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(i) Two types of risks faced by bodholders are interest rate risks and default risks? What are interest rate risks and default risks, and why might a bond exhibit more or less of these risks?
(ii) You see a bond with the following characteristics:
- bond matures in 10 years
- coupon rate = 7% APR compounded semi-annually, paid semi-annually
- face value = $1000
bond price = $900
What is the yield to maturity (YTM) of this bond, stated as an APR with semi-annual compounding?
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- Bonds have a maturity risk premium that can be modeled as the following:MRP = (t-1) 0.3%were t represents the years to maturity. What is the Maturity risk premium of a bond that matures in 8 years? answer in % without the symbolThe following information about bonds A, B, C, and D are given. Assume that bond prices admit noarbitrage opportunities. What is the convexity of Bond D?Cash Flow at the end ofBond Price Year 1 Year 2 Year 3A 91 100 0 0B 86 0 100 0C 78 0 0 100D ? 5 5 105Suppose that y is the yield on a perpetual government bond that pays interest at the rate of $1 per annum. Assume that y is expressed with simply com- pounding, that interest is paid annually on the bond, and that y follows the process dy = a(y0 −y)dt + oydWt, where a, y0, and o are positive constants and dWt is a Wiener process. (a) What is the process followed by the bond price? (b) What is the expected instantaneous return (including interest and capital gains) to the holder of the bond?
- The rate of return that you would earn if you bought a bond and held It to its maturity date is called the bond's yield to maturity (YTM). If Interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to Its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond's price? Briefly explain with necessary numerical data.Consider the following pure discount bonds with face value $1,000: Maturity Price 1 952.38 2 898.47 3 847.62 4 799.64 5 754.38 a). Find the spot rates and draw a yield curve.b). Assume that there is a constant liquidty premium that is equal to 1% across all maturities. Find the forward rates and the expected one period future interest rates.Assume that the real risk-free rate is 2% and the average annual expected inflation rate is 4%. The DRP and LP for Bond A are each 2%, and the applicable MRP is 3%. What is Bond A's interest rate?
- This first table describes prevailing market interest rates. Market Data Yield 0.05 Required: Using the yield above and the information contained in the table below, please calculate the price and duration of the bond as well as all necessary steps. (Use cells A5 to B5 from the given information to complete this question.) Time Until Payment Payment Discounted Payment Weight Time × Weight 1.00 $30.00 2.00 $30.00 3.00 $30.00 4.00 $1,030.00 Price: DurationAssume the real risk-free is 1% and the average annual expected inflation rate is 4%. The DRP and LP for bond A are each 3%, and the applicable MRP is 3%. What is Bond A's interest rate?The rate of return on a bond held to its maturity date is called the bond’syield to maturity. If interest rates in the economy rise after a bond hasbeen issued, what will happen to the bond’s price and to its YTM? Doesthe length of time to maturity affect the extent to which a given change ininterest rates will affect the bond’s price? Why or why not?
- Calculating the risk premium on bonds The text presents a formula where (1+1) = (1-p)(1 +i+x) + p(0) where i is the nominal interest rate on a riskless bond x is the risk premium p is the probability of default (bankruptcy) If the probability of bankruptcy is zero, the rate of interest on the risky bond is When the nominal interest rate for a risky borrower is 8% and the nominal policy rate of interest is 3%, the probability of bankruptcy is %. (Round your response to two decimal places.) When the probability of bankruptcy is 6% and the nominal policy rate of interest is 4%, the nominal interest rate for a risky borrower is %. (Round your response to two decimal places.) When the probability of bankruptcy is 11% and the nominal policy rate of interest is 4%, the nominal interest rate for a risky borrower is %. (Round your response to two decimal places.) The formula assumes that payment upon default is zero. In fact, it is often positive. How would you change the formula in this case?…Consider the following bonds. Bond A B с D Coupon Rate (annual payments) 0.0% 0.0% 3.5% 7.8% Maturity (years) 10 15 15 10 Which of the bonds A to D is most sensitive to a 1% drop in interest rates from 6.7% to 5.7%? Which bond is least sensitive? Provide an intuitive explanation for your answer.Show all workings. Complete the following table and draw a graph showing how bond pricefor each bond changes over time as they move towards their maturitydates. Describe the relationship between bond prices and timeremaining for maturity.YearsreminingtomaturityBOND ACoupon rate = 8% p.a.Market interest rate =6% p.a.BOND BCoupon rate = 6% p.a.Market interest rate =6% p.a.BOND CCoupon rate = 4% p.a.Market interest rate =6% p.a.109876543210