Financial institutions chapter 6

A bank buys a $10,000 Treasury bill (zero-coupon) with a maturity of 1 year. Current market rates are 7%. If interest rates rise to 7.15%, what is the approximate change in the price of the T-bill? 1) -0.02% 2) -140.19% 3) -14.02% 4) -1.40% 5) -0.14%

-0.14% ΔP/P = -[Duration/(1+i)]*Δi =- [1/(1+0.07)]*(0.0715 - 0.07) = -0.14%

A bond's modified duration is 4.3 years. Current market rates are 5.4%. If interest rates increase to 5.65%, what is the approximate change in the price of the bond? 1) -10.75% 2) -1.08% 3) -0.01% 4) 5.40% 5) 0.54%

-1.08% ΔP/P = -[D*]*Δi =- 4.3*(0.0565 - 0.054) = -1.08%

A bond's Macauley duration is 7.25 years. Current market rates are 7%. If interest rates increase to 7.5%, what is the approximate change in the price of the bond? 1) 0.70% 2) -33.88% 3) -0.03% 4) 7.00% 5) -3.39%

-3.39% ΔP/P = -[Duration/(1+i)]*Δi =- [7.25/(1+0.07)]*(0.075 - 0.07) = -3.39%

A bond that has an annual coupon rate of 15% has two years to maturity. If the current discount rate is 8%, what is the bond's Macaulay's duration? 1) 2.00 years 2) 1.77 years 3) 1.88 years 4) 1.66 years 5) 1.99 years

1.88

A bond's Macaulay duration is 3.4 years. If the current annual interest rate is 11%, what is the modified duration of this bond? 1) 3.06 years 2) 3.40 years 3) 2.96 years 4) 4.13 years 5) 4.00 years

3.06 3.4 / 1.11 = 3.06

Which of the following are sources of a bond's total return? 1) Coupon interest 2) Reinvestment income 3) Capital gains or losses realized at maturity 4) All of the above are sources of a bond's total return 5) a. and c. only

all of the above are sources of a bond's total return

Bond prices and interest rates move in the same direction. 1) True 2) False

false

The Macaulay's duration of a 10-year, 10% bond with a face value of $1,000 and a market rate of 8%, compounded annually is: 1) 10 years 2) 11 years 3) 12 years 4) 13 years 5) None of the above

none of the above

A stripped security: 1) should sell as a package of zero coupon bonds. 2) has no market value 3) is easier to value than a traditional bond. 4) pays no interest. 5) has no par value.

should sell as a package of zero coupon bonds

If a bond is selling at par value, then: 1) the yield to maturity is less than the coupon rate. 2) the yield to maturity is greater than the coupon rate. 3) its duration must be greater than its maturity. 4) the yield to maturity is equal to the coupon rate. 5) its duration must be equal to its maturity.

the yield to maturity is equal to the coupon rate

If a bond is selling at a discount, then: 1) the yield to maturity is less than the coupon rate. 2) the yield to maturity is equal to the coupon rate. 3) the yield to maturity is greater than the coupon rate. 4) its duration must be equal to its maturity. 5) its duration must be greater than its maturity.

the yield to maturity is greater than the coupon rate

All other things the same, longer maturity bonds have greater relative price volatility than shorter maturity bonds. 1) True 2) False

true

Using a 360-day year results in higher returns than using a 365-day year. 1) True 2) False

false

A bank quotes you an effective annual rate of 6% on a monthly investment. What is the annual percentage rate (APR, or quoted rate)? 1) 6.19% 2) 5.84% 3) 4.83% 4) 6.56% 5) 5.31%

5.84% APR = [ ( (1+EAR)^(1/m) ) -1 ] * m =[ (1.06^(1/12)) -1 ]* 12 = 0.0584

What is the effective annual rate of an investment that offers 8%, compounded quarterly? 1) 8.16% 2) 8.64% 3) 8.24% 4) 8.32% 5) 8.00%

8.24% Effective Rate = (1 + .08/4)4 - 1 = .0824

For a given absolute change in interest rates, the percentage increase in an option free bond's price will be less than the percentage decrease. 1) True 2) False

false

Assuming an 8% return, compounded semi-annually, what is the market value of a 12% coupon bond with three years to maturity? 1) $1,104.84 2) $1,419.68 3) $2,000.00 4) $1,809.35 5) $1,000.00

$1,104.84 Financial calculator solution P/Y = 2 FV = 1,000 PMT = 12%/2 * 1,000 = 60 N = 3 * 2 = 6 I = 8 PV = ? = 1,104.84

If you invested $200 today, another $400 in one year, and another $600 in two years, how much will your investment be worth (to the nearest dollar) in five years, assuming a 7% annual compound return? 1) $720 2) $1,098 3) $770 4) $1,540 5) $600

$1,540 Financial calculator solution Step 1 CF0 = 200 CF1 = 400 CF2 = 600 I = 7 NPV = ? = 1,097.90 Step 2 PV = 1,097.90 I = 7 N = 5 FV = ? = 1,539.86

To the nearest dollar, what is the value today of an investment that pays $1,000,000 in 15 years, assuming an annual opportunity cost of 8%? 1) $3,238,387 2) $555,265 3) $315,242 4) $1,000,000 5) $463,193

$315,242 Financial calculator solution FV = 1,000,000 I = 8 N = 15 PV = ? = 315,241.70

To the nearest dollar, what is the value today of an investment that pays $10,000 in five years, assuming an annual opportunity cost of 6%? 1) $8,626 2) $11,592 3) $10,000 4) $7,130 5) $7,473

$7,473 Financial calculator solution FV = 10,000 I = 6 N = 5 PV = ? = 7,472.58

To the nearest dollar, what is the value today of an investment that pays $15,000 in seven years, assuming an annual opportunity cost of 9%? 1) $15,000 2) $8,206 3) $27,421 4) $7,473 5) $7,130

$8,206 Financial calculator solution FV = 15,000 I = 9 N = 7 PV = ? = 8,205.51

A bank buys a $10,000 Treasury bill (zero-coupon) with a maturity of 1 year. Current market rates are 11.5%. If interest rates fall to 11.05%, what is the approximate change in the price of the T-bill? 1) 403.59% 2) 40.36% 3) 4.04% 4) -0.02% 5) 0.40%

.40% ΔP/P = -[Duration/(1+i)]*Δi =- [1/(1+0.115)]*(0.1105 - 0.115) = 0.40%

A bond with a 7% coupon rate (paid semi-annually) has two years to maturity. If the current discount rate is 9%, what is the bond's Macaulay's duration 1) 1.64 2) 1.90 3) 1.81 4) 2.10 5) 1.72

1.90 Bond Value 6 mths Duration ANNUAL DURATION Time period 1 2 3 4 Cash Flows 35 35 35 1035 Discounted CFs 33.49 32.06 30.67 867.91 964.1247 Weights 0.0347 0.0332 0.0318 0.9002 wxt 0.0347 0.0665 0.0954 3.6008 3.80 1.90

What is the Macaulay's duration of a 10 year zero-coupon bond with a face value of $1,000 and a market rate of 8%, compounded annually? 1) 12 years 2) 10 years 3) 13 years 4) 11 years 5) 10.32 years

10 years

A bond with a par value of $1000 and a 13% coupon rate has 20 years to maturity. Coupons are paid semi-annually. If a bond sells for $1257, what is the yield to maturity? 1) 10.78% 2) 10.00% 3) 12.49% 4) 11.56% 5) 11.00%

10.00% Financial calculator solution P/Y = 2 FV = 1,000 PMT = 13%/2 * 1,000 = 65 PV = 1,257 N = 20 * 2 = 40 I = ? = 10

A bond's Macaulay duration is 11 years. If the current annual interest rate is 5%, what is the modified duration of this bond? 1) 11.50 years 2) 1.01 years 3) 10.48 years 4) 11.00 years 5) 12.48 years

10.48 11 / 1.05 = 10.48

A bond with a par value of $1000 and a 8.5% coupon rate has 6 years to maturity. Coupons are paid semi-annually. If a bond sells for $876, what is the yield to maturity? 1) 7.44% 2) 6.54% 3) 8.34% 4) 11.41% 5) 9.24%

11.41% Financial calculator solution P/Y = 2 FV = 1,000 PMT = 8.5%/2 * 1,000 = 42.5 PV = 876 N = 6* 2 = 12 I = ? = 11.41

A bank quotes you a rate of 14% on a CD, compounded continuously. What is the effective annual rate? 1) 15.79% 2) 14.31% 3) 15.02% 4) 16.60% 5) 13.89%

15.02% EAR = e^(0.14) -1

A bond that has an annual coupon rate of 11% has three years to maturity. If the current discount rate is 16%, what is the bond's Macaulay's duration? 1) 2.89 years 2) 3.00 years 3) 2.69 years 4) 2.79 years 5) 2.99 years

2.69

A 45 -day Treasury bill is quoted as having a price of $969. What is its bond equivalent yield? 1) 16.00% 2) 25.95% 3) 8.19% 4) 25.00% 5) 28.80%

25.95% BEY = [(Pf - P0)/P0[]* (365/h) = [(1000 - 969)/969] * (365/45) = 0.2595

A 45 -day Treasury bill is quoted as having a 4% bond equivalent yield. What is the effective annual yield? Correct Response 1) 4.07% 2) 4.00% 3) 5.42% 4) 4.93% 5) 4.48%

4.07% i* = [1 + i/(365/h)]365/h - 1 = [1 +0.04/(365/45)]365/45 - 1 = 0.0407

A bond's Macaulay duration is 5.43 years. If the current annual interest rate is 6%, what is the modified duration of this bond? 1) 6.00 years 2) 5.12 years 3) 6.20 years 4) 4.45 years 5) 5.43 years

5.43 / 1.06 = 5.12

You purchase a 10 - year bond for $968. It pays a semi-annual coupon payment of $40. You expect to sell the bond in 4 years. You estimate that similar bonds will be priced to yield 10% at the time of the sale. If you can reinvest the coupon payments at 6% annually, what is your expected total return for the 4 - year holding period? 1) 5.80% 2) 3.81% 3) 5.04% 4) 6.38% 5) 4.38%

6.38 Step 1: Sale price in 4 years: P/Y = 2 PMT =40 N =6 * 2 =12 I =10 FV = 1000 PV = ? =900.02 Step 2 - Future Value of reinvested coupons: P/Y = 2 PMT = 50 N =4 * 2 =8 I = 6 FV =? = 344.31 Step 3 - Total Return: FV = 900.02 + 344.31 =1,244.33 PV = -968.00 Purchase Price N = 8 I = ? = 6.38%

What is the discount yield on a $1,000 par value Treasury bill with exactly 182 days to maturity, priced at $964.5? 1) 10.20% 2) 7.02% 3) 8.43% 4) 6.38% 5) 9.27%

7.02% Discount Yield = (Pf[ - P0)/Pf ]* (360/h) =[(1000 - 964.5)/1000]*(360/182) = 0.0702

A 60 -day Treasury bill is quoted as having a 7% bond equivalent yield. What is the effective annual yield? 1) 7.93% 2) 7.21% 3) 8.72% 4) 7.00% 5) 9.59%

7.21% i* = [1 + i/(365/h)]365/h - 1 = [1 +0.07/(365/60)]365/60 - 1 = 0.0721

You purchase a 8 - year bond at face value for $1,000. It pays a semi-annual coupon payment of $40. You expect to sell the bond in 2 years. You estimate that similar bonds will be priced to yield 8% at the time of the sale. If you can reinvest the coupon payments at 6% annually, what is your expected total return for the 2 - year holding period? 1) 7.89% 2) 6.86% 3) 4.51% 4) 5.19% 5) 5.96%

7.89% Step 1: Sale price in 2 years: Note: because this bond's expected YTM in 2 years = Coupon rate, calculation is not necessary: we know that the bond will sell at par = $1,000. Step 2 - Future Value of reinvested coupons: P/Y = 2 PMT = 50 N =2 * 2 =4 I = 6 FV =? = 167.35 Step 3 - Total Return: FV = 1,000 + 167.35 =1,167.35 PV = -1,000. Purchase Price N = 4 I = ? = 7.89%

You purchase a 10-year bond at face value for $1,000. It pays a semi-annual coupon payment of $50. If you hold the bond to maturity and can reinvest the coupon payments at 8% annually, what is your expected total return? 1) 6.63% 2) 9.33% 3) 7.53% 4) 8.43% 5) 5.73%

9.33 Financial calculator solution Step 1 P/Y = 2 PMT = 50 N = 10 * 2 = 20 I = 8 FV = Future value of coupon payments = 1,488.90 Step 2 FV = 1000 Face Value + 1,488.90 Future value of coupon payments = 2488.90 PV = -1000 Purchase Price N = 20 I = ? = 9.33%

You purchase a 8 - year bond for $1,015. It pays a semi-annual coupon payment of $40. You expect to sell the bond in 2 years. You estimate that similar bonds will be priced to yield 7% at the time of the sale. If you can reinvest the coupon payments at 6% annually, what is your expected total return for the 2 - year holding period? 1) 8.71% 2) 5.73% 3) 7.58% 4) 6.59% 5) 9.58%

9.58% Step 1: Sale price in 2 years: P/Y = 2 PMT =40 N =6 * 2 =12 I =7 FV = 1000 PV = ? =1,054.11 Step 2 - Future Value of reinvested coupons: P/Y = 2 PMT = 50 N =2 * 2 =4 I = 6 FV =? = 169.86 Step 3 - Total Return: FV = 1,054.11 + 169.86 =1,223.97 PV = -1,015.00 Purchase Price N = 4 I = ? = 9.58%

Everything else the same, if the yield to maturity decreased 1 percentage point, which of the following bonds would have the largest percentage increase in value? 1) A 25-year 11% coupon bond. 2) A 25-year zero-coupon bond. 3) A 3-year bond with a 7.5% coupon. 4) A 25-year 7.5% coupon bond. 5) A 3-year zero coupon bond.

a 25-year zero-coupon bond

Which of the following is false? 1) A bond with a lower coupon will change more in price than a bond with a higher coupon, everything else the same. 2) Long-term bonds change proportionately more in price than short-term bonds for a given rate change, everything else the same. 3) Given an absolute change in interest rates, the percentage increase in a bond's price will be greater than the percentage decrease, everything else the same. 4) A bond's duration is a measure of its price elasticity. 5) As interest rates rise, bond prices rise, everything else the same.

as interest rates rise, bonds prices rise, everything else the same

The greater the compounding frequency, the higher the present value, everything else the same. 1) True 2) False

false

There is an inverse relationship between a bond's duration and its price volatility. 1) True 2) False

false

Duration: 1) rises as the coupon payment rises. 2) is a measure of total return. 3) measures how bond prices change with changes in maturity. 4) is a measure of how price sensitive a bond is to a change in interest rates. 5) is always greater than maturity.

is a measure of how price sensitive a bond is to a change in interest rates

If a bond is selling at a premium, then: 1) the yield to maturity is greater than the coupon rate. 2) the yield to maturity is equal to the coupon rate. 3) its duration must be equal to its maturity. 4) its duration must be greater than its maturity. 5) the yield to maturity is less than the coupon rate.

the yield to maturity is less than the coupon rate

All other things the same, low coupon bonds have greater relative price volatility than high coupon bonds. 1) True 2) False

true

The duration of any security with interim cash flows will be less than the security's maturity. 1) True 2) False

true

The effective annual interest rate will never be less than the simple interest rate. 1) True 2) False

true

The greater the compounding frequency, the higher the future value, everything else the same. 1) True 2) False

true