows of $28 and matures in 2 years. Using this information: 
i. Complete the term structure of interest rates, i.e. determine the one- and two-year discount factors, di and d2, respectively.  
ii. Determine the price of the annuities.  
d) Assuming annual compounding, determine the implied one-period forward rates f2 (i.e. between year 1 and 2) and f3 (i.e. between year 2 and 3) in this economy. What inference can you make about the market's estimate of the one-year spot interest rate at t = 1 if the liquidity preference theory is correct?  
e) Suppose you decide to purchase a 1-year zero-coupon bond today and also contract today to re-invest the proceeds from the bond for the following two years at 16.5% per year. Show that this arrangement presents an arbitrage opportunity. Demonstrate how you would take advantage of this opportunity.  
f) Consider discount factors such that di < d2 < d3. Explain why it would be odd to observe such a situation in a competitive market.  
 

a) Explain why beta is the appropriate measure of risk in this world. 
b) Portfolio Y is known to be uncorrelated with the market. Explain why this property implies that the risk-free rate in the economy is 5%. 
c) It Is known that one of the portfolios X, Y, Z Iles on the efficient frontier (which includes the risk-free asset). Which portfolio is efficient? Explain/justify your answer.  
d) An Investment manager approaches you and offers you an Investment product with a claimed expected return of 12% and standard deviation of 20%. Should you accept this Investment? Why/why not? If not, show how the manager can optimally create a portfolio with an identical return volatility to his proposed portfolio but with a superior expected return. Illustrate your answer graphically, making sure to label all relevant elements of your picture. 
e) Consider an investor who invests $50,000 in a portfolio consisting of X and Z. $10,000 of that investment was funded with risk-free borrowing. The expected return of the investor's portfolio is 9.375%. 
i. Calculate the dollar amounts invested in each of X and Z.  
ii. If the correlation between X and Z is 213, what is the standard deviation of the investors portfolio? 
f) Show that any portfolio on the Capital Market Line (CML) with a positive weight in the market portfolio is perfectly correlated with the market portfolio. Interpret this result.   
 

This Finance Assignment has been solved by our Finance Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.