Find the limiting value of Macaulay duration as maturity is increased to infinity of an 8% coupon bond that is trading at a yield of 8% and pays coupons every 6 months. Please round your numerical answer to the nearest integer.
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- Assume the current Treasury yield curve shows that the spot rates for six months, one year, and one and a half years are 1.0%, 1.1%, and 1.3%, all quoted as semiannually compounded APRs. What is the price of a $1,000 par, 5% coupon bond maturing in one and a half years (the next coupon is exactly six months from now)?Assume the current Treasury yield curve shows that the spot rates for 6 months, 12 months, 18 months and 24 months are 2% ,2.25% , 2.5% and 3%, respectively, all quoted as semiannually compounded APRs. What is the price of a $3000 par, 4.5% coupon bond (with semi-annual payments) maturing in 12 months (the next coupon is exactly 6 months from now)? Please use excel to solve.Assume the current Treasury yield curve shows that the spot rates for six months, one year, and one and a half years are 1%, 1.1%, and 1.3%, all quoted as semiannually compounded APRs. What is the price of a $1,000 par, 4% coupon bond maturing in one and a half years (the next coupon is exactly six months from now)?
- Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.7% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 5% per annum semiannuallyConsider a long forward contract to purchase a coupon-bearing bond whose current price is $910. We will suppose that the forward contract matures in 9 months. We will also suppose that a coupon payment of $45 is expected after 4 months. We assume that the 4-month and 9-month risk-free interest rates (continuously compounded) are, respectively, 3% and 4% per annum. Explain how an arbitrageur can make profits from this scenario.In a given securities market, an investment at time t=0 of £95 generates a return of £105 at time t=2 years. However, an investment of £95 at time t=2 (which is agreed from the outset) generates a return of £108 at time t=5 years. Given that the 5-year par yield is 5.3%, calculate, to two decimal places, the current price of a 5-year bond of £10,000 nominal paying coupons at a rate of 4.5% per annum and redeemed at 95%.
- Suppose GE plans to issue a note that matures in 2 years and has a 3.67% coupon rate. If the market yield is 4.91%, what is the market price?Using both duration and convexity, estimate the new price of a 5-year 9% coupon bind with par calue of $100 and yueld of 9% that experiences a 100-basis-point increase in yield. $96.14 $96.10 $96.16 $96.12Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assume the entire 4.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.) Economy Probability YTM price capital gain coupon interest HPR boom 0.25 10% normal growth 0.50 9% recession 0.25 8%
- What is the most we should pay for a bond with a par value of $1000, coupon rate of 9.6% paid annually, and a remaining life of 16 years? The yield to maturity is 7.1%. Assume annual discounting. (Round your answer to the nearest penny.)Consider a 10-year bond, with face value 1000, coupon rate 6% (annual coupon payment), selling at par. Suppose the coupons can be reinvested at 5% per year. Calculate the realized compound return. Suppose on the maturity date, the company only returns 60% of the par value to the investor (all coupons are paid in full). Recalculate the realized compound return.The ABC stock currently stands at 5000 and has a volatility of 20% per annum. The risk-free rate of interest is 4.25% per annum and the stock provides a dividend yield of 2.5% per annum, both with continuous compounding. Using the Black‐Scholes model, calculate the value of six-month European call and put with an exercise price of $4900.