Fina 4000

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Calculator: 912.44 FV 2 N PV = -$829.73. 80 PMT i = 14.29%

[pic 8]

- A bond with 3 years to maturity and a coupon of 6.25% is currently selling at $932.24. Assume annual coupon payments.

- What is its yield to maturity?

- Compute the duration of the bond.

- If interest rates are expected to decrease by 50 basis points, what is the expected dollar change in price? Percentage change in price?

- Calculator (or Excel): FV=$1,000 N=3 PV = -$932.24. PMT=62.50 y = 8.92% [Note: it is implicit that the FV = $1,000 here]

- Use the yield determined in Part a and plug this into the duration formula from class:

[pic 9]

- Using the equation on slide #12 from class (“BondDuration” slides):

%ΔPB ≈ (-2.82)(-0.005/1.0892)(100) = 1.29%.

Based on the initial will be price of $932.24, the dollar change in price is 1.29% of $932.24, or $12.03, and the new price is $944.27. This is an approximation. The actual new price will be $944.50:

Calculator: 1,000 FV 3 N I = 8.42 62.50 PMT PV = 944.50.

This represents a $12.26, or a 1.31%, increase in the bond price.

- Briefly explain the relationship between bond price volatility and term-to-maturity, and between bond price volatility and the coupon rate.

The longer the term to maturity (all else equal), the greater the price swings for a given change in interest rates. This is due to the fact that the sensitivity of the present value of a future cash flow to changes in the discount rate is larger the further in the future is the date when the cash flow is received.

The smaller the coupon rate (all else equal), the greater the bond price volatility. The intuition behind this result is that a larger coupon rate shifts relatively more of the total value of the bond toward cash flows received earlier in time.

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- Briefly (in a couple of sentences) explain the central assertion of the expectations theory of the term structure. Suppose an economist wants to test the expectations theory, and runs the following linear regression:

[pic 10]

where is the change in the short term yield periods (years) in the future and is the current slope of the yield curve.[1] What does the expectations theory imply about the parameter β? [Should it be positive or negative?] Suppose that the estimate in the data is negative. [Regressions of this sort often do give negative estimates.] How would you interpret this?[pic 11][pic 12][pic 13]

The expectations theory of the term structure asserts that long term yields equal the average of expected future short term yields. Suppose that the current slope of the yield curve is positive. Under the expectations theory, this implies that short term yields are expected to rise in the future. In other words, is expected to be positive. Similar logic indicates that when the current slope of the yield curve is negative, is expected to be negative. The implication is that the current slope of the yield curve should be positively correlated with future changes in short term yields, i.e., the coefficient β should be positive. A negative estimate of β in the data indicates that the expectations theory is incorrect, or at least incomplete. The negative sign of the slope coefficient presumably indicates the relative importance of the risk premium associated with holding longer-term bonds. In fact, it can be shown that a negative β value implies that the risk premium must be positively related to the slope of the term structure. [pic 14][pic 15]

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