15.2 The Yield Curve and Future Interest Rates

Question 1

Fill in the blank

the upward-sloping yield curve is evidence that short-term rates are going to be ____ next year

Forward Interest Rates

Answer 1

higher

Forward Interest Rates

Question 2

the yield curve under certainty

two strategies:
* 2-year zero offering 2-year yield-to-maturity y₂ = 6%
* $890 in a 1-year zero coupon bond with yield-to-maturity of 5%

Calculate the interest rate for 1-year bond when it rolls over next year?

Forward Interest Rates

Answer 2

buy and hold 2-year zero must equal roll over 1-year bonds

$890 x 1.06² = $890 x 1.05 x (1 + r₂)

1 + r₂ = 1.06²/1.05 = 1.0701

Forward Interest Rates

Question 3

Concept

When next year’s short rate, r₂, is greater than this year’s short rate, r₁ …

Forward Interest Rates

Answer 3

the yield curve slopes upward

Forward Interest Rates

Question 4

assuming an arbitrage-free world,

the 2-year spot rate is equal to the geometric mean of …

Forward Interest Rates

Answer 4

this year and next year’s short rates

Forward Interest Rates

Question 5

equation

generalizes our approach to inferring a future short rate from the yield curve of zero-coupon bonds

Forward Interest Rates

Answer 5

(1+y_n)ⁿ = (1+y_n-1)^n-1 x (1+r_n)

Forward Interest Rates

Question 6

equation

solve for the short rate in the last period of an n-year investment

Forward Interest Rates

Answer 6

(1+r_n) = (1+y_n)ⁿ / (1+y_n-1)^n-1

Forward Interest Rates

Question 7

true or false

the forward rate equals the expected value of the future short interest rate

Forward Interest Rates

Answer 7

False;
the forward rate may not even the expected value of the future short interest rate

Forward Interest Rates

Question 8

Fill in the blank

They call the yield to maturity on zero-coupon bonds the ____ , meaning the rate that prevails today for a time period corresponding to the zero’s maturity

Answer 8

spot rate

Question 9

Define

spot rate

Answer 9

meaning the rate that prevails today for a time period corresponding to the zreo’s maturity

Question 10

Define

short rate

Answer 10

for a given time interval refers to the interest rate for that interval available at different points in time

Question 11

Calculate short rate

If the spot rate for a 3-year investment y₃=7%, and y₄=8%, calculate the year-4 short rate r₄

Answer 11

1.08⁴ / 1.07³ = 1.1106 or 11.06%

• recognizing that future interest rates are uncertain, we call the interest rate that we infer in this matter the forward interest rate rather than the future short rate because it may not be the interest rate that actually will prevail at the future date.

Question 12

Define

forward rate for period n

Answer 12

the “break-even” interest rate that equates the return on an n-period zero-coupon bond to that of an (n-1)-period zero-coupon bond rolled over into a 1-year bond in year n.