Reading 68: Yield Measures, Spot Rates, and Forward Rates following, style, black, class

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1．ven the following spot and forward rates, how much should an investor pay for a 3-year, annual zero-coupon bond with a face value of $1,000?

§ One-year spot rate at 3.5%

§ The 1-year forward rate 1 year from today is 11.5%

§ The 1-year forward rate 2 years from today is 19.75%

The investor should pay approximately:

A)   $724.

B)   $720.

C)   $884.

D)   $886.

2．ven the implied annual forward rates of: R₁ = 0.06; ₁r₁ = 0.062; ₂r₁ = 0.063; ₃r₁ = 0.065, what is the theoretical 4-period spot rate?

A)   6.25%.

B)   6.00%.

C)   6.50%.

D)   6.75%.

3．e one-year spot rate is 6 percent and the one-year forward rates starting in one, two and three years respectively are 6.5 percent, 6.8 percent and 7 percent. What is the four-year spot rate?

A)   6.51%.

B)   6.58%.

C)   6.57%.

D)   7.00%.

4．ven the implied forward rates of: R₁ = 0.04; ₁r₁ = 0.04300; ₁r₂ = 0.05098; ₁r₃ = 0.051005, what is the theoretical 4-period spot rate?

A)   4.62%.

B)   2.33%.

C)   4.06%.

D)   6.67%.

5． the current two-year spot rate is 6 percent while the one-year forward rate for one year is 5 percent, what is the current spot rate for one year?

A)   5.0%.

B)   6.0%.

C)   5.5%.

D)   7.0%.

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答案和详解如下：

1．ven the following spot and forward rates, how much should an investor pay for a 3-year, annual zero-coupon bond with a face value of $1,000?

§ One-year spot rate at 3.5%

§ The 1-year forward rate 1 year from today is 11.5%

§ The 1-year forward rate 2 years from today is 19.75%

The investor should pay approximately:

A)   $724.

B)   $720.

C)   $884.

D)   $886.

The correct answer was A)

The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.

Using the formula: (1 + Z₃)³ = (1 + ₁f₀) * (1 + ₁f₁) * (1 + ₁f₂)

Where Z = spot rate and _nf_m = The n year rate m periods from today, (₁f₀ = the 1 year spot rate now)

(1 + Z₃)³ = (1.035) * (1.115) * (1.1975)

Z₃ = 1.3819^1/3 - 1 = 0.11386, or 11.39%

Then, the value of the zero coupon bond = 1,000 / (1.1139)³ = 723.62, or approximately $724.

or, using a financial calculator, N = 3, I/Y = 11.39, FV = 1,000, PMT = 0, Compute PV = 723.54, or approximately $724.

2．ven the implied annual forward rates of: R₁ = 0.06; ₁r₁ = 0.062; ₂r₁ = 0.063; ₃r₁ = 0.065, what is the theoretical 4-period spot rate?

A)   6.25%.

B)   6.00%.

C)   6.50%.

D)   6.75%.

The correct answer was A)

R₄ = [ (1.06) (1.062) (1.063) (1.065) ]^.25 - 1 = 6.25%.

3．e one-year spot rate is 6 percent and the one-year forward rates starting in one, two and three years respectively are 6.5 percent, 6.8 percent and 7 percent. What is the four-year spot rate?

A)   6.51%.

B)   6.58%.

C)   6.57%.

D)   7.00%.

The correct answer was C)

The four-year spot rate is computed as follows:

Four-year spot rate = [(1 + 0.06)(1 + 0.065)(1 + 0.068)(1 + 0.07) ]^1/4 –1 = 6.57%

4．ven the implied forward rates of: R₁ = 0.04; ₁r₁ = 0.04300; ₁r₂ = 0.05098; ₁r₃ = 0.051005, what is the theoretical 4-period spot rate?

A)   4.62%.

B)   2.33%.

C)   4.06%.

D)   6.67%.

The correct answer was A)

[(1.04)(1.043)(1.05098)(1.051005)]^.25-1

5． the current two-year spot rate is 6 percent while the one-year forward rate for one year is 5 percent, what is the current spot rate for one year?

A)   5.0%.

B)   6.0%.

C)   5.5%.

D)   7.0%.

The correct answer was D)

(1+f)(1+r₁) = (1+r₂)²

(1+05)(1+r₁) = (1+0.06)²

(1+r₁) = (1.06)²/ (1+0.05)

1+r₁ = 1.1236/1.05

1+r₁ = 1.0701

r₁ = 0.07 or 7%

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