What are the duration and modified duration of a seven-year

Question

FINA 6202 - Analysis of Financial Institutions and Markets Quiz

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 Excel's 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 x (-1.0 x Duration x (Yield_New - Yield_Old)/(1+Yield_Old)),

[if Excel function]             % Change in Price ≈ 100 x (-1.0 x MDuration x (Yield_New - Yield_Old)),

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 Excel's 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.