The yield on a default-free four-year zero-coupon bond is 3%; the yield on a default-free five-year zero-coupon bond is 4.5%. The bonds have a face value of $1000 and are traded in an open market. You are a money manager and know that you will have a net inflow of $100,000 four years from now, and an obligation (i.e. a net outflow) of $100,000 one year later (i.e. five years from now). Once you get your inflow, you plan to invest part of this inflow (as much as necessary) in risk-free bonds for a year, and immediately pay the rest to your investors in the form of a profit. You would like to hedge the interest-rate risk that is involved in this future bond investment, in order to be able to pre-announce your expected profit today, but also ensure that your obligation is covered. (a) Based on today’s yields, what is the no-arbitrage yield of a one-year forward-rate agreement starting four years from now? (b) Assuming you can obtain such a forward-rate agreement, how much of your inflow will you need to re-invest, and how much will you be able to pay to investors? (c) Now assume that no such forward-rate agreements are being offered in the market. How can you construct one yourself (i.e. replicate one), in order to hedge your interest-rate risk? Carefully describe your strategy, and show that the resulting cash flows mirror those of the forward-rate agreement you are trying to create. Assume you can go either long or short in either bond, and you can also buy or sell fractions of bonds.
Debenture Valuation
A debenture is a private and long-term debt instrument issued by financial, non-financial institutions, governments, or corporations. A debenture is classified as a type of bond, where the instrument carries a fixed rate of interest, commonly known as the ‘coupon rate.’ Debentures are documented in an indenture, clearly specifying the type of debenture, the rate and method of interest computation, and maturity date.
Note Valuation
It is the process to determine the value or worth of an asset, liability, debt of the company. It can be determined by many processes or techniques. Many factors can impact the valuation of an asset, liability, or the company, like:
The yield on a default-free four-year zero-coupon bond is 3%; the yield on a default-free five-year zero-coupon bond is 4.5%. The bonds have a face value of $1000 and are traded in an open market. You are a money manager and know that you will have a net inflow of $100,000 four years from now, and an obligation (i.e. a net outflow) of $100,000 one year later (i.e. five years from now). Once you get your inflow, you plan to invest part of this inflow (as much as necessary) in risk-free bonds for a year, and immediately pay the rest to your investors in the form of a profit. You would like to hedge the interest-rate risk that is involved in this future bond investment, in order to be able to pre-announce your expected profit today, but also ensure that your obligation is covered.
(a) Based on today’s yields, what is the no-arbitrage yield of a one-year forward-rate agreement starting four years from now?
(b) Assuming you can obtain such a forward-rate agreement, how much of your inflow will you need to re-invest, and how much will you be able to pay to investors?
(c) Now assume that no such forward-rate agreements are being offered in the market. How can you construct one yourself (i.e. replicate one), in order to hedge your interest-rate risk? Carefully describe your strategy, and show that the resulting cash flows mirror those of the forward-rate agreement you are trying to create. Assume you can go either long or short in either bond, and you can also buy or sell fractions of bonds.
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