Question

In: Finance

You own a $1,000-par zero-coupon bond that has six years of remaining maturity. She plans on...

You own a $1,000-par zero-coupon bond that has six years of remaining maturity. She
plans on selling the bond in one year and believes that the required yield next year will
have the following probability distribution:

Probability Required Yield
0.1 0.067
0.4 0.0685
0.4 0.071
0.1 0.073

a. What is the expected price of the bond at the time of sale?
b. What is the standard deviation of the bond price?

Solutions

Expert Solution

Price of a Zero Coupon Bond
= Face Value / (1+r)n
Where,
Face Value of Zero Coupon Bond = $1000
The bond is selling in one year, so
n = No of years remaing maturity = 6 - 1 = 5years
r = Required Yield
So,
Required Yield Price of Bond
0.067 = 1000/(1+0.067)5 = 1000/(1.067)5 = 1000/1.3830 = $723.07
0.0685 = 1000/(1+0.0685)5 = 1000/(1.0685)5 = 1000/1.39275 = $718.00
0.071 = 1000/(1+0.071)5 = 1000/(1.071)5 = 1000/1.40912 = $709.66
0.073 = 1000/(1+0.073)5 = 1000/(1.073)5 = 1000/1.42232 = $703.08
Now,
Probability Reqired Yield Price Prob*Price Variance = Prob*(Price - Expected Price)2
0.1 0.067 $723.07 $72.31 0.1*(723.07-713.68)2=0.1(9.39)2=0.1*88.1721=8.81721
0.4 0.0685 $718.00 $287.20 0.4*(718.00-713.68)2=0.4(4.32)2=0.4*18.6624=7.46496
0.4 0.071 $709.66 $283.86 0.4*(709.66-713.68)2=0.4(-4.02)2=0.4*16.1604=6.46416
0.1 0.073 $703.08 $70.31 0.1*(703.08-713.68)2=0.1(-10.6)2=0.1*112.36=11.236
Expected Price $713.68 33.98233
a) Expected Price = $713.68
b) Standard Deviation = √Variance = √33.98233 = 5.83

Related Solutions

(Bonds) A zero-coupon bond has a $1,000 par value, 9 years to maturity, and sells for...
(Bonds) A zero-coupon bond has a $1,000 par value, 9 years to maturity, and sells for $527.82. What is its yield to maturity? Assume annual compounding. Record your answer to the nearest 0.01% (no % symbol). E.g., if your answer is 3.455%, record it as 3.46.
A zero-coupon bond has a yield to maturity of 9% and a par value of $1,000....
A zero-coupon bond has a yield to maturity of 9% and a par value of $1,000. By convention, zero bonds are assumed to pay $0 semi-annually. If the bond matures in eight years, the bond should sell for a price of _______ today.v.
A zero-coupon bond has a par value of $1,000 and a yield-to-maturity of 5%. You purchase...
A zero-coupon bond has a par value of $1,000 and a yield-to-maturity of 5%. You purchase the bond when it has exactly 17 years remaining until maturity. You hold the bond for 6 months and then sell it. If the bond's yield-to-maturity is 9% when you sell it, what is your percentage return over this 6-month holding period? When computing bond prices, use a semi-annual compounding period. Enter your answer as a decimal and show 4 decimal places. For example,...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A 1 7.25 % B 2 8.25 C 3 8.75 D 4 9.25 a. According to the expectations hypothesis, what is the market’s expectation of the one-year interest rate three years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What are the expected values of next year’s yields on bonds with maturities of (a) 1 year; (b) 2...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A...
Consider the following $1,000 par value zero-coupon bonds: Bond Years until Maturity Yield to Maturity A 1 8.50 % B 2 9.50 C 3 10.00 D 4 10.50 a. According to the expectations hypothesis, what is the market’s expectation of the one-year interest rate three years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What are the expected values of next year’s yields on bonds with maturities of (a) 1 year; (b) 2...
A zero coupon bond has a par value of $1,000 and will mature in eight years....
A zero coupon bond has a par value of $1,000 and will mature in eight years. a Calculate the current price of this bond if the market yield is: 1) 7.75 percent; ii) 5.25 percent. b. In each case, calculate the percentage change in the price of the bond if the market yield rises by 1 percent.
Bond A has a $1,000 par value and a 6% coupon rate, three years remaining to...
Bond A has a $1,000 par value and a 6% coupon rate, three years remaining to maturity, and an 8% yield to maturity. The duration of Bond A is _____ years.
A bond has 1,000 par value , 17 years to maturity and pays a coupon of...
A bond has 1,000 par value , 17 years to maturity and pays a coupon of 5.25 per year semi annually. The bond is callable in 7 years at 105% of its par value. if the blnfs yield to call is 5.06% per year, what is its annual yield to maturity
A bond has a $1,000 par value, 14 years to maturity, and pays a coupon of...
A bond has a $1,000 par value, 14 years to maturity, and pays a coupon of 8.25% per year, annually. You expect the bond’s yield to maturity to be 7.0% per year in five years. If you plan to buy the bond today and sell it in five years, what is the most that you can pay for the bond and still earn at least a 9.0% per year return on your investment?
A $1,000 par bond with a 12.25% coupon has 10 years to maturity. If the yield...
A $1,000 par bond with a 12.25% coupon has 10 years to maturity. If the yield to maturity is 12.25%, what is the price of the bond? $1,138.25 $1,047.92 $1,000.00 $889.20
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT