FINS2624 Lecture Notes - Lecture 3: Cash Flow, Approximation Error

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18 May 2018

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3 - Duration

Change in security values due to change in interest rates

Risk measurement must measure sensitivity of market value to changes in interest

rates

Macaulay duration:

• Elasticity of price to the interest rate (sensitivity)

How much you take maturity of a cash flow into account depends on the

contribution of its PV to the price of the bond

Average life/ maturity interpretation – how long on average does it take to get back cost of

investment (in present value)

Duration increases with maturity of a bond – however, at a decreasing rate

The higher a coupon rate a bond pays, the lower its duration

• Higher weights put on cash flows before maturity

Duration increases as yield decreases (future cash flows discounted progressively less)

Duration as specific point is essentially slope of price-yield curve at that point

Approximation error: Price change always smaller (less positive, more negative) than

actual price changes if calculation based on duration (at t=0 rate)

• The greater the convexity of the price-yield curve, the greater approximation error

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Document Summary

Change in security values due to change in interest rates. Risk measurement must measure sensitivity of market value to changes in interest rates. Macaulay duration: elasticity of price to the interest rate (sensitivity) How much you take maturity of a cash flow into account depends on the contribution of its pv to the price of the bond. Average life/ maturity interpretation how long on average does it take to get back cost of investment (in present value) Duration increases with maturity of a bond however, at a decreasing rate. The higher a coupon rate a bond pays, the lower its duration: higher weights put on cash flows before maturity. Duration increases as yield decreases (future cash flows discounted progressively less) Duration as specific point is essentially slope of price-yield curve at that point.

Related Questions

1. Which, if any, of the following statements are false?

A. For a given coupon rate, the sensitivity of bond prices to changes in interest rates increases at an increasing rate as maturity increases.

B. For a given absolute change in interest rates from the same base level, the proportionate increase in bond prices when rates fall is larger than the proportionate decrease in bond prices when rates rise.

C. For identical coupon rates and a given absolute change in interest rates from the same base level, long-term bonds change proportionately more in price than short-term bonds.

D. For identical maturities and a given absolute change in interest rates from the same base level, low-coupon bonds change proportionately less in price than high-coupon bonds.

2. What are the duration and modified duration of a seven-year, 3.5 percent coupon rate, annual coupon payment, $1000 par value government note priced today to yield 3 percent to maturity (use the text formulas or Excelâs Duration and MDuration functions)? What is the convexity of this instrument? [Recall that Bonds and Bond Properties.xls illustrates these calculations.] Using one of the following approximation formulas with yield data in decimal form,

[if text formula] % Change in Price 100 (-1.0 Duration (YieldNew-YieldOld)/(1+YieldOld)),

[if Excel function] % Change in Price 100 (-1.0 MDuration (YieldNew-YieldOld)),

what is the approximate percentage change in this bond's price if yields on comparable securities rise to 4 percent? What is the actual percentage change in this bond's price if yields on comparable securities rise to 4percent (use a financial calculator or Excelâs PV function)?

3. Consider the dividend discount model, the capital asset pricing model, the arbitrage pricing model and the firm valuation model. If these accurately portray the intrinsic values of stock prices and stock returns, then what is the corresponding fundamental relationship between stock prices and interest rates? Explain your answers.

limemouse200

A more accurate measure of the change in bond price due to changes in yield to maturity can be found using both modified duration and __________.

A. Macaulay duration

B. conversion premium

C. time to maturity

D. convexity

One CBOT corn futures contract trades in units of 5,000 bushels and the minimum initial margin is $2,500 per contract. On July 17, 2013, the Sep '13 CBOT corn futures contract settled at $6.50 per bushel. Calculate the amount of leverage inherent in the futures contract using the minimum initial margin.

Holding all else equal, an unexpected fall in interest rates will cause the value of a given outstanding call option to __________.

Please use Excel to complete the problem below.

Immunization

Your company has just built and patented a laser defense system and is planning on installing the equipment in various locations around the country. To finance the installations, you, the CFO, have borrowed $1 billion, which your company will need to repay in five years. The market interest rate is 8%, so the present value of this obligation is $680,583,197. You decide to fund the obligation using three-year zero-coupon bonds and perpetuities that make annual coupon payments.

1. How can you immunize the obligation? (Here, you need to construct an immunized portfolio that consists of the zero-coupon bonds and the perpetuities.)

2. Now suppose that one year has passed and that the market rate is still 8%. You need to ensure that the obligation is still fully-funded and immunized. Is the obligation still fully-funded and immunized? If not, what do you need to do to fully fund and immunized the obligation?

Duration

1. What is the duration of a 10-year, 6% bond if the market rate on bonds of similar quality is 5.8%?

2. Now suppose that the yield to maturity has changed to 5.81%. Using Macaulay duration, what is the approximate percent change in the price of the bond? (You do not need to recalculate Macaulay duration using 5.81%. Use the duration value that you found in Problem 1.)

3. Using convexity, what is the approximate percent change in the price of the bond?

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FINS2624 Lecture Notes - Lecture 3: Cash Flow, Approximation Error

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