Reading 65:Yield Measures, Spot Rates, and Forward Rates- current, forward

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Q7. If the current two-year spot rate is 6% while the one-year forward rate for one year is 5%, what is the current spot rate for one year?

A)   5.5%.

B)   5.0%.

C)   7.0%.

 

Q8. Given 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)   6.67%.

B)   2.33%.

C)   4.62%.

 

Q9. The one-year spot rate is 6% and the one-year forward rates starting in one, two and three years respectively are 6.5%, 6.8% and 7%. What is the four-year spot rate?

A)   6.51%.

B)   6.58%.

C)   6.57%.

 

Q10. Given 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)   6.75%.

B)   6.00%.

C)   6.25%.

 

 

Q11. Given 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)   $720.

B)   $884.

C)   $724.

 

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Q7. If the current two-year spot rate is 6% while the one-year forward rate for one year is 5%, what is the current spot rate for one year?fficeffice" />

A)   5.5%.

B)   5.0%.

C)   7.0%.

Correct answer is C)

(1 + f)(1 + r₁) = (1 + r₂)²

(1 + 0.05)(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%

 

Q8. Given 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)   6.67%.

B)   2.33%.

C)   4.62%.

Correct answer is C)

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

 

Q9. The one-year spot rate is 6% and the one-year forward rates starting in one, two and three years respectively are 6.5%, 6.8% and 7%. What is the four-year spot rate?

A)   6.51%.

B)   6.58%.

C)   6.57%.

Correct answer is 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%

 

Q10. Given 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)   6.75%.

B)   6.00%.

C)   6.25%.

 

Correct answer is C)

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

 

Q11. Given 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)   $720.

B)   $884.

C)   $724.

Correct answer is C)

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 + ffice:smarttags" />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; CPT → PV = 723.54, or approximately $724.

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